Stark deceleration methods for cold molecule experiments
by
Yomay Shyur
B.A., Wellesley College, 2011
M.S., University of Colorado Boulder, 2014

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2018This thesis entitled:
Stark deceleration methods for cold molecule experiments
written by Yomay Shyur
has been approved for the Department of Physics

Prof. Heather Lewandowski

Prof. John Bohn

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

iii
Shyur, Yomay (Ph.D., Physics)
Stark deceleration methods for cold molecule experiments
Thesis directed by Prof. Heather Lewandowski

The growing field of cold molecule physics has demonstrated many methods of quantum
control for precision measurement and molecular interaction studies. One particular method is
Stark deceleration, which uses electric field gradients to produce packets of slow polar molecules.
Since Stark deceleration does not increase phase-space density, the efficiency of the deceleration
process is critical in determining the final cold molecule density. This dissertation describes threedifferent Stark deceleration techniques. The first type of deceleration is pulsed-pin deceleration. We
use this technique to produce slow OH molecules that can be trapped for cold collision studies. A
two photon state-selective detection system, which includes a 118 nm photon, is used to determine
the density distribution of OH in the trap. We explore the advantages and limitations to creating
118 nm light.
The second and third types of Stark deceleration are pulsed-ring and traveling-wave methodsof running a ring-geometry decelerator. Ring-geometry decelerators present improved deceleration
efficiencies due to the cylindrical symmetry of the electrodes and true three-dimensional confinement. The pulsed-ring mode of the ring decelerator uses commercial high-voltage switches to apply
discrete pulses to the ring electrodes. The continuous operation mode of the ring decelerator uses
varying sine-wave voltages to create a traveling Stark potential well and has proven to be incrediblychallenging due to the analog high voltage requirements of the system. In order to bring ND3 seededin krypton (∼415 m/s) down to rest in the laboratory, sine wave voltages with amplitudes up to±10 kV, currents up to 500 mA, and a bandwidth of 30 kHz down to DC are required. We describe
a high-voltage amplifier that can be used for traveling-wave deceleration. The traveling-wave Stark
deceleration mode is then compared to the pulsed-ring Stark deceleration mode and cases where
one mode is superior to another are discussed.

Dedication

To my parents.

Acknowledgements

It is a pleasure to thank the people whose many efforts have made this dissertation possible.
First, I would like to thank my advisor, Heather Lewandowski. She believed in me and entrusted
me with an electronics project when I had very little background coming in. She always provided
encouragement even when amplifier land seemed endless and bleak. She has been a patient mentor,
who has taught me how to tell a story using data and brainstorm solutions to a myriad of scientificproblems. All these skills will serve me well in future endeavors.
I also owe my gratitude to all the Lewandowski lab members I have worked with. Eachone of you has taught me so much. Noah Fitch had the ambition to embark on the high-voltage
amplifier journey, and provided valuable documentation and help even after moving to Europe. His
groundwork in design, construction, and simulations for the ring decelerator have been critical toits operation. Travis Briles taught me a lot about optics and lasers and could provide references forseemingly endless cold molecule topics. Maya Fabrikant was always eager to help solve problems
both in the lab and outside of lab. The construction of the ring decelerator and amplifiers would
not have been possible without the work of David Macaluso, Kentaro Hoeger, and Ian Collett. I
have also had the pleasure of working with John Gray and Jason Bossert, their eagerness to work on
challenging experiments, persistence in finding the root of the problem, and ability to keep things
upbeat in the lab have been invaluable. I wish both of them the best of luck as they continue theirwork on collision and reaction experiments. Additionally, help from and conversations with Philipp
Schmid, James Greenberg, Kyle Miller, Cameron Straatsma, and Ben Saarel have been incredibly
useful.

vi
I have greatly benefited from discussions with the JILA cold molecule community. In particular, David Reens and Hao Wu have always provided keen insights into OH and Stark decelerator
improvements. The construction, upkeep, repair, and upgrades to these mechanically and electronically complex decelerator experiments would not have been possible without the help of the JILA
machine and electronics shops. Specifically, Terry Brown from the electronics shop deserves special
recognition for the initial design of the amplifiers and many subsequent discussions.
Before embarking on my journey at JILA, I had many professors and mentors who encouraged
me and guided me. I am thankful of the Wellesley College physics community where I have always
found a home and Glenn Stark who gave me international physics research experience in my firstyear at Wellesley. Recognition also goes to Chris Arumainayagam, Juliet Pickering, Gillian Nave,and Gretchen Campbell who opened up their labs to me so that I could learn new things.
Thanks also goes out to Catherine Klauss, the best roommate ever, and my friends in Boulder
for all the ski trips, cooking endeavors, encouragement, and support. And to my friends from afar,
particularly Amanda and Rachel, who checked in regularly and were always interested in what wasgoing on in the lab.
Lastly, I wish to thank my parents for their endless encouragement, without their support I
would have never taken this journey.

Contents

Chapter
1 Introduction

1

1.1

Molecules in electric and magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2

Beam Manipulation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.3

Outline of this dissertation

7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Stark Deceleration
2.1

2.2

9

Applications of Stark Decelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.1.1

Pin decelerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2

Ring decelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.3

Other Stark related techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Stark Decelerator Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1

Pulsed-pin Stark deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2

Traveling-wave Stark Deceleration . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.3

Pulsed Ring Stark Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3

Phase-space Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4

Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5

Experimental Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.1

Supersonic Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.5.2

Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

viii
2.5.3
2.6

Our experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Decelerator comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3 Molecules of Interest
3.0.1
3.1

3.2

Rotational states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.1

Stark effect in ND3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.1.2

ND3 REMPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

OH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.1

Hund’s Coupling Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2.2

OH structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.2.3

OH in electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4 Pulsed Ring Stark Deceleration
4.1

55

67

Pulsed-Ring versus traveling-wave Stark deceleration . . . . . . . . . . . . . . . . . . 67
4.1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1.2

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.3

Simple model of deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.1.4

Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.1.5

Experimental Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 78

4.1.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2

Implementing PRSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3

Decelerating with PRSD

4.4

Transverse Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.5

Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.6

8-ring periodicity PRSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

ix
5 High-Voltage Amplifiers
5.1

High-Voltage Amplifier Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1.1

5.2

5.3

105

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Design of the high-voltage amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2.1

Leader Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.2.2

Follower Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.2.3

Feedback and control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.2.4

Physical Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Amplifier Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.3.1

Testing Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3.2

General Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3.3

Voltage Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.3.4

Chirped sine waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.4

Conclusion

5.5

Individual amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.6

Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.7

5.8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.6.1

Amplifier bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.6.2

Amplifier walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.6.3

Optoisolator Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Operating multiple amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.7.1

Digital and analog signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

5.7.2

Master Interlock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.7.3

Enabling amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Amplifier Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.8.1

Component value changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.8.2

Parts not in use anymore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

x
6 Electrostatic trapping of OH

164

6.1

OH experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.2

OH REMPI Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.3

OH 1+1’ REMPI with 118 nm photons . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.4

OH in electric and magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.5

6.4.1

Hamiltonian for OH in electric and magnetic fields . . . . . . . . . . . . . . . 179

6.4.2

Electrostatically trapped OH with a uniform magnetic field . . . . . . . . . . 180

6.4.3

Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

118 nm light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.5.1

Creating 118 nm light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

6.5.2

Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.5.3

Limitations to 118 nm light production . . . . . . . . . . . . . . . . . . . . . 191

6.5.4

Possible explanations for the limitations . . . . . . . . . . . . . . . . . . . . . 197

Bibliography

203

Appendix
A Circuit Diagrams

218

B Modifications summary

245

B.1 Amplifier bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
B.2 Amplifier breakout boards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

B.3 Control boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
B.4 Master interlock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
B.5 Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

TablesTable
2.1

Typical values for the full width at half maximum (FWHM) of the initial distributionof molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2

Properties of the two decelerators used. . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.1

Properties of ND3

4.1

Switching rise times for PPSD vs PRSD . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.1

Technical parameters of the amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.2

Small-signal amplifier parameters. Rise and fall times, tr and tf , and delay d were

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

taken with a 1 kHz square wave with an output of V on a load capacitance of Cl .
The rails were held fixed at ±11 kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3

RTVS 3-95-1 properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.4

Changes to amplifier boards resistor values . . . . . . . . . . . . . . . . . . . . . . . 159

5.5

Changes to amplifier breakout boards . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.6

Changes to control boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Figures

Figure2.1

End on view of the Stark decelerators in our laboratory . . . . . . . . . . . . . . . . 15

2.2

Molecule in a dipole field

2.3

Potentials created in a pin decelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4

Timing molecule potentials for φ0 = 0◦ . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5

Phase angles on a longitudinal potential . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6

Potentials used for various phase angles . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.7

Position of molecules ahead and behind the timing molecule when the potentials switch 23

2.8

CAD drawings of one ring electrode and the full decelerator . . . . . . . . . . . . . . 25

2.9

TWSD voltages on ring electrodes and the resulting potentials . . . . . . . . . . . . 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.10 Energy lost, ∆K per stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.11 The longitudinal (z axis) separatrices for phi0 = 0◦ , 20◦ , 40◦ , 60◦ , 80◦ . . . . . . . . . 32
2.12 The effective longitudinal potential for an initial velocity of 415 m/s and various
final velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.13 Normalized longitudinal potentials for TWSD, PRSD, PPSD, and a cosine . . . . . . 36
2.14 PRSD acceleration as a function of phase angle . . . . . . . . . . . . . . . . . . . . . 36
2.15 Experimental setup for a general Stark deceleration molecule . . . . . . . . . . . . . 40
2.16 Simple model of LIF and REMPI detection . . . . . . . . . . . . . . . . . . . . . . . 44
2.17 Time-of-flight measurements for both the PZT and NVP valves . . . . . . . . . . . . 46
2.18 A CAD drawing of the pulse-pin decelerator . . . . . . . . . . . . . . . . . . . . . . . 48

xiii
2.19 Electrostatic trap used with the pulsed-pin Stark decelerator . . . . . . . . . . . . . 48
2.20 The longitudinal on axis potentials for the trap on (blue) and half on (red) configurations of the trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.21 Physical assembly of a ring decelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.22 The ring trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.23 On-axis longitudinal potentials for PPSD, PRSD, and TWSD modes in our pin andring decelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1

The rotational levels of ND3 in the electronic and vibrational ground state . . . . . . 60

3.2

The Stark energy as a function of electric field for ND3 and NH3 . . . . . . . . . . . 61

3.3

The 2+1 REMPI scheme for detecting ND3 . . . . . . . . . . . . . . . . . . . . . . . 62

3.4

The rotational structure in the electronic and vibrational ground state of OH . . . . 65

3.5

The Stark splitting in OH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.1

A schematic of the experimental setup for PRSD . . . . . . . . . . . . . . . . . . . . 71

4.2

Ring number, applied voltages, positions of electrodes, and longitudinal Stark potentials of ND3 for TWSD and PRSD . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3

The instantaneous TWSD and PRSD transverse Stark potentials in the x-direction
for the voltage configuration in Fig. 4.2 and at z=0 mm . . . . . . . . . . . . . . . . 75

4.4

The PRSD and TWSD Stark potential wells with applied linear fictitious potentials
for various accelerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.5

Time-of-flight traces of a molecular beam decelerated with PRSD . . . . . . . . . . . 79

4.6

Time-of-flight traces of a molecular beam decelerated with TWSD . . . . . . . . . . 80

4.7

ND3 signal verses acceleration for both TWSD and PRSD . . . . . . . . . . . . . . . 81

4.8

Longitudinal phase-space distributions for TWSD and PRSD for an initial velocityof 415 m/s and final velocities of 320 m/s and 200 m/s . . . . . . . . . . . . . . . . . 82

4.9

Simulated integrated ND3 signal verses acceleration for both TWSD and PRSD . . . 83

4.10 The acceleration at the crossing point of simulated TWSD and PRSD signal . . . . . 85

xiv
4.11 Electrode voltages for PRSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.12 Recommended Behlke control circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.13 PRSD at ±7.5 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.14 LPSA for PRSD at different peak voltages . . . . . . . . . . . . . . . . . . . . . . . . 91
4.15 LPSA for PRSD at ±7 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.16 LPSA for PRSD at ±10 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.17 Stark Potential energy surface xz(y=0) plane . . . . . . . . . . . . . . . . . . . . . . 95
4.18 Transverse potential for TWSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.19 PRSD and TWSD transverse potential progression . . . . . . . . . . . . . . . . . . . 97
4.20 Time-of-flight uncalibrated and calibrated PRSD scans . . . . . . . . . . . . . . . . . 100
4.21 Electrode voltages for 8R PRSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.22 Comparison of 4R PRSD and 8R PRSD simulations . . . . . . . . . . . . . . . . . . 104
5.1

An optically coupled, all N-channel push-pull amplifier . . . . . . . . . . . . . . . . . 110

5.2

A leader stage of the high-voltage amplifier . . . . . . . . . . . . . . . . . . . . . . . 112

5.3

A follower stage of the high-voltage amplifier . . . . . . . . . . . . . . . . . . . . . . 115

5.4

A photograph of the amplifier with the top lids removed . . . . . . . . . . . . . . . . 120

5.5

The test setup for measuring the output voltage and current . . . . . . . . . . . . . . 122

5.6

Measured gain of the amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.7

Measured output sine waves and their respective Fourier transforms for 4 and 30
kHz input sine waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.8

Ratio of voltage dropped between the final follower stage (F9) and the leader stage(L) on the bottom bank for three different frequencies . . . . . . . . . . . . . . . . . 127

5.9

A linearly chirped voltage waveform from 30 kHz to DC at ± 10 kV . . . . . . . . . 129

5.10 The high-voltage amplifier with its probe and breakout box . . . . . . . . . . . . . . 132
5.11 Amplifier control box front panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.12 Setup for individual amplifier testing on the bench . . . . . . . . . . . . . . . . . . . 133

xv
5.13 Probing an amplifier bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.14 ±8 kV output without and with the amplifier box filled with SF6 . . . . . . . . . . . 135
5.15 Persistent current oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.16 ±12 kV output voltage at 5 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.17 A thin layer of RTVS 3-95-1 potting material on one amplifier bank . . . . . . . . . 140
5.18 Fully potted amplifier banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.19 Cross section of custom high voltage cable . . . . . . . . . . . . . . . . . . . . . . . . 143
5.20 Current dips caused by proximity to polycarbonate . . . . . . . . . . . . . . . . . . . 143
5.21 Amplifier box polycarbonate walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.22 Pictures from an amplifier that had a short . . . . . . . . . . . . . . . . . . . . . . . 146
5.23 Shorting out the current monitoring optoisolator . . . . . . . . . . . . . . . . . . . . 147
5.24 A simplified schematic of amplifier electronic and control connections . . . . . . . . . 148
5.25 Digital timing sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.26 Decelerator rod voltage with grounded and non-grounded amplifier input . . . . . . 158
5.27 Control board rail monitor circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.1

The gas mixing system, valve, and discharge plates for creating a supersonic beamof OH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.2

The detection region configuration for detecting trapped OH . . . . . . . . . . . . . 168

6.3

The length in time versus the stage number for one mixed deceleration timing sequence169

6.4

A diagram of two different OH trap loading schemes . . . . . . . . . . . . . . . . . . 171

6.5

An energy level diagram of OH showing the relevant states for 1+1’ detection . . . . 173

6.6

The central density OH in the trap for two different loading schemes . . . . . . . . . 175

6.7

The FWHM of trapped OH over time . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.8

The width of the OH cloud as it expands after the trap is turned off . . . . . . . . . 177

6.9

The electric field in the trap along a longitudinal (a) and transverse line (b) . . . . . 178

xvi
6.10 The electrostatic trap with Helmholtz coils to produce a uniform magnetic field at
the center of the trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.11 OH energy levels in a uniform 90 G magnetic field with varying β and electric field . 181
6.12 OH energy levels in a uniform 500 G magnetic field with varying β and electric field 182
6.13 OH energy levels in a uniform 800 G magnetic field with varying β and electric field 183
6.14 The region in the x-z plane (y=0) of our trap where he electric field is greater than
6 kV/cm is shown in red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.15 Plot of |F1 (b∆k)|2 in the tight-focusing limit and for b = 1 . . . . . . . . . . . . . . . 188
6.16 A diagram of the 118 nm gas mixing cell and the ionization and detection region . . 191
6.17 Phase-matching curves at different pressures of Xe . . . . . . . . . . . . . . . . . . . 193
6.18 A picture of the fluorescence streak that appears near the 355 nm focal point . . . . 193
6.19 A phase-matching curve, with PXe =50 torr, taken while monitoring both the 118
nm flux and the fluorescence intensity . . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.20 A comparison of the 118 nm signal and fluorescence streak signal at different xenonpressures for a phase-matched mixture with Ar (Ar:Xe Ratio = 11.3) and Kr (Kr:Xe
Ratio = 4.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.21 A spectrum of the fluorescence streak created in a xenon-argon mixture . . . . . . . 196
6.22 A spectrum of the fluorescence streak created in a xenon-krypton mixture . . . . . . 197
6.23 A cartoon of the 118 nm gas mixing cell, absorption cell, and ionization and detection
region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6.24 Diagram depicting the feedback mechanism of electric field induced SFG . . . . . . . 201

Chapter 1

Introduction

Pushing the limits of quantum control of atoms has led to the discovery of new states ofmatter [1, 2] and a greater understanding of quantum phenomena. Studies of cold atoms havelead to new discoveries in fundamental physics [3], precision measurement [4–6], and quantum
processes [7, 8]. The field of cold molecule research is a natural and challenging extension of cold
atom research. Currently, several experimental techniques have been able to cool down molecules tothe millikelvin temperature range, and select techniques using specific molecules have reached themicrokelvin range and lower. Molecules have many more degrees of freedom due to their ability tovibrate and rotate, and these motions can couple together to provide a rich spectroscopic landscape.
However, these additional degrees of freedom make molecules more complex and more difficult tocool than atoms.
Cold molecules can be used for spectroscopic, precision measurement, collision, and reaction studies. Low temperature spectroscopy provides improved spectral line resolution and limits
spectral congestion, since fewer quantum states are populated [9]. Cold molecules can be used as
precision measurement tools and tests of fundamental physics, including studies of the fine structure
constant and proton-to-electron mass ratio [10, 11] and the electron electric dipole moment [12, 13].
At cold temperatures, applied electric or magnetic fields can be used to control the energies of thereactants in order to form a better understanding of chemical reactions. These fields can be helpful
for control of molecular orientation [14, 15] and stereochemistry studies [16, 17]. Cold molecules
provide the opportunity to gain control over molecule collisions and reactions. At low tempera-

2
tures, interactions are dominated by quantum mechanical effects. Tunneling and resonances areimportant to the understanding of chemical dynamics when the energy available is lower than theactivation energy of the process. By “freezing” out certain energy levels and restricting molecules
to one or a few quantum states, state selective processes can be studied. One goal of these studies
is full quantum control over a reaction, including well-defined states of the reactants and products,
which will allow for a true quantum understanding of basic chemical reactions.
The field of cold molecules encompasses all techniques used to create cold molecules, manyof which are tailored to specific categories of molecules. Here, we provide an overview of many of
the techniques that have been demonstrated and explored in just the last twenty or so years inorder to provide a context for the main technique discussed in this dissertation, Stark deceleration.
However, this is by no means an exhaustive list and the reader is encouraged to consult the plethoraof review articles have been written on cold molecules [18–27].
There are two methods of creating cold molecules, indirect and direct. Indirect methods
take cold atoms and associate them to form molecules. This can be accomplished by photoassociation [28, 29] or magneto-association [30] and forms molecules that are ultracold, in thehundreds of nanokelvin range [31]. These techniques generally can produce molecules that aremuch colder and with higher densities than direct techniques, but they are limited to alkali andalkali-earth atoms that can be laser cooled before association. Direct methods, on the other hand,take molecules from near room temperature and make them cold. They are applicable to many
atmospheric and astrophysically relevant species such as NH3 , OH, NH, and CH. For the most part,the molecules can only be made cold, in the range of a few degrees Kelvin to millikelvin, and not
ultracold. However, recent developments in laser cooling of molecules have reached temperaturesin the microkelvin range [32, 33]. Direct methods are the focus of the remainder of this chapter.
Within direct cooling methods, there are phase-space compressing methods and non-phasespace compressing methods. Phase-space compression represents true cooling, where an irreversible
process has removed entropy from the system. These techniques include RF evaporation [34],optoelectrical Sisyphus cooling [35], buffer gas cooling [36–38], and laser cooling of molecules [32,3
33, 39–42]. While laser cooling and magneto-optical trapping have been fundamental for cold atomstudies, they rely on cycling transitions that allow atoms to scatter light on the same transition manytimes. Molecules have complex energy structures due to their additional degrees of freedom, which
severely restricts the options for cycling transitions and thus laser cooling molecules. Nonetheless,laser cooling of diatomic molecules has been demonstrated with SrF [39], YO [40], CaF [41], andYbF [33], and these molecules can also be loaded into MOTs [32, 42].
Non-phase-space-compressing methods involve filtering or slowing and generally result in low
densities of molecules. These non-compressing methods typically begin with a room temperature
molecular beam, but could also be loaded from a cryogenic source [43]. Many of these moleculesof interest are highly reactive and must be created in-situ using either photodissociation or anelectric discharge. While precision control of molecular beams is an established technique [44–46],
directly cooling these beams is a more recent development [24]. These experiments are generally
not in thermal equilibrium, and the description of “cold” is a measurement of the kinetic energy
stored in the degrees of freedom and not a measurement of temperature. For example, a supersonic
expansion produces a “cold” beam. It has molecules that are internally cold (close to the rovibronic
ground state) and with a narrow velocity distribution. However, this beam may still be moving fast
(300-600 m/s) in the laboratory frame. Non-phase-space-compressing direct techniques can thenbe used to slow down the beam and reduce the average velocity. These techniques are able to slow
down the molecules in the laboratory frame, but they do not make the sample “colder.”1.1

Molecules in electric and magnetic fields
Externally applied electric and magnetic fields are commonly used to control atoms andmolecules. While it is common to think of controlling ions in this fashion, it may not be immediately
clear that this is a useful technique to use on neutral molecules. However, if a molecule has anelectric (magnetic) dipole moment, it will experience an energy shift in the presence of an electric(magnetic) field due to the Stark (Zeeman) effect. If the field is inhomogenous the changing energy
shift will be experienced as a force. This force serves as a handle to manipulate the molecules and4allows them to be accelerated, decelerated, and trapped.
Direct cooling methods, which decelerate molecules from a molecular beam, generally exploit
inhomogenous fields as the decelerating force. To motivate the need for inhomogenous fields andthe importance of field gradients, we examine the behavior of an electric dipole in an external field.
In the classical picture, the Hamiltonian for the interaction of a dipole moment with a electric fieldis
Hf ield = −µe · E,

(1.1)

where µe is the electric dipole moment and E is the electric field. This gives the potential energyof the system to be
U = −µe · E,

(1.2)

F = −∇U = µ~e · ∇E.

(1.3)

and the force to be

Equation 1.3 indicates that molecules with electric dipole moments can be controlled using inhomogeneous fields since the gradient of the fields sets the force applied to the molecules. As will beseen extensively in Chapters 2 and 4, the gradient of the field and how it is applied are the mostimportant aspects to the success of any deceleration method.
In this classical picture, the dipole will minimize the potential energy by aligning with thefield. However, in the quantum mechanical picture, the dipole moment cannot freely rotate and its
projection on to the applied field is quantized. For the case of the potential energy (Equation 1.2)
U = −µe · E = −|µe ||E| cos (θ) ,(1.4)

where θ is the angle between µe and E, and both |µe | and θ are fixed, this leads to the sign of U
being dependent on θ. The molecule’s energy either increases or decreases when a field is applied.
Molecules whose energies increase with the field are referred to as weak-field-seeking, and those
whose energies decrease with the field are referred to as strong-field-seeking. Strong-field-seeking
states are attracted to regions of strong fields, which are found near the surfaces of electrodes. This5
makes them difficult to work with since it is not possible to confine strong-field-seeking molecules
in any static potential. Instead, it is much easier to work with weak-field-seeking molecules since
it is possible to create areas of low electric fields in free space.
These same arguments can be made for a magnetic dipole in a magnetic field by replacingµe with the magnetic dipole moment µb and the electric field E with the magnetic field B. While
there are many similarities between the interactions of a dipole and an electric and magnetic field,
the key differences is that the magnetic dipole is permanent and always exists in a molecule, andthe electric dipole moment is induced and exists only when a field is present.

1.2

Beam Manipulation Techniques
While this dissertation uses Stark deceleration of weak-field-seeking states to create cold

molecules, many other beam manipulation techniques have been used to decelerate molecules. A
detailed description of deceleration of weak-field-seeking states and the history of the technique isprovided in Chapter 2.
The complement to standard weak-field-seeking Stark deceleration is alternate gradient deceleration for strong-field-seeking molecular states [47–50]. This technique has been used to decelerate
CO [47], OH [51], YbF [48], and benzonitrile (C7 H5 N) [52]. However, alternate gradient deceleration is not as stable as weak-field-seeking methods since it is highly dependent on the alignment of
the decelerator and longer decelerators have rapidly decreasing efficiencies. Also, using the Stark
effect, Rydberg-Stark deceleration can be used to decelerate long-lived Rydberg states [53, 54],
which are readily polarizable even if the ground state molecule is not. Rydberg-Stark deceleration
has also been demonstrated on chips [55] and decelerated H-Rydberg state molecules have beenbrought to a stop [56].
Apart from electric fields, similar inhomogenous field techniques have been demonstrated withmagnetic fields. Zeeman deceleration has been used with atomic hydrogen [57, 58] and neon [59].
Zeeman deceleration offers the ability to decelerate non-polar free radicals, which cannot be donein a Stark decelerator.

6
Other methods of decelerating molecules from a beam, which do not make use of inhomogenous fields, have also been constructed. These include filtering, collision based schemes, opticalmethods, and physical translation methods. Quadrupole velocity filtering uses a bent quadrupole
to select slow molecules out of an effusive beam [60–62]. Crossed-beam kinamatic cooling brings
molecules to rest using one collision with a particle of carefully chosen mass and velocity suchthat the collision partner’s momentum vector is opposit that of the molecule to be cooled [63, 64].
Optical methods include carefully selected photodissociation, such that the recoil speed of the fragment of interest equals the molecular beam speed [65]. Additionally, optical Stark deceleration uses
time-varying red-detuned optical lattices [66], and has been demonstrated experimentally using nitric oxide [67] and benzene [68]. Both pulsed [69] and traveling-wave versions [70] of optical Stark
deceleration have been proposed.
The last approach involves physical rotation of the molecular source or decelerating apparatus
in order to change the velocity of the molecules in the laboratory frame. One technique places themolecular beam source on a rotating stage such that it moves backwards during the expansion[71,72]. The beam out of the translating source is slower in the lab frame than had the source beenstationary. Another technique uses a novel centrifuge decelerator [73]. It uses a spinning quadruple
to guide and decelerate molecules up a centrifugal potential energy hill toward the central axis.
This technique has the benefit that it can produce truly continuous sources of slow molecules if
the inital source is continuous. The centrifugal decelerator has also been loaded from a cryogenic
buffer gas cell in a system called a cryofuge, which has been used to decelerate fluoromethane anddeuterated ammonia [74].
Once the molecules are decelerated, the slow beam can be used directly in crossed-beamexperiments [75–78], used with other further deceleration techniques [79], loaded into molecularstorage rings [80, 81] and synchrotons [82, 83], or loaded into a trap. Molecule traps can include
electrostatic [84–86], magnetic [87, 88], and ac traps [89–91], and they can be used in beam-trap[92, 93] and cotrapped experiments [94].
The last category of experiment, cotrapped experiments, allows for longer interaction times

7of the trapped species. Although trap densities are generally not large enough to see reactions,collisions with a separate denser sample can yield important measurements of collisional crosssections [94]. Within a cotrapped experiment, there are two types of collisions, elastic and inelastic.
In elastic collisions, the internal energies of the constituents do not change and only momentum
is exchanged between the collision partners. On the other hand, in inelastic collisions, internal
quantum states of the particles change. Since only specific quantum states can be held in a trap,
inelastic collisions will lead to trap loss and a decreased density of the trapped sample. If elastic
collisions occur, then two samples of particles with different temperatures can thermalize in the
trap. This allows for sympathetic cooling, one goal of cold molecule research that has yet to be
demonstrated.

1.3

Outline of this dissertation
This dissertation addresses several improvements to Stark decelerated cold molecule experi-ments, including improvements to molecule deceleration and molecule detection. These techniques
come together in the last chapter in a discussion of cotrapped hydroxyl (OH) and rubidium. Threedifferent Stark deceleration techniques are utilized in this dissertation. The first technique is adiscrete mode, where set voltages are pulsed on and off on a decelerator made up of crossed pin
electrodes. This mode is referred to as pulse-pin Stark deceleration (PPSD). The second and third
techniques are both performed on a ring electrode decelerator. The second technique is a discretemode and is referred to as pulsed-ring Stark deceleration (PRSD). The third tehcnique is a continuous mode, called traveling-wave Stark deceleration (TWSD), where analog smoothly-varying
voltages are applied to the ring electrodes. Chapter 2 discusses all three types of Stark decelerationand gives an overview of the decelerators in our lab. Chapter 3 covers the main molecules, deuterated ammonia (ND3 ) and OH, that are used to test these deceleration techniques. Both methodsof running a ring-geometry decelerator are discussed in Chapter 4. This includes a comparison between the traveling-wave and pulsed-ring methods, how to determine when one method is superior,and how to implement the pulsed mode of the ring Stark deceleration. In order to implement the8traveling-wave mode of a ring decelerator, analog high-voltage amplifiers are required. Amplifiers
that can produce the required voltage waveforms for the ring decelerator in our lab were first presented in Noah Fitch’s dissertation [95]. In Chapter 5, we discuss the required modifications forboth components and the construction of the amplifiers in order to keep them operating successfully. A complete set of updated circuit diagrams for the amplifiers can be found in Appendix A
and a full list of changes between the circuits presented in Noah’s dissertation and this dissertation can be found in Appendix B. Lastly, an experiment that blends Stark deceleration and cold
trapped atoms is discussed from molecule creation to detection. Cold electrostatically trapped OH
and ultracold magnetically trapped rubidium atoms provide an interesting landscape for studying
the effects electric and magnetic fields on OH and collision cross sections for the system. Here, amodified method of running a pulsed-pin decelerator and an improved method of state-selective
detection of OH molecules are discussed.

Chapter 2

Stark Deceleration

Stark deceleration uses spatially inhomogeneous and time-varying electric fields to decelerate
neutral polar molecules resulting in a beam of slow molecules with a tunable average final velocity.
The molecules experience a force, due to the Stark effect, which will increase or decrease the energyof a quantum state as a function of the strength of the electric field. Quantum states where theenergy increases with the strength of the electric field are known as weak-field-seeking states, andthose where the energy decreases with the strength of the electric field are known as strong-fieldseeking states. The changing Stark energies due to inhomogeneous electric fields are exploited
to create a slow beam of molecules by arranging electric fields such that a beam of molecules
must always climb up a potential energy hill. In standard Stark deceleration, only the weak-fieldseeking states can be decelerated in this manner. This chapter provides an introduction to thedevelopment and uses of Stark decelerated beams and is followed by a detailed description of threedifferent types of Stark deceleration. We then discuss the phase-space acceptance calculations,molecular trajectory simulation of molecules in the decelerator, and, lastly, experimental setup of
the decelerator experiments. The subsequent chapters will cover many of these topics in more
depth.

2.1

Applications of Stark Decelerators
Stark decelerated beams are advantageous for collision and crossed-beam experiments since

the final velocity of the beam, and thus the energy can be carefully controlled [75]. Decelerated

10
beams, usually less than 100 m/s, have been used in used in crossed beam [77, 78, 96, 97], molecular fountain [98], beam-trap [92, 93], and cotrapped [94] experiments. These various moleculeinteraction configurations can be used to study high-resolution spectroscopy [10, 98, 99], collision
physics [100], radiative lifetimes of molecules [101, 102], blackbody optical pumping rates out oftrapped states [103], and tests of fundamental physics [10, 104, 105].
Stark deceleration is a useful tool for creating velocity tuned, cold and slow beams ofmolecules. Molecular packets are introduced to the Stark decelerator with pulsed valves. The
packet is internally cooled during the supersonic expansion, but maintains a high forward velocity,
the deceleration process then slows down the beam. There is no phase-space compression during
deceleration since it is a conservative process. Stark decleration does not produce a pure quantum state beam [106], instead other filtering techniques are required if a completely pure beam
is desired. The only ways to increase the signal, the number of slow and detected molecules, area better source, more efficient deceleration, or more efficient detection (improved signal-to-noise).
Improvements to the source and detection are discussed in Section 2.5 and below we briefly cover
the developments and improvements to Stark deceleration since its first experimental realization.

2.1.1

Pin decelerators

The first Stark decelerator, which we refer to as the pulsed-pin Stark decelerator, was constructed in 1999 by Bethlem et al. [107]. It had 63 stages and was used to decelerate CO from 225
m/s down to 98 m/s. Since then, the molecules NH3 /ND3 [84], OH [108], H2 CO [109], NH [76],
LiF [110], SO2 [111, 112], CaF [50], and NO [113] have been decelerated using PPSD.
The molecules from a pulsed-pin Stark decelerator can be loaded into electrostatic and magnetic traps. The type of trap will depend on the molecule, type of study, and how much opticalor physical access to the trap center is required. For example, the simplest electric quadrupole
trap consists of three electrodes [84], but does not have easy access for a detection laser. To remedy this, a small hole can be drilled in the center electrode for optical access [84] or the centerelectrode can be split into two electrodes [85]. Both these solutions slightly alter the trap from a11perfect quadrupole. Thus far NH3 /ND3 [84, 85, 114], NH [115], and OH/OD [86, 103] have been
trapped electrostatically and OH [87] and NH [88] have been trapped in magnetic traps. A highfield-seeking state of 15 ND3 has been trapped with an ac trap after the low-field-seeking state wasdecelerated and the molecules were pumped via a microwave transition into the high-field-seeking
state [49, 89, 91].
The majority of Stark deceleration experiments have been conducted with beams from PPSD.
Beam and trapped PPSD experiments are often limited by the low numbers of successfully decelerated and detected molecules. While careful optimization of beam production and decelerator
loading can improve the density of the decelerated beam [116], the density at the end of the decelerator is still limited by the initial gas pulse, decelerator dynamics, and molecule detection efficiency.
Additionally, there are distinct differences between the phase-space output of the pin decelerator
and the phase-space acceptance of any trap placed after the decelerator which will further reduces
the efficiency.
Many efforts have been made to improve efficiency of a pin decelerator [117–120]. Various
timing schemes and operating modes can improve specific aspects of the performance of the pulsedpin decelerator, however the crossed-pin electrode geometry fundamentally limits the efficiency due
to longitudinal and transverse coupling. Alternative deceleration methods include not using all
the stages for deceleration [117, 119] and adjusting how many times the decelerator switches incomparison with the number of deceleration stages [118, 120]. In the first category, a subset of thedecelerator stages are used for deceleration and the remaining stages are used for bunching, wherethe velocity of the beam does not change but the molecules are “bunched” together in phase space.
By using more aggressive deceleration in a subset of stages, the resulting packet has a narrower
velocity spread due to the smaller phase-space acceptance at higher deceleration phase-angles. Thiscan be accomplished by either bunching at the beginning [119] or bunching at the end [117]. Whilea similar packet could be obtained with a shorter decelerator, modifying the length of a decelerator
is time consuming. Additionally, if the decelerator is to be used with multiple types of molecules
or carrier gases, building the decelerator to the longest required length and then using alternative

12
deceleration sequences, when changing to different molecules, will save the most time. Bunching at
the beginning yields slightly more molecules in the decelerated packet for vf <50 m/s because there
are fewer losses when bunching at higher velocities compared to lower velocities since less time isspent in the decelerator. Bunching at the end of the deceleration increases the separation in time
between the undecelerated packet and the decelerated packets, which can be useful for collisionexperiments.
In the second category of alternate deceleration methods, the number of timing switches isaltered and not equal to the number of pin stages [118, 120]. One mode of operation switches
the voltage configuration once for every three sets of pins the timing molecule traverses. In thisconfiguration, only every third set of pins is used for deceleration, the other two sets of pins provide
transverse focusing. This method is known as S=3, where S indicates the stage periodicity fordeceleration. Traditional PPSD, where every stage decelerates, is referred to as S=1 deceleration.
The reduction in stages used for deceleration means that either a longer decelerator is requiredor less deceleration is achieved. Scharfenberg et al. [118] found that for a 2.6 m long decelerator
and a beam of OH molecules with an initial velocity of 350 m/s, S=3 deceleration is more efficientthan S=1 down to a final velocity of 100 m/s. Although S=3 is more efficient at moderate final
velocities, at lower final velocities, S=1 is more efficient, since fewer pin pairs result in molecules at
low velocities spend less time in the decelerator. The S=3 and S=1 modes have also been combinedsuch that S=3 is used initially and then the decelerator is switched to S=1. This must be completed
before the molecular packet reaches the cross over threshold velocity around 100 m/s. Additionally,methods have been used where S=3 and S=1 methods are intermixed (see Section 6.1).

2.1.2

Ring decelerators

The first use of macroscopic traveling-wave Stark potentials with a ring-geometry decelerator
was in 2010 by Osterwalder et al. [121] using a beam of CO, which was decelerated from 288 m/s
to 144 m/s. While TWSD has many advantages, it is more challenging to implement than PPSD
because it requires high-voltage analog amplifiers with demanding specifications to generate the

13moving Stark potential wells. Early TWSD experiments were limited by the lack of availabilityof high-voltage amplifiers with a large bandwidth. The amplifiers used to generate the voltages
for the electrodes in the first TWSD experiment operated at ±8-10 kV with 10-30 kHz sinusoidal
voltages [121, 122]. The limited bandwidth of the amplifiers meant that the decelerator could
achieve only moderate deceleration and the molecules could not be brought to rest.
Commercial amplifiers (Trek 5/80 ), which are capable of a larger frequency range (0-60kHz) and outputs up to ±5 kV, make it impossible to decelerate a supersonic beam down to restwith a decelerator that is only one meter long. For example, a beam of SrF seeded in Xe withan initial velocity of 290 m/s would require a ∼5 m long decelerator [123]. However, amplifiers,
such as the Trek 5/80, with limited maximum voltages are particularly useful for the TWSD ofheavy molecules used in precision measurements, since the electric fields produced are low enoughto keep the molecules in the weak-field seeking regime, where the Stark energy increases withincreasing electric field [124]. To date, YbF [125] and SrF [123] have been decelerated using TWSD
and the longest demonstrated decelerator (4 m) slowed SrF from 290 to 120 m/s using ±5 kV
amplifiers [126].
A combination deceleration method has also been used, to take molecules to rest and trap
them within the ring electrodes. It couples a traveling-wave decelerator to the end of a pulsed-pin
decelerator [127]. In this combination technique, the molecules are decelerated in the pin decelerator
to velocities around 100 m/s, and then enter the traveling-wave Stark decelerator where they arebrought to rest. The molecule packet can also be temporarily held inside the ring decelerator. This
coupled deceleration method combines the simplicity of PPSD with the low velocity advantages of
TWSD. It takes advantage of the cylindrical symmetry of the ring geometry at low velocities, but it
relaxes the requirement to have either extremely high maximum voltages or a very long decelerator
to reach electrostatically trappable velocities. Using this combination technique, NH3 , ND3 , andCH3 F have been trapped, manipulated, and adiabatically cooled within the ring decelerator [127–130].
Deceleration of a supersonic beam moving at 300-450 m/s to rest using only TWSD in a ring

14
decelerator has been challenging to achieve due to electronic and hardware requirements and has
not been completed to date. However, many strides have been made toward this goal and highvoltage amplifiers to help achieve this are described in Chapter 5.

2.1.3

Other Stark related techniques

To date, pin-geometry decelerators have been the dominant form of Stark deceleration implemented in the lab. Only a few groups work with ring-decelerators. In addition to rod and ring
decelerators, a few other decelerator geometries have been proposed. One has sets of ‘U’ shaped
electrodes and transverse charged confining wires [131]. While similar to the pin configuration,
this particular geometry has true potential wells since each stage has transverse confinement in two
axes. In this configuration the voltages required for transverse confinement are very high (26 kV),and thus is very challenging to build.
Several Stark deceleration techniques have also been demonstrated in miniature with microelectrodes on a chip. Meek et al. [132] first demonstrated the idea for spatially modulated
potential wells on a microstructured chip used to guide and then decelerate and trap metastable
CO molecules [133, 134]. These systems have been used to study how magnetic fields can be used
to suppress non-adiabatic losses of electrostatically trapped CO [135] and to manipulate the temperature of trapped CO [136].
While only weak-field-seeking molecules have been discussed so far, deceleration techniques
for strong-field-seeking molecules have also been developed with limited success. These alternate
gradient decelerators have been used to decelerate CO [90, 114] and YbF [48].
Finally, a few other useful beam manipulation tools can be used in addition to decelerators.
Hexapoles and additional crossed rods can be used for longitudinal focusing and cooling [137]and molecule storage rings/synchrotrons of various geometries [80–83] can be placed after the
decelerator. A recent demonstrations of a beam merger made of electroplated 3D printed plastic[138] opens up exciting new possibilities in a variety of macroscopic beam guide and manipulation
techniques. This technique allows for easy construction of electrode geometries that were previously

15
too difficult or impossible to machine. Selective electrode plating of a 3D printed object allows foruniquely shaped electrodes and electrode supports in ways that were previously not possible.

2.2

Stark Decelerator Operation
Decelerators come in two main geometries, pins and rings, Figure 2.1. The pin decelerator

is always run with high-voltage pulses, while the ring decelerator can be run with high-voltage
pulses or high-voltage sine waves. The decelerators will be discussed in the order that they wereexperimentally realized.

(a) Pin decelerator(b) Ring decelerator

Figure 2.1: End on view of the two Stark decelerators in our laboratory.

2.2.1

Pulsed-pin Stark deceleration

A molecule in a weak-field-seeking state near a strong electric field created by two charged
rods sees a potential energy hill, Figure 2.2. As the molecule travels into the electric field, it
exchanges kinetic energy for potential energy. If the molecule is allowed to travel past the peakof the potential energy hill, it will accelerate back to its initial velocity. However, if instead, theelectrodes turn off right as the molecule reaches the peak of the hill, kinetic energy in the forward
direction will have been removed from the molecule. This sequence can be repeated over and overin order to removed significant forward velocity and decelerate a molecule.
The potential energy hills are created by sets of crossed pins, typically mounted in four sets

16

Figure 2.2: A weak-field-seeking molecule (green) with a dipole moment p and velocity v approaches
a non-uniform electric field. Due to the Stark effect, the molecule sees the high-field region as apotential energy hill and experiences a force opposite its velocity.

of rods running the length of the decelerator (Figure 2.1). Pins are then placed into each rod
at set distances such that when the four rods are assembled there are alternating sets of crossed
pins. In the physical decelerator, the electrode pairs are oriented perpendicular to each other. This
combination of rods and pins simplifies the electronics required to run the Stark decelerator. All
pins on one rod have their voltage switched simultaneously, and only four high voltage switches are
required to run the entire decelerator.
Figure 2.3 shows how applying a voltage to alternating sets of electrodes produces periodic
Stark potential wells that shift longitudinally. For this series of pin electrodes (depicted as circles),only two voltage configurations are required to create a time-averaged, over all the deceleration
stages, moving potential well. The longitudinal potential for each voltage configuration is given
immediately below the pin diagram. The two configurations are almost identical, but the potential
well shifts longitudinally by half a period between the two configurations. By alternating between
these two configurations at the correct times, a molecule can be decelerated.
To determine the correct timing sequence for the voltage configurations, we will initiallyconsider only one molecule traveling along these longitudinal Stark potential wells and always

17

Figure 2.3: The two voltage configurations in a pin decelerator and the potentials they create. In
each voltage configuration, red corresponds to positive high voltage, blue to negative high voltage,
and white to ground. The Stark potentials are plotted below each voltage configuration. The values
for the potentials are for ND3 in the pin decelerator in our lab operated at ±12 kV.

confined to the central axis of the decelerator. In this dissertation, the decelerator axis will bereferred to as the z-axis. This molecule that travels only on the z-axis with no transverse (x ory) motion is called the timing molecule. While in practice, there will not be a molecule withzero transverse motion in the decelerator, this one-dimensional calculation for the timing moleculeis helpful for determining how an entire packet of molecules should be decelerated. The timing
molecule is also referred to as the synchronous molecule, but in order to be consistent with othertypes of Stark deceleration that will be discussed later, it is called the timing molecule here. In
practice, an entire molecular packet centered around the timing molecule will be decelerated.
As the potentials alternate, the potential well that the timing molecule occupies travels down
the length of the decelerator. In the simplest method of running the decelerator, no deceleration
occurs and the average velocity of the potential wells is the same as the initial velocity of the

18beam. This configuration is called bunching because the molecular packet will not be decelerated,
but instead will be forced into “bunches” of molecules. Bunching occurs if the potentials switch
after a time t = vli where l is half the distance between Stark potential peaks in one configuration.
Figure 2.4 shows the potential wells from Figure 2.3 overlaid in blue and red dashed curves, while
the black curve gives the trajectory of the molecule on the two potential surfaces. Each time themolecule switches from one potential to another is referred to as one stage of deceleration. In thisconfiguration, the molecule gains the same amount of energy that it loses during each stage.

Figure 2.4: The black curve depicts the potential experienced by the timing molecule as it travels
through the two potentials (red and blue) for φ0 = 0◦ , the case where the molecule does not change
velocity.

The configurations are switched each time the molecule is at the exact same position on thelongitudinal potential. The position of the timing molecule during the switch is typically given
as an angle and is called the phase angle, φ0 . The conversion between the position of the timing
molecule within a well, z0 , and the phase angle in radians is
φ0 =

πz0
,
l

(2.1)

where z0 = 0 is the position at which φ0 = 0◦ . The phase angle gives a measurement of thelongitudinal position within the decelerator that is independent of that pin separation, l, which

19
makes it both a useful, and sometimes frustrating, parameterization. The phase angle gives thelongitudinal distance of the timing molecule as a fraction of the pin stage length, and has units ofdegrees or radians. It is a useful characterization of the magnitude of deceleration since it gives asense of whether a lot or a little energy is removed per deceleration stage, but it does not give any
information as to the final velocity of the beam.

Figure 2.5: The longitudinal potential for the given electrode configuration is given in red. Various
phase angles, φ0 , relative to this potential are marked.

Figure 2.5 shows where the phase angles of 0◦ , 45◦ , and 90◦ are located relative to a given
potential (red). The phase angle φ0 = 0◦ is defined as the position of the timing molecule in thecase where the final velocity of the molecule is the same as the initial velocity. Figure 2.4 shows
the longitudinal trajectory of a molecule that switches potentials each time it reaches the position
φ0 = 0◦ . This molecule neither gains nor loses energy. φ0 = 0◦ is not at the bottom of a well but
instead at a distance l/2 away from a pair of pins. The height of the Stark potential at φ0 = 0◦ will
most likely not be at half the amplitude of the longitudinal potential. Instead the energy where
φ0 = 0◦ occurs will depend on the gradient of the potential well. The phase angle increases from
φ0 = 0◦ to φ0 = 90◦ for z0 = 0 to z0 = l/2. A phase angle of −90◦ < φ0 < 0◦ , which occurs at

20
l/2 < z < l, accelerates the molecule since the timing molecule will always be traveling down thepotential energy hill. Phase angles of 90◦ < φ0 < 270◦ are unstable.
Figure 2.6 shows deceleration with phase angles of φ0 = 30◦ and 60◦ . Here, the moleculechanges potential energy surfaces each time the voltages are switched as indicated by a dashedvertical line. As the phase angle increases from φ0 = 30◦ to φ0 = 60◦ , more energy is removed perstage, indicated by ∆K. The deceleration extreme is a phase angle of φ0 = 90◦ , which switches
when the timing molecule reaches the peak of the potential energy hill. This is the maximum
energy that can be removed per stage. The total kinetic energy removed from a timing molecule
will beKtotal (φ0 ) = ∆K (φ0 ) × number of stages.

(2.2)

For typical pin decelerator geometry (>100 stages) and voltages, a small molecule such as OH or
ND3 will have ∆K (φ0 = 50◦ ) ≈ 1 K (or 1 cm−1 ). However, this is only an estimate and ∆K isdependent on the Stark shift of the molecule being decelerated.
The longitudinal kinetic energy removed from a molecule by the entire decelerator and for agiven phase angle (Equation 2.2) is dependent on electrode geometry, which sets ∆K and lengthof the decelerator. This can only be calculated if the gradient of the potential is known. Thus
Ktotal (φ0 ) is usually not a very intuitive function and it is difficult to guess the final velocity of thetiming molecule from the phase angle. The relationship between the final velocity and phase angle
for a timing molecule that undergoes n deceleration stages, each of which removes ∆K of energy,
can be found via conservation of energy
11
mvi2 = mvf2 + n∆K(φ0 )22r2n∆K(φ0 )vf (φ0 ) = vi2 −
.
m

(2.3)

The value of ∆K(φ0 ) is determined by building a model of the decelerator pins in COMSOLMultiphysics, a finite element analysis software package, and solving for the electric fields. While
the full decelerator is many stages long, only a small section that is 2l long needs to be modeled,since the potentials repeat on this length scale.

21

Figure 2.6: The two potentials that can be formed in PPSD are show in blue and red. For eachphase angle, φ0 = 30◦ and 60◦ , the path that the timing molecule travels is given in black. The
times when the molecule reaches vertical-dashed lines indicate when the voltage configurations
should switch.

To effectively implement deceleration at a given phase angle, a timing sequence for when
the potentials switch must be calculated. The velocity of the timing molecule decreases with eachstage, which increases the time each stage remains on as the molecule travels the length of thedecelerator. The timing sequence for switching the potentials for a given phase angle is generated
by simulating the motion of a timing molecule along the COMSOL generated longitudinal potential.
The molecule is fixed to have no transverse displacement or transverse velocity, so its motion only
on the longitudinal axis needs to be considered.
To find the time that the timing molecule spends in each stage, we use
vf (φ0 ) =

dφ
π dz
=
dt
l dt

(2.4)

22
and Equation 2.3 with n = 1, because we are referring only to one stage, to get
l
dz
q
,
π
0)
vi2 − 2∆K(φ
m
Z φ0
dz
l
q
.
tstage =π −π+φ00)
vi2 − 2∆K(φ
m
dt =

(2.5)

Here, vi is now the initial velocity of the timing molecule at a given stage. The process of determining tstage is usually completed numerically. Using the COMSOL model of the decelerator, an
acceleration file is generated. It specifies the acceleration of a molecule along the central axis of thedecelerator. A single timing molecule with an initial longitudinal z-velocity is propagated along z
using a time step of ∼10 ns. Each time the timing molecule reaches the switch point (phase angle),
the acceleration file is shifted by l in the z-direction and the time recorded. The final list of switch
times then corresponds to the switching sequence for that phase angle. The final velocity can also
be extracted from this calculation, though it is a much more complex method than Equation 2.3 itgives identical results.
Up until now, we have considered only one timing molecule moving in the Stark potential well;in reality, an entire packet of molecules will be decelerated. Here, it is important to consider the
packet of molecules in phase space, the 6D space of position and velocity. The area that successfully
decelerated molecules occupy is known as the phase-space acceptance. The molecules that are near
the timing molecule in phase space are the ones that will also be decelerated, and Figure 2.7 gives
an example of this using φ0 = 45◦ . The timing molecule on the black trajectory switches from theblue potential to the red potential when it reaches the phase angle φ0 = 45◦ . The lagging moleculea (orange), which was behind the timing molecule on the blue potential, ends up at a higher Stark
potential than the timing molecule on the red potential. This causes molecule a to loose less energy
than the timing molecule. This allows the lagging molecule move a little faster and to “bunch”
with the timing molecule. The opposite is true of molecule b (green), which was ahead of the timing
molecule. Molecule b experiences a greater energy loss when it switches to the red potential. Thiseffect allows the rest of the packet to appear to catch up with the forward molecule. Only molecules

23
a given distance away in phase space from the timing molecule will experience this restoring force.
Once a molecule is outside the phase-space acceptance, it cannot maintain a stable orbit inside thedecelerating potential well and will not be decelerated. In the case of φ0 = 90◦ , molecule b will
have already crossed over to the accelerating portion of the potential well and all other molecules
ahead of the timing molecule will not be decelerated. This model shows how phase angles close to
φ0 = 90◦ are less effective for decelerating appreciable numbers of molecules.
2.0

Energy (K)

1.5

b
●
a●
●

1.0

0.5

0.0
0

●●
●
2

4

6

8

z (mm)

Figure 2.7: Molecules traveling on the blue potential behind (orange) and ahead (green) of thetiming molecule (black) experience longitudinal bunching due to the differing amounts energy loss
when they switch to the subsequent (red) potential.

The alternating sets of crossed pins in the decelerator provide alternating transverse focusing.
For energized stages, the highest electric field is near the rods, and on any particular stage, themolecules are focused toward the electric field minimum lying halfway between the two rods. By
alternating the directions of the pins, there is overall transverse focusing.
There are three main effects that reduce the decelerator efficiency, one that can occur at any
velocity and two that predominantly occur at velocities below 100 m/s. At any velocity in the
decelerator, coupling between the longitudinal and transverse motions can amplify the transverse
motion of molecules on each stage of deceleration, thus forcing the molecules transversely out ofthe decelerator [139]. At velocities <100 m/s in the decelerator, the phase-space acceptance is24drastically reduced due to “over aggressive” deceleration of portions of the packet through two
effects, usually referred to as transverse over focusing and longitudinal reflection [140]. At low
velocities of the decelerated packet, it becomes more likely for a stage to over focus in the transverse
direction and squeeze the molecules out of the well (transverse over focusing). A second effect isthat some low velocity molecules may not make it over the last deceleration stage when the average
longitudinal kinetic energy of the packet is of the order of the potential energy hill (longitudinalreflection). Longitudinal reflection is particularly applicable to molecules away from the central
axis where the longitudinal potential is higher. At these low final velocities, the molecules spend
longer in the decelerator and have a greater chance to be lost.

2.2.2

Traveling-wave Stark Deceleration

The losses that are present in pin decelerators can be mitigated by using ring-shaped electrodes. The ring shaped electrodes can use a fundamentally different mode of applying voltages tothe electrodes. Instead of pulsed voltages, chirped sinusoidally varying voltages are applied to thering electrodes. This produces a traveling-wave potential well that continuously guides or decelerates the molecular beam. While PPSD produces a time averaged moving potential well, TWSD
produces a genuine moving three-dimensional (3D) potential well. This provides an inherently stable deceleration process that has a true 3D trapping potentials and no longitudinal and transverse
coupling loss. Continuous application of the decelerating force also allows for lower instantaneous
accelerations and more efficient deceleration.
A ring decelerator is made up of a series of ring electrodes with every p rings electricallyconnected. Just like in PPSD, each set of rings that are electrically connected are referred to as
a rod. The rods i are typically labeled i = 0, ..., p − 1. Figure 2.8 shows a CAD drawing of one
ring (a) and our ring decelerator (b). In this case, the rings are tennis racket shaped with the two
wires flaring out at the end. Other ring decelerators [122] have not use the flared configuration,and instead kept the two wires together to equal success. The eight ring periodicity (p = 8) of thedecelerator can be seen in Figure 2.8b, where a CAD drawing has each rod, and its corresponding25(b) Ring decelerator(a) One ring electrode

Figure 2.8: CAD drawings of one ring electrode (left) and the full decelerator (right). Each ring isheld in place on its mounting rod with two set screws and every eighth ring is electrically connected.
The decelerator has been color coded to more easily distinguish the periodicity. Even though thering is not a perfect circle, the rings are mounted in a spiraling pattern and the pinch does not
significantly contribute to any changes in the potential well from a perfect ring [95]. Taken from [95]Figure 5.16

rings, color coded. Figure 2.1b shows the end of the decelerator in our lab.
Instead of each rod being on or off at a given time, in TWSD, the ring electrodes have varying
sine-wave voltages Vi (t) on each rod i. The timing molecule no longer climbs successive potential
energy hills, instead it travels along with the potential well. In order to create this moving well,
the sine-wave voltages on the rings will have the formVi (t) = Va sin

2πi− ωt for i = 0, ..., p − 1.
p

(2.6)

Here ω sets how fast the potential well translates in time. If ω = 0, then there is only a static
potential well. If ω 6= 0, a constant frequency longitudinally translating sine-wave voltage, which
would correspond with bunching, would be produced. For a decelerator with ring-to-ring spacingsof l, the velocity of the well is the distance the well travels in one period, pl, multiplied by theifrequency f of the sine wave, v = f pl. For bunching at the initial velocity of the beam, ω = 2πv
pl .

In order to decelerate a beam, the velocity of the well itself must change. This is accomplished26
by chirping the frequency of Vi (t). The simplest frequency chirp is a linear one wheref (t) = f0 + αt,ω(t) = ω0 + 2παt,(2.7)

and where α is a constant acceleration given byα=

ff − f0
vf − vi
=
.
T
plT

(2.8)

Here T is the total time required to travel the length of the decelerator and is determined by
T =

2L
.
vf + vi(2.9)

L is the full length of the decelerator and l is the distance between adjacent rings; they are relatedbyL = l × (number of rings − 1) .

(2.10)In order to incorporate the frequency chirp, now instead of having a ωt term, Vi (t) must havea time dependent phase Φ (t) t term, and Equation 2.6 becomesVi (t) = Va sin2πi− Φ (t) t for i = 0, ..., p − 1.
p(2.11)

Φ (t) is the integral of the instantaneous frequency (Equation 2.7),ZΦ (t) =

ω (t) dt = ω0 t + παt2 .

(2.12)

Now by substituting Equations 2.8 and 2.9 into Equation 2.12, Φ (t) can be reexpressed asπvf2 − vi2 t2
2plL

π
2πv0
Φ (t) =
t−vi2 − vf2 t2
pl
2plL
"
#
vi2 − vf22π
Φ (t) =
v0 −
t t.
pl
4L
Φ (t) = ω0 t +The full chirped sine-wave voltage (Equation 2.11) then becomes"#!
vf2 − vi2 2
2πi 2πVi = Va sin−
v0 t −tfor i = 0, ..., p − 1.
ppl
4L

(2.13)(2.14)

27

Figure 2.9: The 3D (A) and cross section (B) view of the instantaneous electric potentials for ±12
kV sine-wave voltages on the ring electrodes and (C) the resulting molecular potentials in kelvin for
ND3 . For a sine-wave potential spanning eight rings, two Stark potential wells are formed. Eachwell is 0.7 K deep along the longitudinal axis. Figure taken from [95] Figure 5.1.

These voltages create 3D moving potential wells on the ring electrodes. Figure 2.9 shows theelectric potential created by sine-wave voltages on the ring electrodes and the resulting molecularpotential wells for ND3 . Although one period of the sine-wave covers eight rings, two potential
wells are created for every eight rings because the Stark energy depends only on the magnitude of

28
the electric field and not the sign (see Section 3.1.1). For a maximum voltage of ±12 kV on thering electrodes, each well is 0.7 K deep along the longitudinal axis. While this is shallower thantypical wells in PPSD (∼2 K), continuous confinement of molecules in TWSD yields more efficient
deceleration. The instantaneous accelerations applied to the molecules is lower, but it is applied
constantly instead of discretely. The cylindrical symmetry and continuous nature of TWSD makes
it a more efficient deceleration technique than PPSD, but the required sine-wave voltages make it
more difficult to implement.

2.2.3

Pulsed Ring Stark Deceleration

Since TWSD is difficult to implement, pulsed-ring Stark deceleration, an alternative runningmode for operating a ring-geometry decelerator was proposed by Hou et al. [141]. It uses pulsed
voltages, just like in PPSD, but on ring electrodes. This creates discrete potentials wells similar to
PPSD, but with a slightly different potential well shape. The voltages on the electrodes are varied
in an identical manner to that of PPSD. This makes many of the techniques from PPSD, suchas calculating the timing sequences and the phase-space acceptance, directly transferable between
the two methods. PRSD takes advantage of the cylindrical symmetry provided by the rings andis simpler to implement than TWSD, since it uses commercial high-voltage switches instead ofhigh-voltage analog amplifiers. The PRSD method is discussed in detail in Chapter 4.

2.3

Phase-space Acceptance
A molecule that travels only along the axis of the decelerator would be stable in an infinitely

long decelerator. However, in reality, the molecules have off-axis velocity and position components.
In all deceleration modes, the transverse potentials within the decelerator drive these molecules
towards the decelerator axis. At the same time, the longitudinal potentials push molecules aheadof and behind the timing molecule toward the timing molecule (see Section 2.2.1).
Depending on the geometry of the decelerator, voltage on the electrodes, and the phaseangle, only molecules a given distance away in position and velocity from the timing molecule will

29
be successfully decelerated. The boundary in phase space between the molecules that are stably
decelerated and those that are not is called the separatrix. The area inside the separatrix is called
the phase-space acceptance. If considering only the position and velocity along one coordinate (sayz and vz in the case of the longitudinal phase-space acceptance) this is a 2D phase-space acceptance.
However, in the case of all six phase-space coordinates, the phase-space acceptance is 6D and has
units of (mm)3 (m/s)3 .
Ideally, the phase-space acceptance will be well filled with molecules from the initial molecularpulse that enters the decelerator, however this is not always the case. This incomplete filling canbe due to two reasons, the first is instabilities in the deceleration process that cause holes within
the phase-space acceptance and the second is the initial pulse was smaller in phase-space than thephase-space acceptance of the decelerator. The first issue will play a role in PPSD since it has
well-characterized instabilities and loss mechanisms that are enhanced at low final velocities [139].
In particular, coupling between the longitudinal and transverse motion leads to amplification of thetransverse motion. The second issue of underfilled phase space by the initial molecular packet will
not be discussed because the initial pulse used in these experiments is much larger in phase spacethan the acceptance of either decelerator.
The phase-space acceptance of the decelerator can be calculated via two methods, by examining the restoring force on molecules near the timing molecule and calculating their equations of
motion, or by looking at the combination of the fictitious force from the deceleration of the welland the Stark potential well. These two methods are considered in 2D slices in the longitudinal (z)directions. Here, we also address only S=1 deceleration, where a set and uniform amount of energy
is removed in each stage of the decelerator.
In the first method, we consider the motion of the timing molecule and the difference in theforce applied to the timing molecule and a molecule near the timing molecule. The separatrix isthen the boundary between stable and non-stable orbits of these molecules. First, we examine thetiming molecule decelerated with a phase angle of φ0 = πzl 0 (Equation 2.1). To find the average force
on the timing molecule per deceleration stage, an approximate functional form for the potential

30
well is required. The longitudinal potential hill can be expressed as a Fourier series of the form
∞

∞

X
X
1
W (z) = a0 +an cos (nz) +bn sin (nz) .
2
n=1(2.15)

n=1

The potential should be expressed as a function of the longitudinal distance (φ), which is given in asimilar fashion to the phase angle (φ0 ) such that φ = πzl . We change the potential W (z) from thelongitudinal distance z to the phase angle φ and expand around φ0 = π2 . a0 is a constant energy
shift and is set to zero for now. All bn terms vanish since the potential is symmetric about φ0 . If
the rods are spaced such that l, the longitudinal spacing between adjacent rods, is approximately
equal to the transverse center-to-center spacing, the potential closely resembles just the first termof an , a cosine wave [142]. This gives the potential W (φ) asπ.
W (φ) ≈ a1 cos φ +2(2.16)

The coefficient a1 is the amplitude of the cosine wave potential hill. Thus, if the height of thepotential well is Wmax then 2a1 = Wmax .
The average force on the timing molecule per deceleration stage at phase angle φ0 can be
determined from the loss of kinetic energy per stage. This is illustrated in Figure 2.10 where∆K =Ered −Eblue . Since Eblue =Egreen and the energy at Egreen is W (φ0 + π),∆Kl1
F 0 = (W (φ0 ) − W (φ0 + π)) .
l
F0 =(2.17)A substitution of Equation 2.16 into Equation 2.17 gives an average force of




a1
π
3π
F0 =
cos φ0 ++ cos φ0 +
l
2
2
2a1
F0 =
sin (φ0 )
l
Wmax
F0 =
sin (φ0 ) .
l(2.18)

Any molecules near the timing molecule will experience a similar force, but off by ∆φ, the longitudinal distance it is away from the timing molecule in radians. The average force on a molecule

31
located at φ0 + ∆φ is
F =

Wmax
sin (φ0 + ∆φ) ,l(2.19)and the average force difference between this molecule and the timing molecule is
F diff = F 0 − F =Wmax[sin (φ0 ) − sin (φ0 + ∆φ)] .
l(2.20)

Figure 2.10: The timing molecule switches from the red potential to the blue potential at the phaseangle φ0 . The energy lost per stage is ∆K and is the same as Ered −Eblue =Ered −Egreen =W (φ0 ) −W (φ0 + π).

Now, the equation of motion for a molecule located near the timing molecule and relative tothe timing molecule can be written down from Newton’s second law,d2 z
= Fdiff
dt2
ml d2 φ= Fdiff
π dt2
Wmax
ml d2 φ=[sin (φ0 ) − sin (φ0 + ∆φ)]2
π dtl
ml d2 φ Wmax
0=−[sin (φ0 ) − sin (φ0 + ∆φ)] .
π dt2
l
m

(2.21)

Molecular trajectories can now be calculated relative to the timing molecule. The boundary between
stable and unstable trajectories around the timing molecule is the separatrix. In order to calculate
the phase-space acceptance, it would be easiest to work in z and Vz where the timing molecule isdefined to be at z = 0 m and Vz = 0 m/s. We use ∆φ = πzl to change Equation 2.21 to z. Although
φ0 = πzl 0 , φ0 is left as is since φ0 and z0 are constants and pulsed deceleration is typically describedby the phase angle in degrees and not the exact distance, z0 , that the timing molecules moves.
Equation 2.21 now becomes0=d2 z Wmax h
πz i
−
sin
(φ
)
−
sin
φ
+
.
0
0
dt2
ml
l

(2.22)

32
Equation 2.22 can be numerically integrated to determine the separatrix for a given phaseangle φ0 . Figure 2.11 gives an example of a few separatrices obtained for PPSD of ND3 . The areabound by the a given separatrix is the phase-space acceptance.

Figure 2.11: The longitudinal (z axis) separatrices for φ0 = 0◦ , 20◦ , 40◦ , 60◦ , 80◦ . The area boundby a given separatrix is the phase space acceptance. The z coordinate here is the distance awayfrom the position of the timing molecule.

The second method of determining the phase-space acceptance examines the non-inertial
reference frame of the decelerating potential relative to the inertial lab frame. In the non-inertial
frame, the molecules experience an opposing fictitious force Ff
dUf
= Ff
dz
dUf
−
= −ma
dz
Z
Uf = ma dz−

Uf = maz,(2.23)

where a is the average acceleration of the potential well and Uf is the fictitious potential. Since weare discussing deceleration, a is negative. The effective potential that the molecules experience isthe sum of the actual potential, U , and the fictitious potential
Ueff = U + maz.

(2.24)

33
In a pulsed mode of deceleration, the time-averaged effective potential, Uef f , can be foundfrom the force difference (Equation 2.20) between a molecule located at z and the timing molecule,Wmax[sin (φ0 ) − sin (φ0 + ∆φ)]liWmax h πz −F diff =sin φ0 +− sin (φ0 )
l
l
h

i
dU diffWmax
πz =
sin φ0 +− sin (φ0 )
dz
l
l
Z
h

i
Wmax
πz 
U diff =sin φ0 +− sin (φ0 ) dz
l
l


 πz

Wmax
Wmax
U diff = −msin (φ0 ) z +cos+ φ0 .
mlπl
F diff =(2.25)

Again, here, we use the slightly strange convention of φ0 + πz
l which has units of radians. Equation
2.25 has been written in a suggestive format that matches Eequation 2.24. The term inside thesquare brackets is the relative accelerationa=Wmaxsin (φ0 ) .
ml(2.26)

By multiplying Equation 2.26 by m we get F or Equation 2.19 for the timing molecule. The far
right term of Equation 2.25 is the averaged potential well centered on the timing molecule. It is afactor of π2 different from Equation 2.16 due to the need for averaging across one deceleration statein the pulsed mode.
In the traveling-wave mode, since the forces are applied continuously and the potential does
not change significantly relative to the timing molecule, Equation 2.24 does not require the timeaveraged force derived in Equation 2.25. Instead U is simply the Stark potential well (usuallycalculated via COMSOL) and the acceleration isa=vf2 − vi2
2L,

(2.27)

where L is the length of the decelerator.
This second method allows for easy visualization of the possible phase-space acceptancewithout having to do much calculation. By plotting Equation 2.24, it is easy to see when the Stark
potential well ‘tilts’ over to the point of no longer being able to trap molecules. Figure 2.12 shows

34
several longitudinal potentials for ±8 kV TWSD in the ring decelerator in our lab. The initial
velocity is set to 415 m/s. If no deceleration is applied, the well shape remains symmetric. As more
acceleration is applied the well tilts and the downstream (right) wall of the potential well lowers inheight. For this given potential well, deceleration down to 100 or 0 m/s is not very feasible since
the potential well almost completely flattens out.

Figure 2.12: The effective longitudinal potential (Equation 2.24) for an initial velocity of 415 m/s
and various final velocities for ±8 kV TWSD. As more acceleration is required to reach lower final
velocities, the well tilts over significantly. For this voltage configuration, final velocities of 100 and
0 m/s have almost no potential wall on the right-hand-side. Thus very few molecules can be phasestable in that deceleration sequence.

The longitudinal phase-space acceptance can also be calculated using the Uef f potential(Equation 2.24) and conservation of energy. The separatrix is set by molecules that can just escape
the Ueff potential well. In order to stay phase stable, molecules must have less than or equal energy
to the downstream (lower) maximum Stark energy,
1
mv 2 + Ueff = Ueff max .
2(2.28)

Solutions to Equations 2.22 and 2.28 produce identical phase space acceptances.
Up to this point, all pulsed deceleration phase spaces have been examined using the first termin a fourier series as the potential. While this is an acceptable approximation, it is important to35note that there are differences in the shape of the potential. Figure 2.13 shows the longitudinalpotentials for all three types of deceleration (TWSD, PRSD, and PPSD) in addition to a the cosine
potential given by Equation 2.16. The cosine potential more closely resembles the potential wellin the pin decelerator than the ring decelerator. In the ring decelerator the vertex at the bottomof the well cannot be easily modeled with a cosine. The difference between the cosine potential
and actual potential will change the shape of the separatrix and also affect the acceleration as afunction of phase angle/final velocity.
In the cosine wave approximation of the potential, the acceleration is given by Equation
2.26. However, in the actual experiment, the average acceleration is determined by Equation
2.27. Although the acceleration is not applied in the same fashion in pulsed and traveling-wave
deceleration, once averaged over the total deceleration time, they are the same. This is only
true because we use a constant acceleration in all our experiments. If this was changed, different
calculation would be required. Figure 2.14 shows the acceleration as a function of phase angle forboth equations, where black is the calculation using Equation 2.27 and blue is the calculation using
Equation 2.26. Red is a sanity check and is the acceleration averaged over one stage of deceleration.
It is determined by taking average value of the piece-wise acceleration function at different phaseangles. The acceleration determined using this method matches Equation 2.26 exactly.

36

Figure 2.13: Normalized longitudinal potentials for TWSD, PRSD, PPSD, and a cosine (Equation
2.16). All potentials have been normalized so that they have a height of one and the same longitudinal periodicity. Both potentials in the ring decelerator the have a vertex at the bottom of thepotential well.

Figure 2.14: The acceleration for the PRSD potential as a function of phase angle. The acceleration
calculated from vi and vf (black) and from averaging over one deceleration stage (red) are identical,so the black curve appears underneath the red curve.

2.4

Simulations
In order to fully explore the dynamics in any deceleration mode, three-dimensional (3D)

molecular trajectory simulation are required. These 3D simulations are particularly important
for the PPSD mode, due to coupling effects that cannot be replicated in a 1D model. Thesesimulations are semiclassical. The potential energy surfaces are determined by the Stark energy of37
Table 2.1: Typical values for the full width at half maximum (FWHM) of the initial distributionof molecules
Phase-space value
x,y-position
z-position
x,y-velocity
z-velocity

Gaussian FWHM
3 mm
30 mm
5 m/s
30 m/sthe molecules (a quantum calculation), but the trajectories are treated classically. In general, thesimulations follow this procedure:(1) Create a Gaussian distribution of initial position and velocities using Monte Carlo techniques. Table 2.1 gives typical initial parameters. The distribution is centered at thelocation of the pulsed valve.
(2) One molecule, typically the first molecule, is set to be the timing molecule. It will have notransverse displacement or velocity and will be constrained to evolve only in the longitudinal
direction. This molecule will determine when the potentials in the decelerator change.
(3) Propagate the distribution to the entrance of the decelerator. This is the free flight section
and no forces are exerted on the molecules.
(4) Propagate the distribution through the decelerator via the chosen mode of deceleration.
The potentials will change as dictated by the timing molecule and desired phase angle orfinal velocity.
(5) Record the final phase-space distribution (a set time) or the time-of-flight (a set position)
for the molecules.
Typically, modified Euler integration is used for the molecule trajectories in the simulations. The
time scale (3-6 ms) for deceleration is short enough that no appreciable errors build up. For trap
simulations, a more complex symplectic integrator must be used because errors can accumulate
when holding molecules in the trap for an extended period of time (1-2 s).

38
In all simulations, acceleration files for the given molecule of interest are generated fromelectric potentials calculated in COMSOL. In pulsed mode simulations, the acceleration file is
specified for a length of 2l (spanning three pairs of electrodes). This file is then propagated forward
by l each time the decelerator potentials switch. In traveling-wave mode simulations, 25 versionsof the accelerations are generated, which correspond to the bottom of the potential well being in
25 equally spaced locations between two rings. Again the potentials are propagated forward by lwhen the bottom of the potential well moves from ring n to ring n + 1.
Molecules may be lost from the simulation because they end up in the following locations:outside the entrance area of the decelerator, hitting a ring, or outside decelerator phase space.
Molecules in the last category will typically travel the length of the decelerator, but not be decelerated. They will exit before the decelerated packet. They are not within the phase-space acceptanceand are not decelerated. In the case of mild decceleration (<| 25 | km/s2 ), there could be many ofthese molecules since the undecelerated beam may not be fully separated out from the decelerated
packet and not all molecules that arrive in the time window of the decelerated peak will be within
the phase-space acceptance of the decelerator. The decelerated molecules can be selected for byplotting all molecules in phase space and picking only those that fall within the calculated 1D
phase-space acceptance in each direction (x, y, and z).
Simulations are also able to provide information regarding what is happening inside thedecelerator that can never be extracted from an experiment. These include the phase-space information for molecules at intermediate times and individual particle trajectories in the decelerator.
To save on memory, the molecules that “crash” can be removed from the simulation, and recording
when and where these molecules are lost can also be very helpful for studying various deceleration
schemes.
These simulations are written in C++ and run on the JILA’s ‘Terra’ cluster. Depending on
the initial density of molecules and the number of desired decelerated molecules, it is often desired
to begin a simulation with several million molecules. Instead of propagating all the molecules atonce, since there are no inter-molecule dependencies in the simulation, many smaller distributions

39
of molecules can be run in parallel or series. All results can be summed at the end.
In all of these simulations, the timing molecule is artificial and must be removed from themolecular distribution before the results are analyzed. This is especially true if running many
iterations or very spread out initial packets. For example, if 100 iterations of 10,000 molecules
were used to generate 1 million molecules. One hundred of the molecules were forced to arrive inthe decelerated packet. If the decelerated packet is small, only a few hundred molecules, then thetiming molecules will artificially boost the decelerated and detected molecules.
Trapped molecule simulations are conducted in a similar fashion to the process outlined above.
The Stark potentials created by the electrostatic trap are modeled in COMSOL and exported. The
molecule distribution is taken from the output of a trap loading simulation. Since time spent in thetrap is significantly longer than time spent in deceleration or trap loading (seconds compared tomilliseconds), it is critical to use a symplectic integrator. The total energy of individual moleculesin the trap should be checked to ensure that they neither gain nor lose significant energy.

2.5

Experimental Layout
Figure 2.15 gives the layout for a typical deceleration experiment that contains a pulsed valve,

skimmer, decelerator, interaction and detection region. The configuration of the interaction anddetection region may vary widely depending on the intended experiment.
The molecule of interest is seeded in a carrier gas, and the gas mixture enters the vacuum
chamber via a pulsed valve. The supersonic expansion of the gas from the gas reservoir into thethe vacuum system cools the internal degrees of freedom of the molecule, but the beam maintains
a large forward velocity. Typically, krypton or xenon is used as the carrier gas in order to have a
low initial velocity even though heavier carrier gases are also more likely to form clusters, whichcause higher temperatures.
The beam passes through a skimmer, which both selects for a collimated beam and allows fordifferential pumping between the source chamber and decelerator chamber. This way the majorityof the gas loaded into the vacuum system remains in the source chamber. The flared geometry of

40

Figure 2.15: A general Stark deceleration experiment contains a pulsed valve, skimmer, decelerator,
and an interaction and detection region. Here a pin-geometry decelerator is depicted and thedetection system is a 1+1’ resonance-enhanced multiphoton ionization (REMPI), time-of-flight(TOFMS), and microchannel plate (MCP) system.

the skimmer reduces interference from molecules reflected off of the outside wall and build up ofmolecules inside the skimmer. Other versions of a skimmer, including a cooled skimmer, have shown
greater cold molecule densities in the beam, but have not been tested with a decelerator [143].
After the skimmer is the Stark decelerator, which can come in several different geometries
and electronic configurations as discussed in Section 2.2. The decelerator should be placed as close
as possible to the skimmer to reduce the molecules lost in free flight after the skimmer and before
the decelerator. While the pressure in the source chamber is on the order of 10−5 torr, to conduct
trapped molecule experiments with satisfactory trap lifetimes, the pressure in the science chambershould be under 1 × 10−9 torr. To achieve these pressures, additional differential pumping will most
likely be required in the decelerator chamber. This can be achieved by adding separation plates
between pumping sections. The plates should closely surround, but not touch, the decelerator.
At the end of the decelerator, the decelerated molecules can be trapped, guided, or collided
with other species. After the experiment has been completed, the molecules are typically detected
in a state-selective manner. Molecules are usually detected at the end of the decelerator, but they
can also be detected in the middle of the decelerator [118].

41
2.5.1

Supersonic Expansion

Most Stark deceleration experiments begin with a supersonic expansion from a pulsed valve,
however they could also be loaded from effusive [73] or buffer gas beams [43]. Pulsed valves come inmany varieties and operate using one of three mechanisms: forces on current carrying conductors,
solenoids, or piezoelectric actuators (PZT). Current-loop valves use pulses of opposing currents on
two parallel conductors to force apart the two conductors, which opens an o-ring seal [144,145]. One
current loop valve worth noting is the Jordan Pulsed Supersonic Valve C-211, which is commerciallyavailable. Another valve that opperates on current carrying conductors is the Nijmegen pulsed
valve [146], which can be built at a fairly low costs. In this valve, a current is run through ametal strip place between two magnets. The geometry of the system causes the metal strip to lift
when a current is applied. The second type of valve, a solenoid valve, uses a solenoid to actuatea ferromagnetic arm connected to a poppet, which seals the valve opening [147]. These valves
include the Parker Series 9 and Series 99, which were originally produced by General Corp andare often referred to as General Valves, and the Even-Lavie valve [148]. The last design is the PZTvalve [149, 150]. The PZT flexes when a voltage is applied across it, retracting a poppet, which
has an o-ring at the end. When the poppet is pulled back, in both the solenoid and PZT valves, apulse of gas is let into the chamber.
Stark deceleration is a conservative process, meaning no cooling or phase-space compression
will occur during deceleration. Gas expansion through the valve opening sets the maximum densityof the decelerated beam, which will set the maximum achievable signal for the experiment. This
makes the choice of the molecular source very important. A slower beam is easier to decelerate,
however it tends to have lower initial density and is more expensive to create.
Supersonic beams have a narrow velocity spread around a mean velocity, which makes thema good source of internally cold, but fast moving molecules. As the gas expands from the highpressure gas reservoir through the aperture (typically ∼1 mm) and into the vacuum region, it
undergoes many collisions. These collisions cool the internal (vibrational and rotational) degrees of42
freedom of the molecule of interest. In the reservoir, the molecules have no net flow, but once they
expand into the vacuum chamber, they form a directed jet perpendicular to the valve aperture.
The forward velocity of the beam in the ideal case where all enthalpy of the gas is converted
into kinetic energy is [151]sv (T0 ) =2kB T0 γ,m γ−1(2.29)

where T0 is the temperature of the gas reservoir, m is the mass of the atom or molecule, and γ
is the adiabatic constant. For a monatomic ideal gas, γ = 53 . In a real system, the heat capacity
ratio γ depends on the gas density and is a function of the pressure and temperature. γ(p0 , T0 )should be used instead and calculated from the heat capacities at constant pressure, Cp (p0 , T0 ) andconstant volume Cv (p0 , T0 ).
Lighter carrier gases produce denser beams at a faster velocity. However, this requires moreaggressive deceleration in order to reach low velocities, which decreases the phase-space acceptanceof the decelerator. Haas et al. [116] found that the trade-off between increased density and increased
phase angle leads to similar decelerated signals. This means if more aggressive deceleration ispossible, it is better to run with a lighter carrier gas since it will be cheaper. If more aggressive
deceleration is not possible, either higher voltages need to be applied to the decelerator or the
decelerator must be made longer.
From Equation 2.29, using a room temperature of 300 K, the velocities of an expansion ofargon, krypton, and xenon give beam velocities of 559 m/s, 386 m/s, and 308 m/s, respectively.
In practice, when working with a seeded gas, we observe slightly higher average velocities. For
example, when working with ND3 or OH seeded in krypton we set the timing sequence for amolecule with an initial velocity of 410-450 m/s.
Not all molecules that are typically Stark decelerated come ready in a bottle like ammonia;
some must be created in the chamber by an electric discharge or photodissociation. For example, wecreate our second most commonly used molecule, OH, via a electric discharge of H2 O. A molecularpulse created from a electric discharge or dissociation will be not be as broad as one from a bottle,

43since the time scale for the discharge pulse or dissociation laser pulse is short compared to thelength of the molecular pulse and these types of sources will fill fewer wells in the decelerator thana molecule from a bottle.
Many factors must be taken into account when choosing the carrier gas and valve for a Stark
deceleration experiment. The molecule and decelerator geometry set the maximum accelerationthat can be achieved. Limits to the maximum acceleration may set a maximum on initial velocity,which in turn sets a which carrier gas can be used. The final decision on the valve will depend on
the carrier gas, operational temperature, and any need for additional attachments such as discharge
plates.

2.5.2

Detection

The two most common state-selective molecule detection methods are laser-induced fluorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). A simplified model of both
detection schemes is shown in Figure 2.16. In LIF, the molecule is excited to an excited stateand spontaneous emission from the excited state is detected, typically with a photomultiplier tube
(PMT). In REMPI, the molecules are ionized in a step-wise resonant process. One or more photons
excite the molecule to an intermediate state where it is then ionized. The ions are typically detectedwith a microchannel plate (MCP).
An m + 1 REMPI scheme means that m photons are required to reach the excited state
and then an additional photon is required to ionize it. If the photons are not all of the same
wavelength, then the second photon is denoted by 10 indicating that it is two-color REMPI process.
Figure 2.16 depicts a 1+1 REMPI scheme where both photons are of the same wavelength andeach step requires only one photon. Once ionized, the molecules are detected via a time-of-flightmass spectrometer (TOFMS). An electric field is applied that accelerates the ions toward a MCP
detector. The arrival time at the MCP of the molecules is dependent on their mass-to-charge ratio.
Both types of detection processes are quantum-state selective since the first step to the excitedstate is tuned to a particular transition. If a molecule is not in that desired state, it will not be44

Figure 2.16: A simple model of both LIF and 1+1 REMPI detection. In both cases a resonant
photon excites the molecule from the |1i state to the |4i state. In LIF, the |4i state decays toanother state which could be |3i, |2i, or |1i and emits a photon, this photon is the detected signal.
Here the decay is depicted on the |4i → |3i transition. In REMPI, a second photon ionizes themolecule from the |4i state into the continuum. The resulting ion is detected. If the molecule
started in the |2i state instead of the |1i state it does not reach an excited intermediate state, andmolecules in the |2i state are not detected.

detected. This is opposed to single photon ionization processes, which are not state selective. BothLIF and REMPI detection tend to use wavelengths that are more easily accessible than one-photon
ionization process in the UV. For LIF and REMPI processes, the first photon is typically in the near
UV and can be produced by a tunable dye laser. Since both of these processes are state selective,
only one quantum state can be detected at a time. However, the tunability of the first wavelengthmeans that by adjusting this wavelength various states can be detected [152].
There are advantages to each technique. In REMPI, only a small portion of a trapped sample
is ionized and detected while in LIF the entire sample can be detected at once. In REMPI wherem>1, the laser beam(s) are focused down, and only a small portion of the sample is detected ineach run of the experiment. If the focus of the laser beam(s) can be scanned, then the shape of

45
the trapped molecules can be mapped out. Individual ions can be detected in REMPI making
it a more sensitive system, which can be used to map out the density distribution of a trappedsample [153]. LIF uses a collimated beam to illuminate the entire trapped sample. The signal islimited by the accessible solid angle for collecting photons. This can be difficult, particularly inelectrostatic traps, since only a small solid angle is available to collect photons and there are many
shiny electrodes for the excitation photons to reflect off of.
Often the detection technique chosen is dependent on the molecule in question, the available
lasers, and the dynamics of the study. Other detection techniques aside from LIF and REMPI havebeen used, including non-resonant multiphoton ionization followed by mass and velocity selection.
This was first demonstrated with CH3 F [130]. This non-resonant method is not dependent on
having a convenient and accessible excited state, and could open up the possibility of decelerating
and detecting more molecules that do not have a convenient REMPI or LIF detection scheme.
However, it more difficult to set up since it requires careful ion optics and a velocity map imaging
system.

2.5.3

Our experiments

In our lab, we have two decelerators, a pin decelerator and ring decelerator. Besides thedecelerators, both experiments are fairly similar. They used the same type of valve and detection
system. The detection system must be adjusted for the molecule of interest, but both system canbe used with both ND3 and OH. The molecular structures and detection schemes of ND3 and OH
are discussed in more detail in Sections 3.1 and 6.2 respectively. In these experiments, we use
primarily krypton as the carrier gas. Beams seeded in argon are too fast to decelerate to rest ineither of our systems given the length of the decelerator, however argon is occasionally used to
debug a free flight beam. The molecule of interest is mixed with krypton in a 1-2% mixture witha partial pressure of 40-60 psi of krypton.
The gas is let into the chamber via a PZT valve, which is typically operated with a 100 µs, 300500 V pulse. Figure 2.17 shows the ND3 time-of-flight distribution from our PZT valve in addition

46
to that of an in-house built NPV. The NPV has not been used with deceleration experiments, but
it appears that it would produce a similar beam profile to that of the PZT valve. Both beams
were detected after a skimmer and with 2+1 REMPI. A Beam Dynamics Inc. skimmer with a 2
mm orifice diameter is placed ∼15 cm down stream of the valve face. The exact distance between
the valve and skimmer is adjustable since the valve is mounted on a xyz-translation stage andits position can be adjusted from outside the vacuum chamber. The arm of the translation stage
must be as straight as possible, so that the valve face is parallel to the entrance of the decelerator.
Having the valve closer to the skimmer means a denser beam, however too close to the skimmer
and the skimmer will cause significant beam interference.

Figure 2.17: Time-of-flight measurements on ND3 for both the PZT and NVP valves. This measurement using a skimmed beam and detected ND3 via 2+1 REMPI. Taken from [154]The decelerator is placed 3 mm after the downstream end of the skimmer. In this dissertation,
only REMPI is used, but both decelerator systems are built to also accommodate LIF detection.
The laser for either method enters the vacuum chamber perpendicular the to the molecular beam.
A vacuum window is located right above the exit of the decelerator in both detection chambers
and allows for placement of a PMT. For REMPI, the MCP is placed along the molecular beamaxis, 20-30 cm downstream of the detection region. Either a simple two plate TOFMS is installed
immediately after the decelerator or an electrostatic trap can be turned to a TOFMS voltage
configuration to accelerate the ionized molecules. For all experiments, we use a 40 mm two-stage

47
chevron configuration MCP. The molecule signal is detected as a current, which is then converted
to a voltage using a transimpedance amplifier and the resulting voltage versus time signal for thedesired mass channel is integrated.
The laser system used for detection is a pulsed dye laser (Sirah PrecisionScan PRSC-D-24SLwith a doubling stage) pumped by 532 nm light from a doubled-pulsed Nd:YAG laser (QuantaRay
Lab170). Conveniently, we detect ND3 using a 2+1 REMPI process (see section 3.1.2) and only
one laser wavelength is required. To detect OH, on the other hand, is slightly more complicatedsince it uses a 1+1’ system. The first photon at 282 nm is generated using the dye laser. The
second photon, 118 nm, is generated by frequency tripling 355 nm light from a tripled Nd:YAG in axenon-argon gas cell. This procedure covered in Chapter 6. The two beams are counter propagatedthrough the chamber as shown in Figure 2.15.

2.5.3.1

Pin Decelerator

The pulsed-pin Stark decelerator in our lab has 150 pairs of pins. Typically ±12 kV is applied
to the pin in this decelerator. In PPSD, in order to create the correct shape potential well, the firstpair of pins must start grounded. This creates a defined potential well between the first two setsof pins. A defined well does not exist before the first pair of pins. This means a decelerator with
150 pin pairs has 149 deceleration stages. Figure 2.18 shows a CAD drawing of the decelerator
from two angles and has pin-to-pin spacing labeled in mm. Each pin has a diameter of 0.125 inches(3.175 mm) and has a center-to-center spacing of 2.04 inches (5.1816 mm) with its corresponding
pin in the transverse direction. The center-to-center spacing in the longitudinal direction between
adjacent (they will be perpendicular to each other) pins is 0.215 inches (5.461 mm).
The pins are set into four mounting rods (see Figure 2.1a), and each rod is connected to a
Behlke HTS-201-03-GSM switch. Four digital logic signals are required to control the four switches.
Although paired rods switch at the same time, the polarity of the Behlke switches means inverted
control signals are required for the negative electric potential rod of each pair. Thus four control
signals and four switches are required to run a pulsed decelerator.

48

Figure 2.18: A CAD drawing of the pulse-pin decelerator along the molecular beam axis (left) andperpendicular to the molecular beam axis (right). All measurements are in mm. Taken from Figure
4.9 in [155]Figure 2.19: The four electrode electrostatic trap used with the pulse-pin Stark decelerator. The
typical voltages used on each electrode are given and this creates a quasi-quadrupole trap potential
with a larger gradient in the x and y direction than in the z direction.

At the end of our pulsed-pin Stark decelerator, we have a four electrode trap (Figure 2.19). It
is similar to the quadrupole trap demonstrated in [85], but with an additional 2 mm slit cut into thelast electrode. This slit was designed to assist with extracting ionized molecules when the detection
lasers are scanned in the vertical (y) direction. Typically, the trap is run with the voltages [-10,10, 10, -10] kV on the four electrodes starting with the upstream electrode. This creats a quasi-

49
quadrupole trap. The electrostatic trap that most closely resembles a pure quadrupole [84, 114]
does not have optical access. By having two center electrodes, instead of just one, an ionization
laser can enter perpendicular to the molecular beam axis. The flexibility of the four electrodes
also allows for a loading configuration, referred to as “half on,” which is achieved using [0, 10, 0,-10] kV on the electrodes. This produces a Stark potential hill with a minimum offset upstream
from the trap center, which is used as an additional deceleration stage before the trap is turnedon (Figure 2.20). Previously, the two center electrodes were spaced 5 mm apart so that rubidium
atoms could be loaded from the side between the two electrodes as part of a ND3 +Rb cotrapped
experiment [117]. Modifications have been made so that the spacing is only 3 mm. This increases
the trap depth. Additionally, in previous work, the trap was operated at ±8 kV, it is currently
operated at ±10 kV. Lastly, a 5 mm hole was cut in the last trap electrode so that the Rb atoms
can still be loaded into the trap, but now from the back of the trap instead of from the side [155].

Figure 2.20: The longitudinal on axis potentials for the trap on (blue) and half on (red) configurations of the trap. The half on stage is used as an extra deceleration stage during trap loading.
The center of the trap is located near 13 mm and the extra potential energy hill in the trap on
configuration is created by the grounded decelerator electrodes and the first electrode of the trap.

50
2.5.3.2

Ring Decelerator

The ring decelerator in our lab has 624 rings. Each ring is made of 0.04 inch (1.016 mm)diameter tantalum wire. The rings are each shaped like tennis rackets (Figure 2.8a) and held in
the rods with two set screws. The decelerator has a periodicity of eight, with 78 rings per rod.
In order for the decelerator to function properly and hold the correct voltages, the surface quality
and cleanliness of the rings is very important. The rings are mechanically polished on a buffing
wheel, electropolished, and then thoroughly cleaned before they are instilled into the decelerator.
Figure 2.21 shows various steps of assembling the decelerator. Each decelerator rod is made ofmany sections each with 10-20 rings. Once the rings are attached to each section, the rods areassembled and the eight rods placed into their mounts. The decelerator is placed in a mounting
cage, which keeps it ridged and assists with alignment and installation inside the UHV chamber.
Once assembled in the cage, the rings must be aligned to ensure all rings are centered on the
decelerator axis and are parallel to each other. Careful alignment is completed with Teflon coatedtools so that the rings are not scratched in the alignment process.
After installation into the vacuum chamber, the full chamber with the decelerator inside was
baked to reduce the background pressure in the chamber. The decelerator was voltage conditioned
using 200 µs pulses up to ±10.5 kV. However, we believe better conditioning resulted from using
the amplifiers on the decelerator and slowly increasing the voltage of chirped sine-wave over thecourse of several weeks.
An eight ring trap has also been designed for our decelerator (Figure 2.22). It maintains
the same size rings and ring spacing as the decelerator, but each ring is electrically isolated. It
is mounted via a stainless steel plate and Macor standoffs. This allows for more flexible voltage
waveforms in the trapping region, since the entire decelerator does not need to remain at highvoltage while the trapping potentials are on. The trap can also be used in a TOFMS configuration
with the addition of a voltage divider box that evenly divides down the voltage from 1 kV to groundin eight steps. Although this trap provides significant flexibility for trapping studies, it also requires

51

Figure 2.21: The steps involved in assembling a ring decelerator. A) Rings are attached to rod
sections. B) Each rod is comprised of 4 sections. C) The sections are assembled into rods. D)The
rods are arranged in the correct order such that the ‘legs’ of each ring form a helical pattern. E)
Align the rings so that they are all concentric about the same axis. F) Fully assembled decelerator
in its support rack.

eight amplifiers in addition to the eight already on the decelerator, making it a significant challenge
to have sixteen analog high-voltage amplifiers operating at the same time. With the eight electricallyisolated rings attached to the end of our decelerator, we were able to use REMPI detection between
the fourth and fifth rings of the trap as a TOFMS and detect decelerated molecule signal. However,the full trapping configuration still remains to be realized. For the studies discussed in Chapter
4, the trap was removed from the experiment in favor of a simple TOFMS configuration made oftwo parallel plates with a circular 5 mm diameter center opening. Typically 1 kV is applied to the
upstream plate and the second plate is grounded.

52(a) CAD drawing of ring trap(b) Ring trap

Figure 2.22: The ring trap

2.6

Decelerator comparison
Choosing the appropriate decelerator geometry and running mode for a given application

will depend on the molecule in question and initial and final velocities. The many details of Stark
deceleration will be discussed in subsequent chapters, but here we present a general overview anda comparison of the two decelerators constructed in our lab.

53
The molecule Stark energy and the decelerator geometry and voltage will set the gradient of
the Stark potential well experience by the molecules. The initial and final velocities of the beamand length of the decelerator will determine the linear acceleration required (Equation 2.27). The
initial velocity of the beam will be set by the source and the final velocity is often set by the limitsof the experiment. The biggest trade off that must be decided on is length versus voltage. A
longer decelerator means lower voltages and accelerations can be used, but it increases the costs
and difficulties to build and maintain. Sometimes, this is unavoidable due to the molecule being
decelerated, for heavy molecules that do not have linear Stark shifts, a longer decelerator may be
the only solution. Generally, a longer decelerator of any kind will have an increased capacitanceand will require sourcing more current to keep the decelerator at the right voltages. A longer pin
decelerator may lead to more transverse losses unless a mode such as S=3 is used. Additionally,
for any decelerator geometry, the more electrodes there are, the more difficult it is to build, align,and voltage condition. Higher voltages, on the other hand, increases the potential well gradientand the accelerations it can accommodate, but increase the difficulty of the electronic and voltage
conditioning. How much voltage can be supported across two electrodes in vacuum is set by theirseparation distance and surface quality.
2.0

Energy (K)

1.5
TWSD 7kV
TWSD 12kV

1.0

PRSD 7kV
PRSD 12kV
PPSD 12 kV

0.5

0.0
-6

-4

-2

0

2

4

6

z (mm)

Figure 2.23: On-axis longitudinal potentials for PPSD (green), PRSD (red), and TWSD (blue)
modes in our pin and ring decelerators. For both modes of the ring decelerator, both ±7 kV (solid)
and ±12 kV (dashed) potentials are shown. All potentials are for ND3 .

54
Table 2.2: Properties of the two decelerators used.
Geometry
Number of electrodes
Stage length
Total length
HV Electronics

Crossed pins
150
5.461 mm0.81 mSwitchesRings
624
2.032 mm
1.27 mSwitches or Analog amplifiers

It is difficult to universally compare Stark deceleration methods since the efficiency is highly
dependent on the exact geometry and voltages applied. Each decelerator is designed and built to fit
the space and application it is to be used for. Just for reference, here, we compare the two physicalgeometries and three modes used in this dissertation, but these comparisons do not carry over into
other pin/ring decelerators. Table 2.2 gives a summary of the two physical decelerators and Figure
2.23 shows the on-axis longitudinal potentials for PPSD (green), PRSD (red), and TWSD (blue)
modes in our decelerators. For both modes of the ring decelerator, both ±7 kV (solid) and ±12
kV (dashed) potentials are shown. ±7 kV is used in this dissertation, but ±12 kV is also shown
so that the wells for the same maximum voltage can be compared. It is straightforward to see theeffect of geometry and voltage from these plots. The shape of the bottom of the potential wellis very different and longitudinally longer from the pin decelerator to the ring decelerator. Evenfor the same maximum voltages, the well for the pin decelerator is much deeper. However it has
significantly fewer stages and more loss mechanisms as mentioned above. Between the two ring
decelerator modes, PRSD has a smaller Stark potential well, but with a larger gradient, which plays
an important role in its efficiency. A well with steeper gradients can experience more acceleration
before it can no longer successfully decelerate any molecules.

Chapter 3

Molecules of Interest

In this dissertation, we decelerate deuterated ammonia (ND3 ) and hydroxyl (OH) in weakfield-seeking states. This chapter presents a review of some basic molecular structure importantto understanding the Stark deceleration and detection of these molecules. We then discuss the
structure of ammonia and OH and how they behave in electric fields.
Molecules can be exited electronically, vibrationally, or rotationally. This provides moredegrees of freedom and a significantly more complex energy-level structure than in atoms. As
molecules vibrate, this changes the internuclear spacing between the constituent atoms, which
affects the moments of inertia of the molecule and its rotational energies. Similarly, centrifugal
forces during rotation distort the equilibrium distances between atoms, which affects its vibrations.
This coupling between rotational and vibrational energy leads to rich rovibrational energy levelstructures within molecules. While Stark decelerated molecules remain in the rovibrational groundstate, the excited state vibrational and rotational energy levels are important for state-selective
detection of these molecules.
The Schrödinger equation for even the simplest molecule, two protons and an electron, cannot
be solved analytically. To allow for analytical solutions, the Born-Oppenheimer approximation
is made, which allows the electronic and nuclear motions to be decoupled and separated. Thisapproximation is based on the relative speeds of the nuclei compared to the electrons. Since themasses of the nuclei are much greater than the masses of the electrons, the approximation assumes
that the electrons instantly adapt to changes in the position of the nuclei. The molecular wave

56
function, Ψmol , can then be separated into electronic and nuclear components|Ψmol i = |Ψelec i |Ψnuc i .

(3.1)

This solution has a total energy given by Emol = Eelec + Enuc .
The Hamiltonian for the molecule can now be considered to have separate electronic andnuclear components. An additional relativistic component is not considered here, but can be treated
perturbatively. The electronic wave functions can be solved for different nuclear configurations.
The nuclear component can be additionally divided into motion about the equilibrium position(vibrations) and motion about the center of mass (rotations). This results in the Hamiltonian
Hmol = Helec + Hnuc ,Hmol = Helec + Hvib + Hrot ,(3.2)

where the energy of the molecule is give by Emol = Eelec + Evib + Erot . For the most part, theseenergies occur on different scales. The electronic energy levels are the largest and have energy
separations that occur in the visible or ultraviolet region of the electromagnetic spectrum. The
vibrational energy-level spacings are typically found in the infrared region, and rotational energylevel spacing are in the microwave region.
Electronic states of molecules have spectroscopic term symbols just like those of atoms. They
are dependent on the symmetry of the molecule and how the many sources of angular momentum
couple together. Only after analyzing the many angular momentum terms can the term symbols
and selections rules be determined. For diatomic molecules, molecular term symbols are written
as 2S+1 ΛΩ , where 2S + 1 is the spin multiplicity. Λ is the projection of the total orbital angularmomentum on the internuclear axis. Λ takes on the values of 0, 1, 2... which correspond with theupper case Greek letters Σ, Π, and ∆ respectively. Typically, the lowest electronic state is labeledwith the letter X and subsequent energy levels are labeled using A, B, C,..., with A being the firstexcited state above the ground state. If the molecule has states with different spin multiplicity,
those states are labeled using lower case letters (a, b, c,...) in order to differentiate them from thosethat can be accessed from the ground state by an electric dipole transition.

57
For the Stark deceleration experiment discussed here only the ground rovibrational states
are significantly populated. Here, we present a quick discussion of rotational states in molecules,
which is primarily based on [156], and the rotational states of ammonia and OH in the groundstate, which will aid in selecting a good detection scheme for these molecules.

3.0.1

Rotational states

To first order, we consider the molecule to be rigid. The moment of inertia of a rigid system
about an axis q isIq =X

mi (ri (q))2 ,

(3.3)

i

where mi is the mass of each atom and ri (q) is the distance of the atom to the axis q. Since weare considering a rigid system, the classical kinetic energy of a rotating body can be used, and theenergy of the system is
E=

1X
1 X Jq 2
Iq ωq 2 =,2 q
2 q Iq(3.4)

where ωq is the angular frequency and Jq is the angular momentum about the axis q. This leads
to the Hamiltonian for rotational energy in Cartesian coordinates to be
H=

Jy 2
Jx 2
Jz 2
+
+
.
2Ix 2 2Iy 2 2Iz 2(3.5)

In order to determine good quantum numbers for the rotational states of a molecule, Equation
3.5 can be simplified based on the symmetries of the molecule of interest. Ammonia is a symmetric
top molecule so two of the moments of inertia are identical, and Equation 3.5 becomesJx 2 + Jy 2 Jz 2
+
2I⊥
2Ik


J2
1
1
+
−
Jz 2 ,=
2I⊥
2Ik 2I⊥H=(3.6)

where the total angular momentum has been re-expressed using J 2 = Jx 2 + Jy 2 + Jz 2 . We now
recall that the eigenvalues of the J 2 operator are J(J + 1)~ and those of Jz are m~; however, inthe case of molecules, the quantum number K is used instead of m, since M is reserved for the
projection of J onto the laboratory frame. The good quantum numbers are now:58
• J = 0, 1, 2...
• K = −J, −J + 1, ..., J − 1, J
• M = −J, −J + 1, ..., J − 1, J.
Due to the cylindrical symmetry of a symmetric rotor, the molecule’s rotational energy depends
on only the magnitude of K and thus K may be specified as K = 0, 1, ..., J. This comes aboutbecause of the Jz 2 term in Equation 3.6.
Rearranging Equation 3.6 gives
 Jz 21J 2 − Jz 2 +
2I⊥
2Ik

= B0 J 2 − Jz 2 + A0 Jz 2

H=

= B0 J 2 + (A0 − B0 ) Jz 2 ,(3.7)

where the constants A0 and B0 are rotational constants specified by
A0 =

1
1
.
andB0 =
2Ik
2I⊥

(3.8)

The energy of the rotational states are then specified by
E(J, K) = B0 J(J + 1) + (A0 − B0 )K 2 .

(3.9)

Here, M has not played a role, but it will once an electric field is applied.
OH, on the other hand, is a linear rotor. In the case of a linear rotor the angular momentum
vector is perpendicular to the internuclear axis, which results in A0 = 0 and K=0. The rotationalenergies for the field free linear rotor are specified by
E(J) = B0 J(J + 1).

(3.10)

With this understanding of rotational structure, we now examine the rotational levels of
the two molecules of interest and how the ground rovibrational energy behaves in the presence ofelectric fields.

59
Table 3.1: Properties of ND3
N-D bond length
Pyramid equilibrium height
Umbrella angle
Electric dipole moment (µe )3.11.02 Å
0.38 Å
68◦
1.48 Debye [161]Ammonia
Ammonia has been widely studied because of its of its symmetry and importance in agricul-

ture and astronomy [157–159]. In particular, it is a useful tool for examining temperatures anddensities in the interstellar medium [160]. Ammonia is often used in Stark deceleration experiments
due to its ease of implementation, large electric dipole moment, low mass, and stability at room
temperature and pressure. This is unlike OH and NH, radicals that are also used in decelerator
experiments, which must be created in situ using discharge plate. Additionally, ammonia can bequantum state selectively detected using only one laser wavelength, which makes detection straightforward to implement. Both deuterated ammonia (ND3 ) and regular ammonia (NH3 ) are used for
Stark deceleration. However, ND3 , is more commonly used because of its smaller inversion splitting, which leads to a larger Stark shift at a given electric field. Here, when we refer to ammonia,
we will be discussing ND3 unless otherwise noted.
Ammonia is a polyatomic symmetric top molecule. It has trigonal pyramidal structure with
the nitrogen at the peak of the of the pyramid and three hydrogens that form the base. Table 3.1
gives some basis properties of deuterated ammonia. An inversion splitting arises from the nitrogen
atom tunneling through the plane of the three hydrogen atoms. This gives Ammonia a double
well potential energy surface. Although inversion is a type of vibration, it occurs in the microwave
regime at a scale even smaller than those of rotations.
An additional symmetry results from the symmetric or asymmetric exchange of the threeidentical nuclei. In the ortho state, K is a multiple of three, while in the para state, K is not a
multiple of three. Conversion between the ortho and para states is not common since the nuclear
spin does not couple to the molecular rotation.

60
Figure 3.1 shows the rotational energy levels of the electronic and vibrational ground statewith the J, K and ortho/para structure labeled. The ground state of ammonia has the term symbol0X̃ 1 A 1 .

Figure 3.1: The rotational levels of ND3 in the electronic and vibrational ground state. The J value
is labeled on top of each state and they are sorted by K, which dictates ortho and para ladders.
The inversion splitting on each rotational level is not shown. This figure is taken from Figure 2.6
in [95].

3.1.1

Stark effect in ND3With no external electric fields, the ground state ND3 does not have a permanent electric
dipole moment. As the molecule undergoes inversion, the effective dipole moment cancels out. It
is only when an external electric field is applied that an electric dipole moment is induced. Sinceammonia is a symmetric top molecule, its Stark shift, Ustark , in a DC electric field is given by [162]

 s

∆Uinv
∆Uinv 2
MK 2
Ustark = ∓±+ µE,(3.11)2
2
J(J + 1)
where ∆Uinv is the inversion splitting, µ is the electric dipole moment, and E is the magnitudeof the electric field. J, K, and M note the rotational state. Now that an external field has been
applied, M , the projection of J on to the electric field, plays a role. The signs in Equation 3.11
correspond to the dipole moment being anti-aligned (top) or aligned (bottom) with the electricfield. This results in the Stark energy increasing (decreasing) with the magnitude of the electricfield, which leads to weak-filed-seeking (strong-field-seeking) states. The Stark shift is quadratic

61
at weak electric fields strengths, but becomes linear at high electric field strengths. Figure 3.2
shows the Stark shift for both ND3 and NH3 in the J=1, K=1 ground state. Here the affect of
the inversion splitting between ND3 and NH3 becomes apparent. The inversion splitting, ∆Uinv ,is 0.79 cm−1 for NH3 and 0.053 cm−1 for ND3 . The smaller inversion splitting for ND3 leads to alarger Stark shift, and explains why it is used more often for Stark deceleration experiments. Moreenergy can be removed from ND3 than NH3 for the same electric field and thus lower electric fields
can be used overall.

Figure 3.2: The Stark energy as a function of electric field for ND3 and NH3 in the J=1, K=1 state.
This figure is adapted from Figure 2.7 in [95].

3.1.2

ND3 REMPIThe ionization potential of ND3 is 10.07 eV, so it can be ionized with one VUV photon, butthat process would not be state selective. In laboratory experiments, state-selective detection of
ND3 is commonly done using a 2+1 REMPI scheme, with one laser at 317 nm [163–166]. A 3+1
REMPI scheme for ammonia has also been demonstrated [167], but is not as commonly used. The
2+1 scheme is convenient because it requires only one laser wavelength, which can be produced
by a doubled dye laser, at 317 nm. Figure 3.3 depicts the states used in this detection scheme.
Ammonia starting in the upper inversion doublet (the one that is weak-field-seeking and can be
Stark decelerated) is excited to the intermediate B̃ 1 E ” , v2 = 5 Rydberg state state via two 317 nm

62photons. There are several allowed ionization pathways from different rotational levels that can be0

used in the B̃ 1 E ” ← X̃ 1 A1 transition [168]. The B̃ 1 E ” state is planar and thus does not have an
inversion splitting. From here, ND3 can then be ionized with an additional 317 nm photon.

Figure 3.3: The 2+1 REMPI scheme for detecting ND3 .

3.2

OH
OH is an important radical in atmospheric and environmentally relevant reactions [169, 170].

It also an interesting molecule in crossed electric and magnetic fields since it has both an electric
dipole moment (1.67 Debye) and a magnetic dipole moment (2µb , where µb is the Bohr magneton).
Since OH is a diatomic molecule, before we discuss the OH structure, it is useful to review Hund’s
coupling cases, which categorizations of how the idealized electronic and orbital angular momentaof diatomic molecules couple together

3.2.1

Hund’s Coupling Cases

Determining the Hund’s case for a given electronic state will help guide what quantum numbers are best suited for the given state of the molecule. There are typically five cases (a)-(e), but

63even then these do not describe all situations. For example, OH in strong electric and magnetic
fields is describe by a “Hund’s case (x)” [171]. Here we will discuss cases (a) and (b), which are
the two most common cases.
There are four sources of angular momentum in a molecules: the spin of the electrons (S),the electronic orbital angular momentum (L), the rotation of the nuclei (R), and the nuclear spin(I). The total angular momentum, not including I, is J. If the nuclear spin is included, the total
angular momentum is F. However, nuclear hyperfine effects resulting from the coupling of thenuclear spin with the magnetic field from another angular momentum component is very small andnot considered here. A summary of the angular momentum vectors is:• L is the electronic orbital angular momentum• Λ is the component of L along the internuclear axis
• S is the electronic spin angular momentum• Σ is the component of S along the internuclear axis
• J is the total angular momentum• Ω is the vector sum of L and S along the internuclear axis
• K is the vector sum of Λ and N• N is the total angular momentum but not including the electron spin, N = J − S• R is the rotational angular momentum of the nuclei, R = N − L.
In Hund’s case (a), the electronic state has large spin-orbit coupling and a strong electrostatic
coupling of L to the internuclear axis. As a result of the spin-orbit coupling, S is also strongly
coupled to the internuclear axis. This makes Ω = Λ + Σ a good quantum numbers for this case.
The good quantum number for this case are Ω, Σ, Ω, and J. 2 Π is a typical Hund’s case (a) state.
In Hund’s case (b), the spin-orbit coupling is weak. The orbital angular momentum still
couples to the internuclear axis but the spin does not. Instead, R, the rotational angular momentum

64of the nuclei, couples to the internuclear axis giving R + L = N. In this case, the total angularmomentum J is given by the sum of N + S. 2 Σ states and 2 Π states with large J are typical Hund’scase (b) states.

3.2.2

OH structure

OH is a low mass, open shell radical with a strong electric and magnetic dipole moments. It
has a large rotational constant, which results from the small moment of inertia. The 2 Π3/2 groundstate has non-negligible mixing with the spin-orbit split 2 Π1/2 state. A small (∼1.7 GHz) Λ-doublet
splitting that arises from the coupling of the angular momentum projection Λ and nuclear rotationof excited electronic states. Similar to the case in ammonia, the vibrational levels of the electronic
ground state of OH are too large to be significantly populated at the temperatures in the supersonic
expansion use in these experiments. Thus, we are concerned primarily with rotational splittingsand spin-orbit coupling within the ground state.
The molecular orbitals for ground state OH is(1sσ)2 (2sσ)2 (2pσ)2 (2pπ)3 .

(3.12)OH is an open shell radical since its highest occupied molecular orbital is not completely filled.
The spin and orbital angular momentum of this unpaired electron will dictate the properties of theelectronic ground state of the molecule. In the ground state, the valence electron is in a π orbital,so Λ = ±1 and Σ = ±1/2, and the electronic grounds state of the OH molecule is 2 Π3/2 . The 2 Πelectronic ground state of OH is primarily Hund’s case (a). In the first excited state, a 2pσ electron
is promoted to the 2pπ state giving the electron configuration of(1sσ)2 (2sσ)2 (2pσ)1 (2pπ)4 .

(3.13)The lone σ electron has λ = 0 and no projection on the internuclear axis. This results in the firstelectronic excited state having Σ character and is best described by Hund’s case (b).
Good quantum numbers for the ground state Hund’s case (a) state are Λ, Σ, Ω, J, Mj , and. Ω is the vector sum of L and S and thus can have the values ± 32 and ± 12 . The total angular65
momentum is J=3/2. Ω =| Ω | which gives the two spin-orbit split manifolds of 2 Π3/2 and 2 Π1/2 .
 is the symmetry of the state and can either be positive or negative, it is typically denoted using
either e ( = +1) or f ( = −1). λ-doubling breaks the degeneracy of the rotation about theinternuclear axis. Lastly, there is one more quantum number P, the parity of each state. P arises
because diatomic molecules posses reflection symmetry. This leads to P = ±1 as good quantum
numbers where P = +1 is for an even function under spatial inversion and P = −1 is for an oddfunction under spatial inversion.
For the 2 Π3/2 rovibration ground state the λ-doublet splitting is ∆ ≈ 1.667 GHz (0.0556
cm−1 . The rovibration ground state of OH is J = 23 ,  = e and the J = 23 ,  = f state lies ∆ above
it. Figure 3.4 shows the rotational structure in the electronic and vibrational ground state of OH.

Figure 3.4: The rotational structure in the electronic and vibrational ground state of OH. The
λ-doublet splitting has been exaggerated for clarity. P is the parity of each states.

3.2.3

OH in electric fields

The Stark shift in OH (similar to Equation 3.11) is  s 2
M Ωef f 2
∆
∆
±
+ µE
.
Ustark = ∓22
J(J + 1)

(3.14)

A detailed derivation starting from the Hamiltonian for the Stark energy in the fixed lab frame
and including a transformation between the fields in the labortory frame and the dipole moment

66
in the molecule frame can be found in [155]. A plot of the stark shift for the J = 3/2 rovibrational
ground state is shown in Figure 3.5. A further discussion of OH in crossed electric and magnetic
fields and 1+1’ REMPI detection of OH can be found in Chapter 6.

Figure 3.5: The Stark splitting in OH.

Chapter 4

Pulsed Ring Stark Deceleration

Pulsed ring Stark deceleration combines the cylindrical symmetry of TWSD and the relativeelectronic simplicity of PPSD. Its discrete voltages make it easier to implement than the analog
high-voltage amplifiers required for TWSD. Although TWSD is the “premier” Stark deceleration
technique because of its continuous nature, in certain situations PRSD is more efficient than TWSD
due to an increased longitudinal potential gradient. This is particularly important when there is alimit on the maximum voltage that can be used on the electrodes or on the length of the decelerator.
In this chapter, we present an experimental realization of a ring-geometry Stark decelerator
using both continuously varying (TWSD) and discrete voltages (PRSD). Using the pulsed-ring
method, we demonstrate a newly accessible low velocity regime for moderate peak voltages on thering electrodes. A comparison of experimental and simulated results between traveling-wave andpulsed-ring Stark deceleration is presented along with a simple model for determining when eachmode is more efficient. Section 4.1 of this chapter is adapted from [172] and some material maybe areview of what has already been discussed. The following sections provide a more in depth analysis
of how to implement PRSD and the transverse dynamics of the Stark potential well.

4.1

Pulsed-Ring versus traveling-wave Stark deceleration

4.1.1

Introduction

Stark deceleration uses spatially inhomogeneous and time-varying electric fields to decelerate
neutral polar molecules, and produces a beam of slow molecules with a tunable average final

68
velocity. These beams can be used for high-resolution spectroscopy [99], collision physics [100],
measuring radiative lifetimes of molecules [101,102], and tests of fundamental physics [10,104,105].
The molecules from a Stark decelerator can also be loaded into electrostatic [84–86], magnetic[87, 88], and ac traps [89–91], or used in crossed beam [75–78], beam-trap [92, 93], and co-trapped
experiments [94]. Such experiments are often limited by the number of successfully decelerated
molecules. Improvements to the decelerator efficiency, the percentage of molecules in the initial
pulse that are successfully decelerated, would benefit these types of studies.
The first Stark decelerator, referred to in this paper as the pulsed-pin Stark decelerator(PPSD), was constructed in 1999 by Bethlem et al. [107]. It used high-voltage switches to alternate
between two static voltage configurations on pairs of crossed pin electrodes. Switching between thesevoltage configurations produces a discretely moving Stark potential well to decelerate molecules.
Molecules only within a range of positions and velocities will be decelerated. This portion of phasespace is called the phase-space acceptance. Ideally, it would be well filled with molecules. PPSD has
well-characterized instabilities and loss mechanisms that are enhanced at low final velocities [139].
Particularly, coupling between the longitudinal and transverse motion leads to unstable regions
within the phase-space acceptance. The decrease in phase-space acceptance drastically reduces theefficiency when decelerating to low velocities required for trapping, or when spending long times atvelocities <100 m/s in the decelerator. Although different timing schemes and operating modes canimprove the performance of the traditional Stark decelerator [117–119], the crossed-pin electrodegeometry fundamentally limits the efficiency due to longitudinal and transverse coupling.
The loss present in pin decelerators can be mitigated by using ring-shaped electrodes and afundamentally different mode of applying voltages to the electrodes: chirped sinusoidally varying
voltages. This produces a traveling-wave potential well that continuously guides or decelerates
the molecular beam, as opposed the pulsed nature of PPSD. Traveling-wave Stark deceleration(TWSD) has two characteristic differences compared to PPSD: the cylindrically symmetric electrode geometry and continuously, as opposed to discretely, varying voltages, which produce a
genuine moving potential well. This leads to an inherently stable deceleration process that has

69a true three-dimensional (3D) trapping potential and a well-filled phase-space acceptance. These
factors allow for more efficient deceleration due to the continuous and cylindrically symmetricnature of this deceleration mode. Meek et al. [132] first demonstrated the idea for spatially modulated potential wells on a microstructured chip used to guide and then decelerate metastable
CO molecules [133, 134]. The first use of macroscopic traveling-wave Stark potentials with a ringgeometry decelerator was experimentally shown in 2010 by Osterwalder et al. [121] using a beamof CO, which was decelerated from 288 m/s to 144 m/s.
While TWSD has many advantages, it is more challenging to implement than PPSD because
it requires high-voltage analog amplifiers with demanding specifications to generate the moving
Stark potential wells. The sinusoidal voltage must have an initial frequency such that the Stark
potential well containing the molecules moves with the same initial velocity as the molecular beam.
The frequency of the sinusoidal voltages then must be smoothly chirped down to a frequency suchthat the velocity of the Stark potential well formed by the voltages matches the desired final beam
velocity. Thus, the amplifiers require a large bandwidth to decelerate a typical molecular beam torest. The chirp rate of the sinusoidal voltage will be determined by the initial and final velocities
and the length of the decelerator. For a fixed ring geometry, the magnitude of the maximum
allowable deceleration is set by the bandwidth of the high-voltage amplifiers, maximum output
voltage of the high-voltage amplifiers, and length of the decelerator.
Early TWSD experiments were limited by the lack of availability of high-voltage amplifierswith a large bandwidth. The amplifiers used to generate the voltages for the electrodes in the first
TWSD experiment operated at ±8-10 kV with 10-30 kHz sinusoidal voltages [121,122]. The limited
bandwidth of the amplifiers meant that the decelerator could achieve only moderate decelerationand the molecules could not be brought to rest. Commercial amplifiers (Trek 5/80), which arecapable of a larger frequency range (0-60 kHz) and outputs up to ±5 kV, make it possible todecelerate a supersonic beam down to rest with a decelerator that is several meters long. For
example, a beam of SrF seeded in Xe with an initial velocity of 290 m/s would require a ∼5
m long decelerator [123]. Amplifiers with slightly limited maximum voltages, such as these, are70particularly useful for TWSD of heavy molecules used in precision measurements, since the electricfields produced are low enough to keep the molecules in the weak-field seeking regime, where the
Stark energy increases with increasing electric field [124]. To date, YbF [125] and SrF [123] havebeen decelerated using TWSD and the longest demonstrated decelerator (4 m) slowed SrF from
290 to 120 m/s using ±5 kV amplifiers [126].
To overcome the limitations of PPSD and the demanding amplifier specification of TWSD,
a combination of both Stark deceleration methods can be used. In this combination technique,a pulsed-pin Stark decelerator decelerates molecules to longitudinal velocities around 100 m/s,
and then a traveling-wave Stark decelerator decelerates the molecules to rest [127]. This scheme
is able to take advantage of the cylindrical symmetry of the ring geometry at low velocities toavoid the low velocity losses of the pulsed-pin Stark decelerator, but it relaxes the requirement tohave either extremely high maximum voltages or a very long decelerator to reach electrostaticallytrappable conditions. Using this combination technique, NH3 /ND3 and CH3 F have been trapped,
manipulated, and adiabatically cooled within the ring decelerator [127–130].
Complete TWSD of a supersonic beam moving at 300-450 m/s to rest has been challenging
to achieve due to electronic and hardware requirements. An alternative running mode for operating
a ring-geometry decelerator has been proposed by Hou et al. [141], and uses pulsed voltages on ring
electrodes. The duration of the pulses is varied in an identical manner to that of PPSD. This pulsedring Stark deceleration (PRSD) method takes advantage of the cylindrical symmetry provided by
the rings and is simpler to implement than TWSD, since it uses commercial high-voltage switches
instead of high-voltage analog amplifiers. In this paper, we present experimental results of thisnew PRSD scheme in comparison with TWSD, examine conditions where it is advantageous to run
PRSD over TWSD, and discuss a simple method for determining which mode is preferable basedon the desired final molecule packet properties.

71
4.1.2

Experiment

The experimental setup for demonstrating both deceleration modes is shown in Fig. 4.1.
Both experiments begin with a piezoelectric-actuated pulsed valve that creates a pulsed supersonicbeam of 2% fully deuterated ammonia (ND3 ) in krypton. A skimmer ∼20 cm downstream ofthe valve collimates the molecular beam and allows for differential pumping between the sourceand decelerator chambers. The decelerator begins 3 mm behind the skimmer, and consists of 624
rings mounted in eight longitudinal stainless steel rods such that every eighth ring is electricallyconnected (similar to [121]). Each ring is made of 1.02 mm diameter tantalum wire, and has a
4 mm inner diameter and center-to-center spacing of l, which for the decelerator discussed hereis l = 2.03 mm. The full decelerator is just over 1.25 meters long. For the work presented here,
ND3 molecules are decelerated from 415 m/s down to final velocities of 220 m/s for TWSD and
150 m/s for PRSD. ND3 molecules at the end of the decelerator are ionized in a 2+1 REMPI
scheme using 317 nm photons [166]. Two stainless steel plates, which are electrically isolated fromthe decelerator, are mounted after the rings. They form the time-of-flight mass spectrometer andaccelerate ionized molecules into the microchannel plate detector, where the measured current is
proportional to the number of ionized molecules.

Figure 4.1: A schematic of the experimental setup which includes, from left to right, a pulsed
valve, skimmer, ring decelerator, time-of-flight mass spectrometer (TOF-MS), detection laser, andmicrochannel plate detector (MCP). Not all decelerator rings are depicted. The full decelerator
contains 624 rings. The longitudinal stainless steel mounting rods are also not shown. The entire
system is contained inside a differentially pumped vacuum chamber.

72
The voltage sequences for the two declaration modes create longitudinal potential wells withdifferent ring periodicities and gradients. In the work presented here, both modes of deceleration use
maximum voltages of ±7 kV on the electrodes. PRSD uses four commercial high-voltage switches
and TWSD uses eight custom home-made high-voltage amplifiers. Figure 4.2 shows a longitudinalcross section of the ring decelerator in the upper panel and the longitudinal Stark potential for
ND3 for each deceleration mode in the lower panel. The rings are labeled with their rod number,n, from zero through seven. The instantaneous voltages that create the given longitudinal Stark
potentials are listed in the table at the top. The left most and right most rings, n = 4, areelectrically connected, and the voltage and Stark potential pattern is repeated down the length ofthe decelerator.
The pulsed mode naturally creates wells with greater gradients, which allows it to be more
efficient in certain circumstances. While a pulsed-ring configuration with the same well periodicity
and gradients as TWSD could be configured, it would be less efficient than the pulsed version
presented here. Such a configuration would use the same instantaneous voltages as listed for VTWSDin Fig. 4.2 and create the same instantaneous potentials. The bottom of the Stark potential wellwould shift by two rings each time and there would only be half the number of switching stages.
This reduction in deceleration stages, along with the reduced gradient, greatly diminishes thedecelerating capabilities of such a configuration and thus it is not used here.

4.1.2.1

Deceleration Modes

For the PRSD configuration, each rod is connected to one of four Behlke HTS 201-03-GSMHFB high-voltage switches. These switches are used to produce two voltage configurations thatalternate in time. The two voltage configurations produce two Stark potential well configurations,one of which is depicted in the bottom panel of Fig. 4.2. A detailed description of the electrodeand voltage configuration can be found in [141]. The time interval between switching from one
configuration to another is dictated by the velocity of the molecular beam. These voltages produce
an on-axis longitudinal Stark potential with the bottom of the well shifted by l between the two

4

5

6

7

0

1

2

3

4

VPRSD (kV)

0

7

0

-7

0

7

0

-7

0

VTWSD (kV)

0

-4.9

-7

-4.9

0

4.9

7

4.9

0

Longitudinal potential (K)y (mm)

Ring (n)

73

4
2
0
-2
-4
0.4
0.3
0.2
0.1
0

TW
PR

-8

-6

-4

-2

0

2

4

6

8

z (mm)
Figure 4.2: Ring number, applied voltages, positions of electrodes, and longitudinal Stark potentials of ND3 in units of Kelvin. The table and top panel show the ring number n and instantaneousvoltages for both deceleration modes plotted below and the longitudinal cross section of the decelerator rings. The bottom panel shows the TWSD and PRSD Stark potentials along the center
axis of the ring decelerator. Both Stark potentials are shown at a time when the bottom of thepotential well is centered at a ring.

configurations, similar to the pin decelerator. The timing sequence for switching the voltages on
the electrodes is calculated in a similar fashion, using phase angles, as that of a pulsed-pin Stark
decelerator [114].
For the TWSD configuration, eight analog high-voltage amplifiers are used, one for each rod.
These supply the rings with chirped sine wave voltages, which have a fixed phase offset relative
to one another. The amplifiers (gain = 12,000) are driven by an arbitrary waveform generator(GaGe CompuGen 8152). The high-voltage linear amplifiers used in this work were designed andconstructed in-house. They were tested up to ±10 kV and in the frequency range of 1-30 kHz on
the bench, but were operated at ±7kV and in the frequency range of 13-25.5 kHz for this work.
These specifications correspond to a molecular beam with velocities from 415 m/s down to 210

74m/s. While the amplifiers have a bandwidth of 30 kHz down to DC, the full bandwidth was not
utilized since the lower maximum voltage on the rings results in a shallower molecule trap. The
set length of our decelerator and this shallower trap did not allow for deceleration down to rest forthis particular experiment. However, with ±10kV outputs from the amplifiers, the ND3 moleculeswith an initial velocity of 415 m/s could be brought to rest.
Each amplifier applies the chirped sine wave voltage Vn , for a given rod n, ofVn (t) = Va sin

2πn 2π
−
8
8l



1 2
vi t − at
,
2

(4.1)

where Va is the maximum output voltage, vi is the initial velocity of the molecular beam, a is theacceleration applied by the decelerator, and the 2πn8 term is the phase shift between rods. The
acceleration is given bya=vf2 − vi2
2L

,

(4.2)

where vf is the final velocity of the molecular beam and L is the overall length of the decelerator.
It is important to note that one period of the sine wave extends over eight ring electrodes andcorresponds to two Stark potential wells (see Fig. 4.2). This results from the Stark potential
energy depending on the magnitude of the electric field and not the direction.

4.1.3

Simple model of deceleration

The Stark potential wells for each deceleration method give a basic picture into whichmolecules within the initial phase space can be decelerated. Figure 4.3 shows the transverse potentials for both TWSD and PRSD for the voltage configuration in Fig. 4.2 taken at z=0 mm, thebottom of the longitudinal well for both modes. The transverse potential is identical in the x andy directions due to the cylindrical symmetry of the decelerator. The lower panel of Fig. 4.2 andFig. 4.3 show that for the same peak voltage PRSD has a larger potential well gradient in boththe longitudinal and transverse directions due to the reduced ring periodicity of the configuration.
The larger potential well gradient is particularly important in the longitudinal direction. To
predict which molecules will be successfully decelerated (i.e. within the phase-space acceptance),

75
1

Transverse potential (K)

TWSD
PRSD

0.8

0.6

0.4

0.2

0
-2

-1

0

1

2

x (mm)

Figure 4.3: The instantaneous TWSD and PRSD transverse Stark potentials in the x-direction for
the voltage configuration in Fig. 4.2 and at z=0 mm.

we consider the effects of the acceleration on the Stark potential well. Deceleration of the Stark
potential well is the equivalent of adding a fictitious potential Uf = maz to the longitudinal Stark
potential in Fig. 4.2, where m is the mass of the molecule and z is the longitudinal distance fromthe center of the Stark potential well. For both modes, the average acceleration is determined
only by decelerator length, vi , and vf . The acceleration is applied constantly in TWSD, but istime-averaged in PRSD, where instantaneous accelerations are higher. Fig. 4.4 shows the central
TWSD and PRSD Stark potential wells from Fig. 4.2 with an acceleration of 0 km/s2 , -32.5 km/s2 ,and -47.1 km/s2 added to the Stark potential. For a beam with vi =415 m/s, this corresponds
to vf =415 m/s, vf =300 m/s and vf =230 m/s respectively. This additional fictitious potential
lowers the downstream potential well wall since a is negative, and the effect is referred to as thepotential well tilt. (The tilt model of a Stark decelerator is discussed more in depth in [173].) As
a increases, the well tips over more and cannot contain and decelerate as many molecules. An
acceleration of -47.1 km/s2 shows how the TWSD Stark potential well is aggressively tilted to thepoint of almost having no trap depth. Too much acceleration, and thus too much tilt, leads to asmall phase-space acceptance and deceleration efficiency.

76

0.8
415 m/s, 0 km/s2
300 m/s, -32.4 km/s 2

Longitudinal potential (K)0.6

230 m/s, -47.1 km/s 2

0.4
0.2
0

PRSD
-4

-2

0

2

4

0

2

4

0.6
0.4
0.2
0

TWSD
-4

-2

z (mm)

Figure 4.4: The PRSD (top) and TWSD (bottom) Stark potential wells with applied linear fictitious
potentials for a = 0 km/s2 (solid), a = −32.5 km/s2 (dashed), and a = −47.1 km/s2 (dot dashed).
For a beam with vi =415 m/s, this corresponds to vf =300 m/s and vf =230 m/s respectively.

For either mode, too large of an acceleration means no molecules are phase stable inside the
Stark potential well. The maximum acceleration where the phase-space acceptance is finite is set
by the gradient and height of the Stark potential well. A larger Stark potential gradient allows formore acceleration before the well can no longer hold molecules. In Fig. 4.4 for a =-47.1 km/s2 ,PRSD still has significant well depth, while TWSD has almost none. This is because PRSD has alarger Stark potential gradient. The Stark potential well gradient is set by the deceleration modeand physical decelerator geometry. Decelerating to low final velocities requires either a low initial
velocity, which is set by the gas used in the supersonic expansion, or a long decelerator. For thesame Va on the electrodes, the pulsed configuration produces a Stark potential well with a larger
gradient in both the longitudinal and transverse directions and a smaller volume because the wellonly spans 2l while the traveling-wave well spans 4l. This allows the PRSD well to tilt more andbe stable at larger accelerations than the TWSD well even though it has a smaller volume.

77
4.1.4

Simulations

In addition to experimental results, we use Monte Carlo simulations to help interpret andillustrate the differences between the two operating modes. These semi-classical molecular trajectory simulations allow us to explore a wide parameter space that is not yet accessible in the current
experimental setup. The simulation starts by creating a packet of molecules at the location of thepulsed valve. The molecules have a Gaussian distribution of initial positions and velocities. The
molecular packet is allowed to propagate through a region with no electric field to the entrance ofthe decelerator. Once the molecules enter the decelerator, their trajectories are determined using a
3D matrix of accelerations derived from Stark potentials modeled by the commercial finite element
solver COMSOL. Once the packet of molecules reaches the end of the decelerator both the phasespace distribution (observation at a set time) and the time-of-flight information (observation at a
set z-position) are recorded.
Typical initial packets contain between 1 and 8 million molecules that are sampled from a
distribution that has full-width half maximum of ∆x = ∆y = 3 mm, ∆z = 30 mm, ∆Vx = ∆Vy = 5m/s, and ∆Vz = 30 m/s. This packet extends beyond the phase-space acceptance of the decelerator.
Since the Stark potential well shapes for both deceleration modes are spatially periodic, theelectric field models for determining the molecule accelerations inside the decelerator do not have tospan the entire length of the decelerator. Instead, a modular approach can be taken. The position
dependent molecular accelerations are calculated from electric field models for a unit cell of 3 (9)rings for PRSD (TWSD). Then, a shift of the longitudinal coordinates within the unit cell allows
for molecules to propagate along the decelerator without a model of the entire decelerator. The
number of position dependent 3D acceleration models required depends on the operating mode.
For PRSD, there are only two voltage configurations and the shape of the Stark potential well is thesame for both configurations, but shifted by l. Therefore, only one acceleration model is required
and is longitudinally shifted by l each time the high voltage is switched. For TWSD, there is acontinuum of voltage configurations corresponding to the sinusoidally varying voltages on the rods.

78This is modeled using 25 time steps between the peak of the sine wave being on rod n to the peak
being on the subsequent rod n + 1. Once the simulations have cycled through all 25 modeled time
steps the entire model is longitudinally shifted by l.

4.1.5
4.1.5.1

Experimental Results and Analysis
Deceleration at 7kV

We performed experimental measurements for both PRSD and TWSD at ±7 kV using the
setup described in Sec. 4.1.2 and compared them to simulations. All experiments use a molecularbeam with an initial velocity of 415 m/s. The beam was decelerated to various final velocities.
Figure 4.5 (4.6) shows PRSD (TWSD) signals for decelerated ND3 packets as a function of arrival
time for selected final velocities. Both figures have results from the simulated decelerated packets
on the top and the experimental data on the bottom. There are more decelerated peaks in eachpacket than shown, but, for clarity, only the central and a couple adjoining peaks are displayed.
Both figures have the same vertical scale. The arrival time between peaks in PRSD is more closely
spaced than in TWSD due to the well spanning only 2l instead of 4l. Since there is not enoughdeceleration to separate the decelerated packets completely from the initial pulse, the baselines ofthe signals are not zero and sit on top of the low velocity tail of the initial molecular beam.
With the same initial velocity, vi =415 m/s, and large accelerations such that vf <220 m/s,
TWSD no longer results in observable decelerated signal, but PRSD still produces clear peaks.
PRSD produces observable decelerated molecules down to vf =150 m/s. While TWSD produces
more decelerated ND3 than PRSD at vf >230 m/s, it does not produce clearly decelerated packets
over the same large velocity range as PRSD, and the amplitude of decelerated peaks decreases more
rapidly than in PRSD as the acceleration increases.
The simulations accurately predict the shape and arrival times of the experimental results.
While the amplitude of the experimental results and simulation are comparable at higher final
velocities (small acceleration), the experimental signal is lower than the simulation at lower final

79

1(-5 50
9. m
1 /s
km
/s 2
)

(-5 75
6 m
km /s
/s 2
)

4

2

4

1

2

(-4 40
5. m
3 /s
km
/s 2
)

2

(-5 00
2. m
2 /s
km
/s 2
)

(-3 80
7. m
1 /s
km
/s 2
)

ND3 signal (arb. units)3(-2 20
7. m
6 /s
km
/s 2
)

1

4

4
4
0

4

4.2

4.4

4.6

4.8

4
5

5.2

Time (ms)Figure 4.5: Time-of-flight traces of a molecular beam decelerated with PRSD from an initial velocityof 415 m/s down to the labeled final velocities using the indicated accelerations. The three slowest
packet signals have been multiplied by a factor of 4. The top row shows the results of the simulations
and the bottom row shows the experimental measurements. The results of the simulations havebeen vertically offset for clarity.

velocity (large acceleration). These deviations at large accelerations are likely due to imperfections
in electrode rings and voltages. This may arise from individual ring misalignment or, for TWSD,
deviations in amplifier output voltage from an ideal sine wave. While careful frequency tuning andcalibration can mitigate amplifier fluctuations, any imperfections add jitter to the Stark potential
well. At large accelerations, jitter may distort the already shallow Stark potential well to the pointthat many normally phase-stable molecules fall out. However, this would be less of a concern fora deeper potential well with less tilt such that imperfections in the well are small compared to thedownstream Stark potential well height of the tilted well.
We use the integrated signal above the baseline in the central peak of each packet to determineand quantify the trade-off between the two modes. The integrated signal for both experimental
and simulated results is shown in Fig. 4.7. The x-axis has been changed from final velocity toacceleration using Eq. (4.2), so that the results can be applied to different initial velocities. Now, the

80

0

2

ND3 signal (arb. units)(-4 60
1. m
3 /s
km
/s 2
)
24
(-4 0
5. m
3 /s
km
/s 2
23
(-4 0
)
7. m
1 /s
km
/s 2
)

3

(-3 00
2. m
5 /s
km
28
/s 2
(-3 0
)
7. m
1 /s
km
/s 2
)

1

2

2
2
2

4.1

4.2

4.3

4.4

4.5

4.6

Time (ms)Figure 4.6: Time-of-flight traces of a molecular beam decelerated with TWSD from an initial
velocity of 415 m/s down to the labeled final velocities using the indicated accelerations. The
two slowest packet signals have been multiplied by a factor of 2. The top row shows the resultsof simulations and the bottom row shows the experimental measurements. The results of thesimulations have been vertically offset for clarity.

trade-off between the two modes is clear. There is a cross-over point between the decelerated signals
in TWSD and PRSD. For low accelerations TWSD yields higher overall signal, but at accelerations
greater than -46 km/s2 PRSD yields higher signal. Additionally, PRSD has detectable decelerated
packets at accelerations above -50 km/s2 while TWSD does not. Therefore, if the desired result
is a very low velocity molecular beam, PRSD is preferable for this given electrode voltage andconfiguration.

4.1.5.2

Phase-Space Acceptance

Another method of examining the cross-over point between the two deceleration modes is to
examine the phase-space acceptance, the range of initial molecule positions and velocities that will81

1
PRSD Experiment
PRSD Simulation
TWSD Experiment
TWSD Simulaiton

ND3 signal (arb. units)

0.8

0.6

0.4

0.2

0

20

30

40

50

60

Acceleration (km/s2)

Figure 4.7: ND3 signal verses acceleration for both TWSD (yellow squares) and PRSD (blue triangles). The experimental measurements are given by individual points and the results from Monte
Carlo simulations by a line. The cross over from TWSD to PRSD producing more decelerated
molecule signal occurs near 46 km/s2 .

be decelerated. We define a cross-over point as the acceleration value where at higher accelerations
PRSD begins to produce more decelerated signal than TWSD. One-dimensional (1D) longitudinal (z-axis) phase-space boundary calculations, done in the same manor as [114], are useful for
determining the separatrix, which is the boundary between stable and unstable molecular orbits
in phase space. Figure 4.8 shows two-dimensional phase-space histograms of all molecules in thecentral decelerated peak and longitudinal phase-space separatricies for PRSD and TWSD aboveand below the cross-over point. The phase-space distribution has z = 0 as the entrance of thedecelerator. Only molecules from the initial distribution that are successfully decelerated and in
the central peak are plotted; all other molecules are not shown.
Both modes of deceleration have well-filled phase spaces in both the longitudinal and transverse directions, which differs from the structured phase spaces that are seen in PPSD [117, 139].
Thus, the trade off in total decelerated signal comes from the change in phase-space area and notphase-space filling. From a final velocity of 320 m/s to 200 m/s the phase-space acceptance area of
TWSD decreases significantly more than in PRSD. This is due to the significant decrease in Stark

82
potential well depth from tipping due to the acceleration. While the longitudinal phase-space acceptance captures the phase-space boundary of the decelerated molecules, the area of the phasespace does not accurately model the efficiency of the deceleration at different final velocities. Even
a 3D phase-space volume calculation fails to model the rate of decrease in experimental signal withincreased acceleration. This is because the total number of successfully decelerated molecules isdetermined by the overlap of the phase-space acceptance with the initial distribution of molecules.
To account for the initial distribution of the beam, the deceleration efficiency should be computed
using Monte Carlo simulations.
430

TWSD

-27.6 km/s 2 TWSD
320 m/s-52.2 km/s 2
200 m/s

PRSD-27.6 km/s 2 PRSD
320 m/s-52.2 km/s 2
200 m/s

-2

2

2

1

410
400
420

ND3 density (arb. units)z velocity (m/s)

420

410
400

0

0

4

-2

0

4

z position (mm)Figure 4.8: Longitudinal phase-space plots with TWSD in the top row and PRSD in the bottom
row. The left column has an acceleration of -27.6 km/s2 and the right column has an accelerationof -52.2 km/s2 . For an initial velocity of 415 m/s, this would be a final velocity of 320 m/s and 200
m/s respectively. The solid-red lines are the 1-dimensional separatricies. There is no significant
structure in the phase-space acceptance in either deceleration mode.

4.1.5.3

Determining the Optimal Deceleration Mode

When using decelerated molecules in an experiment, the deceleration mode would ideally bechosen to have the maximum decelerated signal for a given final velocity. This may not always be
an option due to hardware constraints. However, even if the choice is available, it is not always
clear which mode is more efficient. The trade-off between the two deceleration modes is especially83
relevant given experimental limitations of a given decelerator. To determine which mode is best
to use, different voltage regimes were explored using simulations. The same decelerator geometry
as previously described was used while changing the peak voltage in both modes. Results of thesestudies are shown in Fig. 4.9 for 5, 7, and 9 kV. A crossing point where TWSD and PRSD produce
the same signal exists for these voltages and occurs at a larger acceleration for greater electrodevoltages.
1
7kV

5kV

9kV

PRSD
TWSD

ND3 signal (arb. units)

0.8

0.6

5kV

9kV

7kV
0.4

0.2

0

20

30

40

50

60

70

Acceleration (km/s2)

Figure 4.9: Simulated integrated ND3 signal verses acceleration for both TWSD (squares) and
PRSD (triangles) with peak voltages of 5, 7, and 9 kV. A crossing point exists for all voltages
shown.

Generally, TWSD is more efficient for mild accelerations, but for large accelerations, especiallyat low peak voltages, PRSD may be more efficient. The crossing point may or may not be relevant
depending on the parameters of the initial beam and maximum voltage on the electrodes. For
example, while a crossing point for 10 kV (not plotted in Fig. 4.9) exists, it is not accessible inour decelerator using a molecular beam seeded in krypton. The acceleration to bring ND3 seededin krypton from 415 m/s down to rest is -67.9 km/s2 and the crossing point at 10 kV is near -74.3
km/s2 . Thus, for 10 kV on the electrodes, a beam seeded in krypton, and this decelerator geometry,
TWSD will always produce more ND3 at all final velocities.

84
However, at lower peak voltages, PRSD is an important operating mode to consider. The
advantage of the PRSD is that it allows access to higher accelerations than TWSD due to thegreater Stark potential well gradient. As controlling high-voltages is one the largest experimental
challenges for any Stark deceleration experiment, PRSD may be an important tool to investigate
low final molecular velocities given tight voltage constraints. This is because PRSD produces moresignal at higher accelerations and lower electrode voltages and is easier to implement than TWSD.
PRSD also allows the beam to reach a lower final velocity, possibly one that can be trappable,
without having to build a very long decelerator or obtain analog high-voltage amplifiers.
For a given decelerator length, a quick method of determining which mode will yield more
decelerated molecule signal is desirable. Previously, the crossing points between the two modes were
determined by integrating time-of-flight traces from Monte Carlo simulations, which is computationally intensive. Instead, the crossing point can be determined using an efficient 1D separatrix
calculation.
The 1D separatrix area does not accurately model the decrease in experimental signal withincreasing acceleration for either model since it does not account for the initial molecule position andvelocity spread. For the separatrix area to accurately predict the rate of decrease of the decelerated
peaks the overlap of the initial distribution and the phase space must be known. However, thisoverlap function affects the phase space of both modes similarly and does not change the point
where their phase-space areas are equal. Thus, calculating the acceleration when the longitudinal
phase-space areas for both modes is equal gives a good estimate for where the crossing-point will
occur.
Figure 4.10 shows the crossing points determined by both Monte Carlo simulations and
1D separatrix calculations are linear with respect to applied acceleration. The experimentally
determined crossing point, using the data from Fig. 4.7, is plotted with an open circle and agrees
with both calculations. The 1D separatrix calculations agree with the Monte Carlo simulations andis a simple method for determining the crossing point, even if it does not quantify how much betterone mode is compared to the other. This simple 1D separatrix calculation easily predicts when one

85
deceleration mode is more efficient than another without having to run Monte Carlo simulations.
90
MC Simulation
LPSA
Experiment

Acceleration (km/s2)

80
70
60
50
40
30

5

6

7

8

9

10

11

12

Voltage (kV)

Figure 4.10: The acceleration at the crossing-point, where TWSD and PRSD produce similar
decelerated molecule signal, calculated using Monte Carlo simulations and 1D longitudinal phasespace acceptance. The crossing point determined by either method is linear with respect to applied
voltage. The experimental crossing-point (open circle) agrees well with the calculations and simulations.

4.1.6

Conclusion

Stark deceleration has proved to be a reliable source of cold molecules for various applications. However, traditional crossed-pin geometry Stark decelerators have well documented instabilities that reduce their efficiency. An alternative deceleration technology, traveling-wave Stark
deceleration, is predicted to nearly eliminate the problems that reduce the number of decelerated
molecules. However, the difficulty in creating the required sinusoidally varying high-voltage waveforms for TWSD has limited their integration into experiments. To possibly make implementationof a ring-geometry decelerator less challenging, we investigated running this type of decelerator ina pulsed mode.
We demonstrated using experiential measurements and molecular trajectory simulations thatfor the same peak voltage on the ring electrodes, the alternative running mode, PRSD, is more

86
efficient than TWSD at high accelerations. This effect is caused by the larger Stark potential gradient for PRSD, which allows for larger accelerations before the stable phase-space region vanishes.
The crossing point at which the two modes are equally efficient depends on the maximum applied
voltage, among other experimental parameters. The PRSD mode is a particularly important option
for use with lower applied voltages, and gives access to a previously inaccessible low velocity regime.
Thus PRSD provides a useful and straight forward method for decelerating many molecular species
in a ring-geometry decelerator. These results could allow for more groups to be able to implementring-geometry Stark deceleration using the less challenging electronics, and still gain many benefits
from the cylindrical symmetry of the electrodes.

4.2

Implementing PRSD

Figure 4.11: A schematic diagram of a cross section of the ring decelerator. The two voltage
configurations above and below give the two different potentials used in PRSD. The numbers oneach ring correspond to the rod that it is connected to. Thus the left-most and right-most rings
are both connected to rod 7.

The high-voltage electronic configuration in PRSD is similar to that of PPSD, but insteadof four rods that each must be switch between +HV or -HV and ground, there are eight. Two
alternating voltage configurations are used to create the potentials wells, Figure 4.11. Each ring islabeled with its rod number, and the two possible voltage configurations are given above and below
the rings. Although there are more rods in the ring decelerator geometry, only four high-voltage

87switches are required since every fourth ring has the same voltage sequence. This results in two
Stark potential wells formed for every eight rings (Figure 4.2). Here, it is again important to notethat the Stark potential well is only half the longitudinal length in PRSD compared to TWSD.
This will play a significant role in the cases where PRSD is more efficient than TWSD.
The similarities between PPSD and PRSD mean the digital timing sequences for switching
between the two sets of potentials are calculated in the same manner (see Section 2.2). One timing
molecule located at the center of the initial pulse and with no transverse displacement or velocity
is propagated along the on-axis longitudinal potential at a given phase angle. In addition to thesame method of calculating the timing sequence, the physical equipment for implementing PRSD
is straightforward as it uses essentially the same electronics as PRSD. A few modifications to theelectronics maybe necessary due to the longer digital timing sequences in PRSD and the increased
capacitance of the decelerator. The number of digital voltage switches times required will be atleast the number of deceleration stages. For our pin decelerator, this is 149 if operated in S=1
mode. For our ring decelerator this is 623. This is one less than the number of pin pairs/rings in
the decelerator since each deceleration sequence begins with the timing molecule in between thefirst and second pin pair/ring. The number of deceleration stages is then equal to n − 1 where n is
the number of pin pair or rings.
Just like in the case of PPSD, the high voltage potentials are switched using Behlke HTS201-03-GM switches. In our PPSD, we used a Viewpoint DIO64 board to generate the control
sequences for the Behlke switches, but the DIO64 cannot be used for the digital timing sequencein PRSD. It does not have sufficient memory to generated the required timing sequence for PRSD,
which for our decelerator requires over 623 logical switches. At least one voltage switch time isneeded per stage and a few more are needed for the valve and detection sequence. The DIO64
has a maximum of 512 lines of output making it insufficient for this application. Instead, we use
a GaGe 8152 arbitrary waveform generator, which we also use in TWSD, to create the switchingsequence. It has a memory length of 512K samples per channel and is typically run at 37.5 MHz
for a maximum output sequence length of 13.65 ms. Since the GaGe board only has a maximum

88
output voltage of ±1 V, a 1V to 5V amplifier is required in order to convert the output signal to a
TTL to drive the Behlke switch control circuitry. We accomplish this with a Schmit trigger using
an AD790 comparator.
We use four Behlke switches to control the eight rods. An additional high-voltage cablesplitter box is added to each switch output since each high-voltage switch must drive two decelerator
rods instead of one. The two voltage configurations each require a different timing control sequences.
Additionally, for each timing control sequence, one active high version is required for the positive
voltages and one active low version is required for the negative voltages. The GaGe board creates
the active high version, for +HV, of both timing control sequences and then an inverter box produces
the active low sequences, for -HV, from the active high sequence. The inverter box also ensuresthat the control signal for the active low sequence always remains high when the decelerator rings
are not suppose to be switching so that the output remains at ground. While all four switchingsequences could be programed into the GaGe board, this configuration reduces the required numberof channels required.
The +5 V digital timing sequence is passed through an optoisolator before going to the Behlke
control circuit. This protects the computer from high-voltage switching noise or failures. The four
digital timing sequences drive four Behlke switches, which operate in the high frequency burst
mode. The maximum burst frequency for our switch model is fv(max) = 3.3 MHz. The shortest
switch time step, which occurs in bunching mode, is 4.8 µs, which is well within the specificationsof the Behlke switch. However, since there are many more switches per burst required in PRSD
than in PPSD, it is important that the Behlke switch control box have enough capacitance to drive
all the pulses. The recommended Behlke control circuit is shown in Figure 4.12. For the burst
option, the capacitance of C2 and C3 is recommended to be
C = 0.1µF × number of pulses per burst.

(4.3)

Due to space constraints, we use 56 µF capacitors, as larger capacitors do not fit into the control
circuit board. We found that 56 µF is sufficient for our switching sequence even though it is less

89
than suggested by Equation 4.3. Here, it is also important to note that in our circuit we use a 25
µF capacitor for the +5 V supply backing capacitor in place of the 10 µF capacitor between pins
3 and 5.

Figure 4.12: Recommended Behlke control circuit from Behlke HTS-201-03-GSM technical data
sheet. For the burst option the capacitance is recommended to be C=0.1µF× number of pulses per
burst.

The last modification required to switch from PPSD to PRSD is on the output of the Behlke
switch. Since each switch is connected to two rods, this increases the capacitance that each switch
must drive. In order to speed up the switch output, we removed the typical 1.1 kΩ resistor on the
output of the Behlke switch. This normally protects the switch in an over current event such as
an arc. Rise times for various Behlke switch output resistor and decelerator rod or test capacitor
configurations are given in Table 4.1. The rise time for a square wave on the pin decelerator is 0.8µs. In order to achieve a similar rise times to that of the pin decelerator, while still having eachswitch connect to two rods, the output resistor must be removed.

90
Table 4.1: Switching rise times for PPSD vs PRSD
Load
Pin decelerator, 1 rod
Ring, 2 rod
Ring, 2 rod
Ring, 1 rod
250 pF test load

4.3

Output resistance (Ω)
550 or 1.1 K
1.1 K
550
1.1 K
0

Rise time (µs)
0.8
1.6
1.3
0.8
0.7

Decelerating with PRSD
While the comparisons between PRSD and TWSD in section 4.1 were only performed up

to ±7 kV, we continued PRSD to higher voltages. At ±7.5 kV on the decelerator, very clear
decelerated peaks with adequate signal-to-noise can be seen for final velocities down to 75 m/s,
Figure 4.13. We did not pursue lower velocities or higher voltages than this due to an issue withthe decelerator. With ±7.5 kV on the electrodes, the decelerated signal would occasionally drop bya factor of 2-3. This drop could not be attributed to laser or valve behavior, and we believe it was
an issue with the potentials on decelerator rings even though the decelerator had been conditioned
in pulsed mode to higher voltages. Switching the polarities on the decelerator rings recovered thesignal. However, deceleration at ±7.5 kV was not continued since it appears that further voltage
conditioning of the decelerator is required.
As mentioned in Section 4.1.5.2, the 1D phase-space model does not accurately depict thefunctional form of the decrease in molecule signal as a function of acceleration. The 1D LPSA
models can only be interpreted qualitatively and not quantitatively. The relative ratios between
the LPSA at different accelerations is not directly proportional to observed decelerated signal sinceeach phase-space area must also be convolved with the molecule density. However, 1D longitudinal
phase-space acceptance plots are still useful for visualizing the parameter space we are working
with. Here, we take the 1D model for the lowest voltage and velocity configuration that we candetect in the lab as a limit of what it is possible to decelerate. Any voltage and velocity combinationthat has a 1D phase-space acceptance larger than that limit can be decelerated and detected in91

Figure 4.13: PRSD of ND3 from and initial velocity of 415 m/s down to final velocities of 125, 100,
and 75 m/s.

Figure 4.14: Longitudinal phase-space acceptance for PRSD of ND3 from and initial velocity of 415
m/s down to various final velocities using peak voltages of ±7, 7.5, and 8 kV.

our decelerator. This simple model makes the assumption that molecular dynamics are not afunction of phase-space acceptance. 3D molecular dynamics simulations should still be conducted
before drawing any conclusions. However, this model serves as a quick method to estimate what is

92
achievable at different voltages.
Figure 4.14 shows the 1D phase-space acceptance for various final velocities and peak voltages.
The LPSA for the two lowest velocity configurations that we have detected in the lab, ±7 kV,
vf =150 m/s (Figure 4.5), and ±7.5 kV, vf =75 m/s (Figure 4.13), are shown in red and orange
respectively. The smallest phase-space acceptance of these two is for ±7 kV and vf =150 m/s.
Any LPSA that has an area larger than this case should have signal with comparable or better
signal-to-noise than the blue trace in Figure 4.5. For ±7.5 kV deceleration with half the final
velocity (orange), the LPSA is larger than the ±7 kV case, showing the importance of the welldepth and gradient. The green trace shows the LPSA for ±7.5 kV deceleration down to vf =25
m/s, a trappable velocity. Since the acceleration required to reach a final velocity of 25 m/s does
not differ much from that required to reach 0 m/s, the LPSA does not change significantly forvf <25 m/s. This LPSA is only slightly smaller than the ±7.5 kV, vf =75 m/s case and larger thanthe ±7 kV, vf =150 m/s case. This suggests that in our particular decelerator, we can tune over thefull velocity range using ±7.5 kV PRSD. Higher voltages from here will increases the well depth,
which results in greater phase-space acceptance and more decelerated molecules. When the peakvoltage is increased to ±8 kV, all LPSAs are larger than the slowest cases that we have decelerated
experimentally. The ±8 kV LPSA in Figure 4.14 (blue) is the largest acceptance and once again
the LPSA for vf <25 m/s is approximately the same as that for vf =25 m/s. Thus, if one did notwant to use high-voltage amplifiers and TWSD, this decelerator (624 rings, 2.032 mm apart) in
PRSD mode would be able to decelerate ND3 to any desired velocity starting at voltages of ±7.5kV.
Additionally 1D phase-space acceptance model can be useful for visualizing when to use eachdeceleration technique with various carrier gases. Figure 4.15 shows the 1D model for ±7 kV
deceleration. Vertical lines have been placed at the accelerations required to bring an expansion
of ND3 in krypton and xenon to rest. The left side of each vertical line represents the accessible
range for that gas. Here, we see that if working with an expansion in xenon, TWSD will always
be superior at this voltage. PRSD only shows superior performance when more deceleration is

93
required (ie, in a faster krypton beam).
The same style plot is shown in Figure 4.16 for ±10 kV PRSD. For all accelerations thatwould be used when working with a beam seeded in krypton, TWSD is superior. Unless one wanted
to work with argon or did not have access to TWSD, PRSD at ±10 kV is not as useful.

Figure 4.15: The LPSA for ±7 kV PRSD as a function of acceleration. Vertical dashed lines
indicate the acceleration required to decelerate ND3 seeded in xenon and krypton down to rest.

94

Figure 4.16: The LPSA for ±10 kV PRSD as a function of acceleration. Vertical dashed lines
indicate the acceleration required to decelerate ND3 seeded in xenon, krypton, and argon down to
rest.

4.4

Transverse Dynamics
The transverse potential energy landscape between the two deceleration modes evolves dif-ferently over time. However, this does not appear to result in significant differences in the final
decelerated packet. Just like in the longitudinal picture, the well depth is the primary determinantof the phase space acceptance. Figure 4.17 shows the Stark Potential energy surface in the xz (y=0)
plane for both PRSD and TWSD. Both plots are taken at times where the bottom of the potential
well is aligned with a ring electrode located at z=0 mm. Since the decelerator is cylindricallysymmetric, the potential energy surface looks the same in the xz (y=0) and yz (x=0) planes.
Although the two surfaces look similar, except for twice as many wells longitudinally in PRSD
compared to TWSD, in this snapshot in time, they evolve rather differently in time. In TWSD,
potential well bottom is always moving and therefore has an infinite number of configurations.
Luckily, when the bottom of the potential well is not aligned with a ring, the shape of the wellonly changes slightly (Figure 4.18). Here z is given in units of L, the ring spacing, since fractionsof 2.032 mm are difficult to read and remember. The major deviations of the transverse potential

95

Figure 4.17: The Stark Potential energy surface in the xz(y=0) plane for both PRSD (left) and
TWSD (right). Both plot are snapshots for when the bottom of the potential well is aligned witha ring located at z=0. need to add a, b labels to plots

occur at |x| > 1 mm, which is significantly displaced from the bottom of the trap. Figure 4.18bshows a closer view of the bottom of the transverse potential at various locations. While there isvariation, it is small compared to the overall trap depth.

Figure 4.18: The transverse Stark potential for ND3 in the TWSD when the bottom of the well isring aligned (z=0) and gap aligned (z=L/2). The plot on the right is a closer examination of how
the bottom of the potential well varies as it moves from being ring aligned to gap aligned.Maybe
make this an inset instead

In PRSD on the other hand, the electric fields remain static for longer and change discreetly
as opposed to continuously. In this case, the timing molecule traverses the potential energy surface
instead of always residing at the bottom. For example in bunching, the timing molecule starts partway up the side of the potential well, it travels through the bottom of the potential well and up to

96
the same height that it started at. As a result, it encounters a transverse potential that changes
more drastically than in TWSD. The transverse potential encountered by the timing molecule forthe pulsed-ring case can be thought of as taking successive slices of the 3D potential well in theradial direction. In the traveling-wave case, on the other hand, the entire potential well translateswith the timing molecule and the transverse potential does not significantly change as viewed by thetiming molecule. Figure 4.19 shows the transverse potential that the timing molecule encounters
for both types of deceleration. The left most plot z = 0 is where the timing molecule is alignedwith a ring. The right most plot is when the timing molecule is aligned with a gap (exactly between
two rings). Here, PRSD is taken to be in bunching mode, so the potential shifts by L every timethe timing molecule is gap aligned z = L2 . The pronounced different shape between the TWSD
and PRSD configurations is due to the significantly deeper well of PRSD. This can also be seenin Figure 4.18 where the PRSD well has much higher walls (yellower on the edges). Despite thedifferences between the two transverse potential energy landscapes, a preliminary examination of
the transverse phase space for both PRSD and TWSD shows that both are evenly filled and noinherent structure is seen in the distribution of molecules. A detailed analysis of the transverse
behavior of molecules was not carried out. A more in depth analysis is probably needed to see if
weak transverse-longitudinal coupling is present.

97

Figure 4.19: The transverse potential that the timing molecule encounters at various point between
being ring aligned (left most) and gap aligned (right most). In the PRSD case the potential well
does not move while the timing molecule climbs up the potential hill, this results in the bottom of
the transverse potential well increase in energy as the molecule gets close to z = L2 .

4.5

Calibration
Stark deceleration data such as those in Figure 4.5 and 4.6 must be calibrated before directcomparisons can be made between data from different final velocities and between experimentand simulation. Differences in different sets of experimental data and from experimental data tosimulation data must be accounted for. Recording time-of-flight data in deceleration experiments
usually required many measurements of the same deceleration sequence in order to have sufficientsignal-to-noise. Each data set for a given final velocity (each colored trace in Figure 4.5) is referred
to as one scan. The experimental time-of-flight scans presented in Section 4.1 are averages of nruns of the experiment per data point. figure out how much time is actually. During this timethe experimental signal can drift due to changes in temperature and noise from other equipment.
In order to ensure many time-of-flight scan can be compared to each other, a simple calibration

98
method is used to account for day-to-day signal drifts. While the general envelope of the signal
remains the same in day-to-day runs of the experiment, the amplitude can be greatly affected by
the precise gas mixture (a 2.25 L, 60 psi gas mixture will last about 100-120 hours of running at 10
Hz) and laser power, wavelength, and beam profile. To account for these drifts during the courseof a detailed time-of-flight scan (1-2 hours), we use a simple linear calibration between two sets ofpoints to account for laser wavelengths drifts. All PRSD scans presented in this chapter were takenwith a single gas mixture, so in this case we were only calibrating for laser drift.
One scan is typically (give parameters). The data points are usually taken sequentially intime, however they could also be randomized in computer control program. When comparing manydifferent time-of-flight traces to one another, such as in Figure 4.5, one time-of-flight scan must be
chosen as the ‘master scan’ all other scan will then be calibrated to this one. Taking the scansin Figure 4.5 as an example, if the vf =240 m/s scan (yellow) were chosen as the master scan,
all other scans will have their amplitudes calibrated relative to it. The choice of master scan is
not critical since decelerated signal is only compared relative to other decelerated signal, however
the master scan should be one with adequate signal-to-noise and in no danger of saturating thedetection system.
In order to calibrate all scans to the master scan, two calibration points are chosen andmeasured before and after every scan. The calibration points are usually chosen to be near the
peak of one deceleration packet. The two calibration points should be taken from decelerated
packets at different final velocities with significantly different signal amplitudes. This way, in thecase of large laser instabilities that cause one point to go into saturation or become impracticallylow, there is a back up calibration point. Before and after each time-of-flight deceleration scan,a measurement of both calibration points is taken. These points are referred to as Cim and Cf mwhere m is either 1 or 2. Typically only Ci1 and Cf 1 are used, but Ci2 and Cf 2 are recorded as
backup calibration points. Each calibration point is made of measurements from at least 200 shotsof the experiment. Typically this consist of 64-128 averages on the oscilloscope and 3-8 averages
on the computer.

99
Although the source of the drifts may not be linear, the drift between the two points is
assumed to be linear over time. For a time-of-flight scan containing n raw data points yn , eachcalibrated point yadj n is given byCim − Cf m tn − ti Cpm
yadj n = yn 1 +×,
Cim
tf − ti Cim

(4.4)

where
m is either 1 or 2 and refers to whether the first (1) or backup (2) calibration points will beused,
Cim is the initial calibration point for the scan which was taken immediately before the scanbegan,
Cpm is the initial calibration point of the“master” scan that all scans are referenced to, theCpm =Cim for the master scan
Cf m is the final calibration point for the scan which was taken immediately after the scanfinished,tn is arrival the time for the measured point yn ,ti is the arrival time of the first data point of the given time-of-flight scan, it corresponds tothe time at the point y1 ,and tf is the arrival time of the last point in the given time-of-flight scan, it corresponds tothe time at points time at ynmax ).
The initial calibration point for the “master” scan is taken as Cp . If calibrating only one scan, thenCp = Ci . This is particularly necessarily for very long (several hours) time-of-flight scans where
both the underlaying undecelerated peak and the decelerated peaks must be recorded if there arelaser drifts.
In the case of comparing multiple sets of scans taken under different conditions (decelerationmode, laser power, gas mixture, etc.), the master scans for each set can be calibrated to each othervia free flight scans. A free flight (no deceleration) scan should be taken at the beginning and endof each day. The relative peaks of these free flight scans can then be used to scale between two
master scans. This allows for comparisons of relative signal, but should only be used if no major
adjustments to the system (detection laser position, detection voltages) have been made.

100This calibration was found to be reliable when comparing calibrated scans from days when
the laser was rather unstable to days where the laser was more stable. By applying this calibration,
we saw very reliable signal across many days and even spread out across several months. Figure 4.20
shows the difference between raw uncalibrated data and calibrated data. Here, three different raw
time-of-flight scans of ND3 decelerated from vi =415 m/s down to vf =240 m/s are displayed (Figure
4.20a). These scan were recorded on two different days. The uncalibrated time-of-flight traces havewidely varying amplitudes, but once the calibration is applied, all three scans have comparable
amplitudes. The calibration takes into account drifts such as the behavior of the pulsed valve andthe wavelength of the dye laser. Although these effects may not necessarily have linear drifts, thislinear calibration still does a good job of making signal comparable from one day to the next.

(a) Uncalibrated time-of-flight scans(b) Same scans after applying calibration

Figure 4.20: Three ND3 PRSD time-of-flight scans for vi =415 m/s down to vf =240 m/s of ND3 .
On the left is the raw scans. On the right after the calibration is applied and the scans trimmed
to be the same length in time. The colors remain the same between both plots

Once all experimental scans have been calibrated to each other, they maybe compared tosimulations. Since only the relative signal of the experimental scans are being compared, they canbe scaled by an arbitrary factor or normalized such that bunched signal (or any other deceleratedpeak) has a value of one. In the experiment the detected molecule signal is measured in nanovoltseconds (nVs) since is the integral of a voltage versus time trace. The value of the signal is dependent
on the voltage on the MCP detector and gain of the particular detector plates. Thus it should only

101
be viewed as a relative measure and a constant multiplier can be used to compare experimental
scans and simulated scans.
Additionally, due to uncertainty in the free flight distance between the exit of the decelerator
and the position of the detection laser, an arrival time adjustment must be applied to the simulation
data when comparing it with experimental data. The arrival time shift, tshif t , takes the form oftshif t (vf ) =

d0 df
+ ,
v0
vf

(4.5)

where d0 and df are constants that account for differences between the simulation and experiment.
The first term dv00 results from uncertainty in the distance between the valve and the entrance ofthe decelerator. It is a constant time shift regardless of the final velocity of the beam. In thesimulations, the timing molecule can automatically be loaded into the correct potential well since
all distances can be set exactly. In the experiment, the position between the valve and skimmer
can be adjusted to find the best free flight beam. Then the time between the valve firing and thedecelerator turning on can be adjusted for optimal beam loading. However, due to the adjustabilityof the valve position, and the delay between the valve control pulse and when it actually opens,
the time it takes a molecule at the densest portion of the molecular packet to travel from the valve
face to the decelerator entrance is not precisely known. d0 accounts for the differences in free flighttime between the valve and the entrance of the decelerator. df on the other hand, accounts forthe distance between the end of the decelerator and the detection laser. Since the arrival time will
depend on the final velocity, this must be specified as a distance not a time. While these values
will change depending on how close the values used in the simulation are to the experiment, forreference the calibration for PRSD in (Figure 4.5) were d0 = 9.46 cm and t0 = −9.27 mm.

4.6

8-ring periodicity PRSD
The discussion up to this point has been for a voltage configuration where the voltage sequence

repeats every four rings, and four potential wells are formed for every eight rings in the decelerator.
This is referred to as the 4-ring periodicity pulsed-ring Stark decelerator (4R PRSD). Since there are

102
8 electrically isolated rods in our ring decelerator, there are other possible pulsed-ring configurations.
As alluded to in 4.1.2 an 8-ring periodicity pulsed-ring Stark decelerator (8R PRSD) can also be
implemented. This configuration is not as effective since it is more difficult to run and less efficientthan the 4R version at high accelerations, but warrants discussions since it creates instantaneous
Stark potential wells that are identical to those in TWSD.
An 8R PRSD configuration would have the same voltages as TWSD when the bottom of awell is centered on a ring. Thus ±7 kV 8R PRSD would have the same potential as TWSD in Figure
4.2 and the same instantaneous voltages. Figure 4.21 shows both of the 8R voltage configurations.
In one of the static configurations,uuuu every fourth ring is at ground (rings 0 and 4 in the caseof the upper configuration). The rings halfway between the grounded rings are at +HV and -HV(rings 2 and 6), and all the remaining rings (all the odd ones) are at 71% of the high voltage.
The odd rings are at 71% and not at 50% of the high voltage because the smoothest potential iscreated by a sine wave. As seen in the TWSD case for a sine wave voltage when the zero crossing
is centered at a ring, the intermediate rings are at sin π4 = 0.707. If the odd rings were at 50% of
the high voltage the top of the Stark potential hill would have a very small local minimum.
In order to run the two configurations shown in 4.21, four power supplies are required andsix high-voltage switches. It is interesting to note that in this configuration, rods 1 and 5 neverswitch voltage and rods 3 and 7 require bipolar switching. While this is experimentally possible, it
makes running this type of deceleration much more complex than 4R PRSD.
Figure 4.22 shows the comparatively low efficiency of 8R PRSD using simulated data. The
initial velocity for all simulations is vi = 415 m/s and the molecules are decelerated to final velocities
of vf = 415, 360, and 320 m/s. The difference in well periodicity is easily seen in the time-of-flighttraces with two 4R peaks occurring for every 8R packet. While in bunching (vf = 415) the 8R
configuration produces greater time of flight signal, this signal quickly decreases once the Stark
potential wells are decelerated. At a final velocity of 360 m/s (a=-16835 m/s2 ), the peak amplitudeof the decelerated packets is comparable for both periodicities, and at a final velocity of 320 m/s(a=-27578 m/s2 ) the peak amplitude for 8R is significantly less than that of 4R deceleration.

103

Figure 4.21: The two voltage configurations for 8R PRSD are given above and below the crosssection of the ring decelerator. The numbers on each ring correspond to the rod that it is connected
to.

Although the Stark potential well in 8R deceleration is larger, which increases the phasespace acceptance in bunching, due to its lower gradient, it tilts over more quickly as acceleration
is increased. Additionally, since the bottom of the potential well moves by two rings during eachswitch, in 8R PRSD, our decelerator has only half as many deceleration stages. It performs worse
than 4R PRSD except in cases of very low accelerations and bunching, and it always performs worse
than TWSD since the instantaneous potentials are the same, but the well propagates discretely
instead of continuously.
While having identically periodic potentials for the pulsed and traveling-wave method would
be ideal for comparing the detailed molecular dynamics within each of the two methods, 8R PRSD is
not an efficient method of running the decelerator. Instead, 4R PRSD is a straightforward methodthat can be used by groups who may have limited space or voltage constraints. It is a method thatis not more difficult to assemble than PPSD, can produce similar, and in specific circumstances,better results than the much more difficult to implement TWSD method.
Of course there are even more permutations of pulsed configurations, however these become
increasingly difficult to implement experimentally. For example, one can imagine a configuration
where the bottom of the potential well moves only one ring per switch, just like in 4R PRSD, but
now with a potential well that is larger. This would come closer to approximating TWSD but each

104

Figure 4.22: Simulated data of 4R and 8R PRSD at ±7 kV with vi = 415 m/s and vf = 415, 360,
and 320 m/s.

ring would have to switch between three or four voltages and a combination of three and four-stateswitches would be required. This would also greatly change the phase angle calculations since thewell does not move by φ = 180◦ each time. The complexity of these cases illustrates why pulsed-ring
configurations beside the 4R configuration in Figure 4.11 are unlikely to be used experimentally
since, with a subset of the same equipment, it could be operated more efficiently.

Chapter 5

High-Voltage Amplifiers

The most difficult step towards the experimental realization of TWSD is generating therequired high-voltage waveforms. As discussed in Chapter 2, very few experiments have used thistechnique due to the need for stable amplifiers with an output voltage greater than ±5 kV and alarge bandwidth or a long ring-electrode decelerator. Here, we present an amplifier that has beensuccessfully used to decelerate ND3 with ±7 kV output voltages and has the capabilities to reachhigher output voltages. Individual amplifiers have performed adequately at output voltages up to±12 kV, and with a few modifications, these amplifiers will be able to be used for TWSD of a ND3
beam down to trappable velocities.
The first section of this chapter is adapted from a manuscript under review [174]. It discusses
the amplifiers in detail and contains circuit diagrams for important portions of the amplifier circuit.
This is followed by a discussion of the control circuitry and interlock circuitry to illustrate how theamplifiers are integrated into the experiment. For a full in-depth discussion of the amplifiers and all
associated circuitry, background on the individual subcircuits, and tuning and testing procedures
see Noah Fitch’s dissertation [95]. It is important to note that these amplifiers operate at very
high voltages and must be carefully insulated; Section 5.6 discusses construction and insulation
to keep both the user and the amplifier safe. Several changes have been made to the amplifiers
and control circuitry since Noah’s dissertation including small changes to resistor values and a few
larger design changes. These are covered in Section 5.8 and the full updated circuit diagram forthe entire amplifier setup can be found in Appendix A.

106

5.1

High-Voltage Amplifier Electronics

5.1.1

Introduction

Stark deceleration is a molecular manipulation technique that uses time-varying inhomogeneous electric fields to produce packets of slow, cold molecules [107]. In this technique, large
electric-field gradients are created inside a vacuum chamber via application of large potential differences between electrodes. These gradients exert Stark-effect forces on polar molecules in particular quantum states. With the correct electrode geometry and temporal control of the applied
potentials, molecular beams can be decelerated. The resulting beam velocity can be tuned fromseveral hundred m/s down to rest. These beams can then be loaded into static electric or magnetic
traps for collision studies [77, 92, 94, 96] or used in low velocity experiments [98, 129, 130].
There are two main approaches to Stark deceleration, which use distinct electrode geometries
and applied voltage waveforms. The first approach, pulsed-pin Stark deceleration (PPSD), uses
crossed-pin electrodes and discrete digital voltages to decelerate a pulsed molecular beam. While
PPSD is relatively easy to implement using commercially available high-voltage switches to control
the potentials on the electrodes, there are well-documented loss mechanisms [139, 140] that reduce
the efficiency of the deceleration process, particularly at low beam velocities. The second approach,traveling-wave Stark deceleration (TWSD), uses ring electrodes and sinusoidal analog voltages tocreate a continuously moving Stark potential well [121]. Because the molecules are always confined
while being decelerated, TWSD is able to avoid many of the instabilities and inefficiencies [139]inherent in PPSD [107,118]. Additionally, by chirping the frequency of the analog voltages down to
DC, the traveling potential well comes to a standstill and can serve as a trap [127]. Thus, TWSD
also offers the option of efficient loading of the decelerated molecules into an electrostatic trap,
resulting in greater trapped molecule densities than in previous Stark decelerator geometries.
The challenge to implementing TWSD is creating the high-voltage driving electronics. The
traditional approach for creating high voltage waveforms, using transformers, fails at low frequencies, and only has a narrow tuning range. Thus, linear amplifiers must be used to drive the107
traveling-wave decelerator. The necessary bandwidth, voltage, current, and heat dissipation characteristics of an amplifier are set by the particular geometry of the decelerator. Our decelerator isof similar design to previously constructed ring Stark decelerators [121, 122], and has 624 tantalum
ring electrodes with every eighth ring electrically connected. Therefore, TWSD requires eight ormore high-voltage analog amplifiers in order to produce the chirped frequency sine-wave voltages.
The rings are made of 0.04 inch diameter wire with an inner diameter of 0.16 inches. The centerto-center spacing between rings is 0.08 inches. This decelerator is designed to serve a similar role toour pulsed-pin Stark decelerator [153], and will be used with the same high-voltage power supplies,
pulsed valve, and state-selective detection system used previously [106].
In TWSD, the Stark potential well must have an initial longitudinal speed that corresponds
to the initial speed of the molecular beam. The speed of the potential well must then be reduced tothe desired final speed of the molecular packet. Using the initial and final speeds of the molecular
packet and the length of one Stark potential well, we can calculate the required bandwidth of theamplifier. The longitudinal length of one Stark potential well is determined by l, the electrodespacing, and p, the ring periodicity (i.e., the number of rings that create a single period of thesine wave). To produce a potential well with a longitudinal velocity v, the frequency of the output
voltage waveform is
f=

v
.
pl

(5.1)

For most traveling-wave Stark decelerators constructed to date [121, 125–127], including ours, l is
∼2 mm and p is 8. For a supersonic molecular beam seeded in krypton, the initial velocity is
between 400 and 450 m/s, setting the upper end of the bandwidth to 28 kHz. If the molecules
are to be trapped after deceleration, the final velocity must be zero. Therefore, the high-voltage
amplifier must have a bandwidth of at least 28 kHz down to DC. The amplifier presented here isdesigned to run from 30 kHz down to DC in order to provide flexibility with the output waveform.
This bandwidth, on its own, is not extremely challenging to achieve, but there are also demanding
voltage and current specifications to be met.

108
The peak output voltage of the amplifier and geometry of the decelerator set the depth of the
Stark potential well, which in turn sets the limit on the magnitude of deceleration. The larger theamplitude of the voltage and the closer the rings are spaced, the greater the electric fields and depthof the potential well produced. The maximum achievable voltage on a Stark decelerator electrodeis determined by either the high-voltage power supplies or the maximum voltage difference that canbe supported between two adjacent electrodes. While a 1 mm gap can support up to 20 kV [175],
any imperfections in electrode surface quality or alignment may cause arcing at lower voltages. We
aim for a more conservative field of 7 kV/mm between electrodes, which requires operating thedecelerator with sinusoidal voltages that have an amplitude of 10 kV. This gives a maximum onaxis electric field of 3.2 kV/mm and a Stark potential well depth of 0.57 K for deuterated ammonia
molecules (mass ∼ 20 amu, dipole moment ∼ 1.5 Debye).
While there are methods to decelerate with lower peak voltages, such as starting with alower velocity beam [123, 125], using multiple types of deceleration [127–130], or using a longer
decelerator [126], our goal is to decelerate a supersonic beam seeded in krypton using only TWSD
in a 1.25 m long decelerator. This allows us to take full advantage of the signal increase offered by
the cylindrical symmetry and continuous deceleration forces without having to contend with thechallenges of long decelerators [126].
In addition to the voltage requirements, the amplifier must be able to supply the current
required to charge the capacitive load of the decelerator. The effective capacitive load of ourdecelerator is calculated to be 225 pF [95], which does not include the capacitance of any cabling
between the amplifier and decelerator. We estimate our cables add around 40 pF/ft. Even if theamplifiers are mounted close to the vacuum electrical feedthroughs, ∼2 ft of cable is still required.
This adds significant capacitance to the load, which the amplifiers must drive. Using the effective
capacitance of the decelerator, the maximum frequency of 30 kHz, and the maximum ± 10 kV
output, we determine the amplifiers must be able to source and sink a peak current of ∼0.5 A.
In order to allow for added capacitance due to cabling and flexibility in the output waveform, thedesign goal for the amplifiers was set at 1.5 A.

109
Lastly, the design of the amplifier must be able to dissipate the heat generated by the highvoltages and currents present. The electronics of the amplifiers do not prevent the amplifiers frombeing run continuously, however, this would create an unmanageable thermal load and require thedissipation of several kilowatts. Instead, the experiment runs at 10 Hz, and requires the amplifier
to be on for ∼6 ms in order to bring the molecules to rest. This means that an amplifier must beable to dissipate ∼200 W when running in a pulsed mode.
Implementation of TWSD has been limited by these challenging bandwidth, voltage, andcurrent requirements. While several commercial amplifiers are able to meet some of these criteria,
none meet all. The closest is the Trek 5/80 amplifier, which has been used in several TWSD
experiments [123,126,127]. It has a bandwidth of greater than 60 kHz down to DC and a maximum
output voltage of ±5 kV at peak currents of 80 mA. The custom amplifier presented here is capableof ±10 kV peak amplitudes, peak pulsed currents of 1.5 A, and has a bandwidth of 30 kHz down
to DC, which means it can produce the waveforms needed for TWSD in an apparatus that is 1.25
m in length.

5.2

Design of the high-voltage amplifier
The design of the high-voltage amplifier is based on an optically coupled, all-n-channel push-

pull amplifier, shown conceptually in Figure 5.1A. Here, current is sourced to the load when the
top FET (QT ) is conducting and the bottom FET (QB ) is non-conducting. When the opposite
is true, current is sunk out of the load. Since the FETs operate out of phase, a separate opticalcontrol signal is required to drive each FET. A push-pull amplifier could also be made with bothn-channel and p-channel transistors. Here, we use all n-channel devices to take advantage of theirsuperior voltage and power handling specifications.
To determine how many n-channel transistors are required for a given application, one should
consider the maximum voltage drop across a FET. If the output voltage swings the full range fromthe positive to negative rail voltages ( i.e., + HV to - HV), a single FET, QT or QB , will experiencea voltage drop of 2|HV|. If this is greater than what one individual FET can handle, multiple

110

Figure 5.1: (A) An optically coupled, all N-channel push-pull amplifier. The ±HV rails and output
voltage are limited to half the voltage rating of a single FET (QT or QB ). (B) With multiple FETs
connected in series between the HV rails and the output, a higher maximum output voltage canbe achieved. The resistor network divides the voltage between the source and the output such thatthe voltage is shared equally across each FET.

FETs in series will be required. In our design, as multiple FETs are added in series, one FET will
be driven by an external signal, while all other FETs follow in response to the leading FET. A
signal-driven FET is referred to as a leader and the following FETs are referred to as the followers1. Figure 5.1B illustrates how this is accomplished. It has a similar configuration to Figure 5.1A,
with QTL and QBL as the leader FETs being driven by an external signal, but now with additional
follower FETs QTF and QBF . The resistor chain on the right (RTF , RTL , RBF , and RBL ) is apassive voltage divider, which allows each FET that is part of the same bank to share the voltage
equally. When all FETs are off, the majority of the current flows down the resistor chain, and onlya small leakage current flows down the chain of FETs. If all resistors have the same value, the1

In some contexts, these are referred to as master and slave circuits, but here we use the terminology leader andfollower.

111
voltage drop across each FET is the same. If QTL begins to conduct due to a control signal applied
to the gate, the voltage across it and RTL will drop. This reduces the current through RTL . With
the current through RTL less than the current through RTF , the net current will flow into the gate
of QTF and turn it on. Thus, whenever the voltage across QTL does not match that across QTF ,a current will flow into or out of the gate of QTF to maintain the voltage sharing between QTL
and QTF constituting passive, local feedback in each bank. This same process occurs if additional
follower FETs are added in series.
All of the FETs in series, as well as all other components between the +HV (-HV) rail andthe output, are collectively referred to as the top (bottom) bank. Each bank can be thought of asa three terminal device, with an optically controlled gate, a drain end, and source end. Within asingle bank, each high-voltage FET and its associated sub circuits are referred to as one stage ofthe amplifier. Additional follower stages can be added to each bank at the drain end, and eachfollower circuit will follow the leader as outlined above.
While the push-pull design in Figure 5.1B contains the basic block structure of the amplifier,the full design of the amplifier is much more complex. As more followers are connected, additionalcare must be taken to ensure that all stages share the voltage equally, so that the FETs are notdamaged by being over-voltaged. Failure to do this can lead to catastrophic destruction of theamplifier. The full circuits for both the leader and follower, and their relevant sub-circuits, arediscussed below separately before a discussion of the amplifier control, feedback, and physicaldesign.

5.2.1

Leader Stage

The leader stage acts as the control center of each bank. Figure 5.2 shows the full leader
circuit, which consists of four primary blocks labeled with letters: a high-voltage cascode (A),global feedback driving circuitry (B), a local power supply (C), a local feedback network (D), as
well as protection diodes and a few other components for biasing and current limiting. While manyof the components in the leader stage float high above earth ground and experience only a few

C

D

1

B

A

112
1

F1_SOURCE

F1_DIVIDER

R1
10

2
C9
220pF

R6-B
2.5M

A

Q1
IXTF1N400

D2
3kV

D1
15V

3

R21
430

B

R3
100
Q10
3904

R15
10k
C1
1nF

Q12
3906

R16
100

R17
100

R7
400k
C3
5pF

2

C2
47pF

C

Q11

R22
10M

Q2
NJT4031N

R6-A
1.5M

D37

R2
510k

4

D

D4
3.0V

C4
1uF

D5
3.0V

C5
1uF

D6
3.0V

C6
1uF

D7
3.0V

C7
1uF

3

+ C8
10uF

4

Q9-A
Q9-B
5
R9
2k

R10
1k

R5
3

R19
5.11k

5

LEADER_SOURCE

6

7

Figure 5.2: A leader stage of the high-voltage amplifier. Portions of the circuit are boxed to help
6
identify sub-circuits, these include the A) cascode, B) global feedback driving circuitry, C) local
power supply, and D) local feedback. While some components are high-voltage components, others
are standard low voltage components that float up to high potentials, but do not experience a large
voltage difference. Components that are high-voltage components are indicated in the text.
7

volts of potential difference, the HV MOSFET (Q1) of the HV cascode, the local feedback network(R6, R7, C2,
C3), the protection
diodes (D2), and the biasing network (R22, C9) all experience
JILA ELECTRONICS
LAB
8 el s8
HIGH VOLTAGE AMPLIFIER
ectronic
the voltage dropMASTER
across the entire leader stage. These component must all be rated to withstand
DESIGN BY:
N. Fitch / T. BrownBUILT FOR:
Lewandowski
UPDATE:
4/30/2018
VERSION: H DRAWN BY:
N. Fitch
DN:
5/2/2013
SHEET
10OF
at least 4DATE:
kV,
which
is1 themaximum voltage rating of the MOSFETs.
CB
AD
A high-voltage BJT-MOSFET cascode, consisting of Q1 and Q2, is used instead of a single
FET (QT from Figure 5.1B) to handle the primary voltage drop in the leader stage. In the cascodeconfiguration, the BJT driven by an external signal, Q2, will swing only a diode drop between

113
being fully open to fully closed. This is achieved by placing a common-gate, high-voltage stage,
Q1 (IXTF1400 from IXYS), between the signal-driven transistor (Q2) and the load. Overall, thecascode configuration reduces the Miller effect and increases the speed and stability of the highvoltage handling FET [176]. Additionally, the cascode reduces the amount of current required toturn on Q2, and therefore the amount of current pulled from the voltage division chain.
The global feedback driving circuitry for the main cascode is contained in Figure 5.2 Box B(Q10, Q11, Q12, R15, and R16). Q11 is a phototransistor and the end of an optoisolator. This
separates the low, ≤1 V, control signal from the high-voltage potentials on the amplifier and any
associated high-voltage noise. Q10 is a diode-connected transistor, which, together with R15, acts
as a low-current pulldown for the base of Q11, enhancing the turn-off speed of the phototransistor.
Additionally, Q10 and R15 provide emitter degeneration feedback, which helps to stabilize the dc
bias against changes in temperature. Together, Q10-12 form an inverted cascode, which sources
current to the base of Q2. The inverted cascode prevents large voltage swings at the base of Q11,
reducing the amount of current needed to charge and discharge the Miller capacitance, further
increasing the speed of the phototransistor. Q2 then adjusts the voltage on its collector to set thevoltage drop between the gate and the source of Q1 such that Q1 and Q2 conduct the same current.
When no drive current is present, R19 pulls down on the base of Q2 and closes the stage.
In order to source and sink the current required to charge the Miller capacitance of Q1, a
low-impedance voltage source is required. Box C in Figure 5.2 (D4-7 and C4-8) contains a 12
V local voltage supply, which is charged through the high-voltage rail via R6b. For the range ofcurrents drawn by Q1, capacitor backed Zener diodes are an effective low-impedance source. D37
serves as an indicator when troubleshooting to make sure the stage powers up correctly and the
local supply stays charged.
The local feedback and passive voltage sharing chain is shown Figure 5.2, box D (C2, C3, R6b,
and R7). It serves as a replacement for RTL in Figure 5.1. The additional capacitor and resistorcapacitor in parallel help to prevent run away oscillations, while still maintaining fast feedback to
the gates of the follower stages. As seen in Figure 5.1B, this portion of the circuit is relevant only

114
when follower stages are included.
A chain of protection diodes, D2, consisting of seven 429 V TVS diodes in series, limits
the absolute maximum voltage across the leader stage to 3 kV and protects the stage from being
reversed biased. The high-voltage MOSFET, Q1 has a maximum VDSS of 4 kV. The protection
diodes guard against any poor voltage sharing between stages, transient voltage spikes, or effectsof human error during construction and testing.
The final, unboxed components provide current limiting and biasing. R5 limits the instantaneous current that flows down the cascode. Its resistance is chosen so that Q12 will go into
saturation when the emitter current of Q2 is greater than 1.5 A, the maximum current for thisdesign. Biasing of the leader circuit is important to maintain linearity and bandwidth of the optoisolator and stability of the cascode. Biasing Q1 on slightly so that it conducts a small quiescentcurrent increases the turn-on stability, linearity, and speed. This quiescent current is created via
Q9, which acts as an imbalanced current mirror. As long as there is a voltage drop across thestage, current flows through Q9a via R22. The other half of the mirror, Q9b, ensures that Q1 isslightly biased on with a low quiescent current. With rail voltages of ±15 kV the quiescent current
is 300 µA. In addition to the quiescent current, a standing current is applied just before, during,and just after the desired output signal. This is applied through the control circuity and biases on
all stages and the optoisolators to help to reduce non-linear amplifier behavior, such as crossoverdistortion. Typically, the standing current is set at 10 mA and is enabled 1 ms before to 1 ms after
the desired waveform. Larger standing currents would further reduce nonlinearities, but would
require a significant amount of power dissipation.

5.2.2

Follower Stages

The follower circuit, shown in Figure 5.3, is very similar to that of the leader circuit, andwe will discuss the differences, rather than the similarities. The primary objective of the follower
is to mimic the behavior of the leader stage as fast as possible. The communication between theleader and the follower stages occurs through the local feedback voltage divider network. The

4

4

115
F2_SOURCE

C

5
R24
10

Q15
IXTF1N400
D3
3kV

6

D22
C18
220pF

7

R26
100

D25

R25
510k

Q16
2N6660

D23
15V

R27
2M

R28
510k

C19
1nF
R30
100

+
C16
10uF

R32
400k

R31-A
1.5M

R31-B
2.5M

A

F2_DIVIDER

C11
5pF

B

D26
3.0V

C12
1uF

D27
3.0V

C13
1uF

D28
3.0V

C14
1uF

D29
3.0V

C15
1uF

5

C10
47pF

6

R12
270

F1_DIVIDER

7

F1_SOURCE
8 el sectronic

JILA ELECTRONICS
LABstage of the high-voltage amplifier. Portions of the circuit are boxed to help
Figure5.3: A follower
HIGH
VOLTAGEAMPLIFIER
identify sub-circuits, these include the A) cascode, B) local power supply, and C) local feedback.

SLAVE1:2
DESIGN N.
BY:Fitch / T. BrownBUILT FOR:
Lewandowski
UPDATE:
4/30/2018
VERSION:H DRAWN N.
BY:
Fitch
DN:<DN>DATE:
5/2/2013 SHEET
4 10OF
C
D

B

A

voltage drop across each stages is determined by the current flowing through the voltage divider.
Therefore, any current flowing out of the voltage divider will negatively affect the accuracy of thelocal feedback. However, in order for the voltage divider to act as passive feedback, it must source
the current necessary to control the signal driven transistor in the high-voltage cascode, as shownin Figure 5.1. In order to reduce the current needed to turn on the signal-driven transistor, thecascode circuit on the follower (Q15-16) is a FET-FET cascode. The same IXTF1N400 high-voltage
MOSFET (Q15) is used while the lower voltage, signal-driven MOSFET is a 2N6660 (Q16). Q16
then requires negligible drive current from the local feedback network. The pulldown resistor has
also been changed from 5.11 kΩ to 510 kΩ, which greatly reduces the current drawn from the local
feedback network to keep the gate of Q16 charged. Additionally, the FET that is driven by theexternal signal is faster than the BJT. For the leader stage, the linearity of the signal-driven BJT

8116transistor is important because any nonlinearities on the leader are corrected only through therelatively slow global feedback. For the follower stages, any nonlinearities are corrected throughthe fast, local feedback, so the speed of the signal-driven transistor is more important than thelinearity. While global control, like the optoisolator in the leader, could also be employed on thefollower circuit, only local control, via the resistor-capacitor divider chain, is used. This reduces
the complexity of the follower stage and of the global feedback network overall. Therefore, there isno control signal cascode on the follower, although there is still a local power supply to drive thehigh-voltage FET of the cascode. Additionally, there is no biasing circuitry on the follower stages
as they will follow any biasing on the leader stage.

5.2.3

Feedback and control

The amplifier contains both local feedback between the leader and follower circuits of eachbank via the resistor-capacitor chain and global feedback between the external control signals andthe amplifier. The amplifier is operated via a control board that uses control voltages from anarbitrary waveform generator to generate the required amplifier control signals using a PID loop
for global feedback. Additionally, the control board monitors the output voltage, output current,
and various other values such as the temperature of the amplifier. Ultimately, the global feedback,local feedback, and rail voltages determine the fidelity of the amplified output voltage.
In order for the feedback to function properly, the stages must be biased correctly, which isachieved by having the amplifier connected to a power supply that can keep rail voltages adequately
above the desired output voltage. As long as the stages share the voltage equally, one bank withten stages (one leader and nine followers) can support up to a 30 kV potential difference across it.
Ideally, the output will not swing the full range between the rails, but if it does, one bank will see
the full potential between the two rails. This means the maximum rail voltage should be half ofwhat the transistors in series on one bank can handle. In this design, since one bank is designed tohave a maximum potential difference of 30 kV, a maximum voltage on the rails is ±15 kV.
The power supplies for the rail voltages must be backed by capacitors, so that enough current

117
can be supplied when the amplifiers are active. We use a Spellman SL150 and a 1 µF, 20 kV
capacitor for each rail. The supplies cannot charge the backing capacitors as quickly as they are
drained by the amplifiers, and as a result, the rail voltages sag a small amount during the time theoutput is enabled. The smallest possible capacity backing capacitor should be used in order to avoid
unnecessary energy storage. In the event of an amplifier failure, all the energy may be discharged
through some portion of the amplifier. The more energy that is stored, the more dangerous anddestructive a discharge will be.
Under normal operation, the rails are kept a few kilovolts above the desired maximum output
voltage. The amplifier operates best with at least 100 V across each stage at all times. Thus, with10 stages on each bank, the rail voltages should be at least 1 kV above the maximum desired
output voltage. In practice, especially when running in the 20-30 kHz range, having the rails 2
kV or more above the maximum desired output voltage is preferable, due to the increased current
demands that will increase the voltage sag on the backing capacitors. If the rails sag below thedesired output voltage, the output amplitude will be diminished and will clip until the rail voltage
can recover.
A second reason to keep the rail voltages several kilovolts above the output voltage is to help
produce high fidelity waveforms at higher frequencies. As more followers are added to the circuit,delays in the local feedback chain increase and affect the bandwidth of the local feedback, as wellas the voltage sharing between stages. For example, a delay in the local feedback will cause a timedelay between the leader and the followers. At high frequencies, this time delay may be a significant
fraction of a period, affecting the final output of the amplifier. This causes the control signal toturn on/off the leader more than it would in the ideal case in order to make up the difference
between the desired and actual voltage output. When the leader is driven fully open, it has only avery small voltage drop across it, and then must wait for the follower stages to catch up before thelocal feedback circuit can function again. While this does not lead to instabilities in the amplifier,it does lead to distortions in the output waveform.
To provide the error signal for the global feedback, a custom 20 kV 1500:1 high-voltage divider

118
acts as a high-voltage probe to monitor the amplifier output. The high-voltage divider is designed
to have fast rise and fall times of a few hundred nanoseconds and a relatively flat frequency response
between DC and 1 MHz. This feedback is enabled only when the standing current is running andthe optoisolators are biased on. When not enabled, the local feedback provided by the bias chain
is enough to keep the amplifier output near ground. On the control, board the error signal ishalf-wave-rectified, summed with the DC offset that sets the standing current, and sent to eachbank’s optoisolator LED.
Ideally, the amplifier should have constant gain across the entire frequency range. This ismostly accomplished via careful tuning of the global feedback loop. However, if this is not possible
to do to an acceptable level with a particular amplifier, a linear scaling function can be applied in
the control software, which calculates the input voltage waveform in order to force the amplifier
to have a constant amplitude across the frequency range. This allows a final tuning so that each
amplifier will have the same output voltage regardless of variation in components and assembly.
The control circuitry also contains circuits for monitoring the output voltage and current ofeach bank, the cooling fan speed, and the proximity of the output voltage to the rail. If either of thelast two monitors fall out of their normal operating range, the amplifier is disabled. When running
multiple amplifiers, as is required in TWSD, each individual control board communicates with amaster interlock. The master interlock monitors the pressure and flow of the cooling water to all
amplifiers, error state of the high-voltage power supplies, and error state of all running amplifiers,
all in hardware. If the master interlock detects an error on any one of these channels, it will shut
down all amplifiers.

5.2.4

Physical Construction

The full amplifier consists of two banks each with one leader and nine follower circuits.
Schematically, the source end of the first follower circuit connects to the top, drain end of theleader circuit at the points labeled F1 Source and F1 Divider (Figure 5.3). When connecting
multiple followers, each subsequent follower, n+1, is connected to follower n by incrementing the119numbers at the Source and Divider points by one. Because only n-channel high-voltage MOSFETs
are used, the source of the follower stage connects to the drain of the leader. Since the leader must
always be at the lowest absolute voltage, it must be the source end of each bank. This results inthe top bank leader being referenced to the output voltage (just like QT in Figure 5.1A) and thebottom bank leader being referenced to the negative high-voltage rail. The Source and Divider
points of the last (furthest away from the leader) follower are electrically connected to the positive
high-voltage rail (output) on the top (bottom) bank. This configuration leads to both banks being
identical in construction, but a small asymmetry in operating characteristics, as current is sourced
to the load by the leader of the top bank and is drained from the ninth follower of the bottom bank.
Considerations must be taken into account for the safety of the user and the amplifier including circuit layout, cleanliness, insulation, and cooling. The two banks are carefully constructed inorder to minimize possible damage from capacitive coupling, corona discharge, and arcing, which
all lead to degradation or destruction of the circuit. Sharp points and ragged solder joints on thecircuit board lead to corona discharge, which can corrode components. In order to avoid this, thesolder joints for all through-hole components are rounded off to be smooth hemispheres. The layoutof the PCB uses large ground planes that are isolated from the signal traces to prevent capacitive
coupling. Additionally, the components for the global feedback on the leader stage (Q10-12) arelocated on the underside of the PCB board to reduce crosstalk with the HV signal. Finally, thelocal source planes for each stage are separated by 8 mm to prevent arcing between stages.
Care must also be taken to keep the boards clean and free of dust and grease. All handling of
the amplifier banks was performed while wearing gloves to prevent contamination with oils. Solder
with water soluble flux was used to aid in cleaning. Once populated, the circuit boards were lightly
scrubbed and placed in an ultrasonic bath to remove any flux, oils, or dust.
Even with these precautions, the amplifier can exhibit corona discharges and voltage instabilities. These can be suppressed by insulating the high-voltage circuit boards. Each bank is potted in
an insulating, and thermally conductive, room-temperature-vulcanizing silicone, Insulcast RTVS
3-95-1. This material is chosen for its high thermal conductivity and ease of use. The silicone

120
seals around electronic components when it is applied, but does not adhere strongly. This allows
for repairs to the board with no damage from removing the potting material. Other portions of
the setup that sit at the output potential, including the output cable and feedback probe, are also
potted.
The two potted amplifier banks are installed in a custom high-voltage, shielded box withactive cooling (Figure 5.4). The box is constructed in two layers: an internal, insulating layer
made of polycarbonate, and an external, grounded layer constructed from aluminum. Both layersof the box entirely enclose the amplifier assembly with small holes for signal pass-throughs andventilation. The fully assembled box measures 3 inches tall, 17.75 inches wide, and 8 inches deep.

Figure 5.4: A photograph of the amplifier with the top lids removed. The cables between therail voltage supplies and the amplifier are on the right and the output, which can connect to thedecelerator, and the probe for global feedback are on the left. For the top (bottom) bank, theleader TL (BL) and last follower TF9 (BF9) are labeled.

The walls of the box where the high-voltage MOSFETs are mounted must simultaneously
provide electrical isolation and cooling to the amplifier banks. The IXTF1N400 MOSFETs handle
the majority of the voltage drop across each stage, and thus the majority of the power dissipation.
If the amplifier runs from rail to rail at ±15 kV and at 30 kHz, the high-voltage MOSFETs will eachdissipate 340 W, which is nearly impossible to remove via water cooling. By running the amplifiersin a pulsed mode with only a few percent duty-cycle, as they would be during TWSD, the heatgenerated drops to roughly 10 W per MOSFET. While this thermal load is manageable, watercooling of the MOSFETs is required. Typically, the MOSFETs can be cooled directly throughthe isolated back tab, which is normally held at ground. However, because each stage floats many

121kilovolts above earth ground, the MOSFET back tab can not be grounded. Instead, the back tabof each MOSFET is electrically connected to its source. Thus, cooling the MOSFETs requires amethod that is thermally conductive, but electrically insulating, so that the source plane of each
MOSFET remains isolated from all the other MOSFETs. To accomplish this, the sides of thebox have boron nitride sheets set into the polycarbonate and water cooling lines are run throughthe grounded, metal sides. Boron nitride is a ceramic with good thermal conductivity and is also
electrically insulating. The boron nitride is sandwiched between the MOSFET and the watercooled aluminum wall, thus maintaining insulation between the large potential differences of the
MOSFETs and the exterior grounded box. The boron nitride pieces are glued in place using MG
Chemical’s 4226 Super Corona Dope. The interior wall and the outer aluminum wall are screwed
together and thermal paste is applied between them on the boron nitride portions in order tofacilitate cooling. The IXTF1N400 MOSFETs are mounted such that their back tab is in directcontact with the boron nitride.

5.3

Amplifier Performance

5.3.1

Testing Setup

The amplifier is tested on the bench using a high-voltage capacitor, Cl , connected as a test
load to substitute for the Stark decelerator. A schematic diagram of the testing setup is shown in
Figure 5.5. The amplifier has been tested with loads that vary from 125 pF to 500 pF in order totest different current requirements without changing the output voltage. A 10 Ω sense resistor isplaced between the load capacitor and ground in order to monitor the load current. A Tektronic
P6015A 1000X probe is used to measure the output voltage of the amplifier.
The amplifier is tested with single frequency and chirped sine-wave pulses 1-5 ms long, as
well as with low frequency square-wave pulses. The length of the pulses is limited by the size ofthe backing capacitors. With larger capacitors or a power supply capable of sourcing 1.5 A, thelength of the pulses would be limited only by the cooling of the amplifier. Single-frequency pulses

122

Vin
+15kV

Fdbk
In

PID

Out

1F
HV
AMP

-15kV

1F

Cl

V
1000x

10

V 1x

Figure 5.5: The test setup for measuring the output voltage and current. The 250 pF capacitor
acts as the output load. The 1000X probe is used to measure the output voltage of the amplifier.
The 10 Ω resistor is a current sense resistor and the 1X probe is used to monitor the output currentof the amplifier. All components other than the 10 Ω sense resistor must be rated for high-voltage.

are used to characterize gain, phase-slip, and distortion across the bandwidth of the amplifier.
Square-wave pulses are used to characterize rise and fall times, and time delays. Finally, while
there are many types of sinusoidal pulses that can be used to decelerate molecules, linearly chirped
sine-wave pulses are shown because they will be the signals used most typically with traveling-wave
Stark decelerators.

5.3.2

General Specifications

The general specifications for the amplifier are listed in Table 5.1. The amplifier is designed
for a peak output voltage of ±12 kV, but has only been tested in this work to ±10 kV in order tomaintain linearity and stability. Thus, the gain is designed to be 12,000 with a maximum input of±1 V. The design goals for the amplifier emphasize bandwidth, output voltage, and current. The
bandwidth of an amplifier can be classified in a number of ways, with the most common being the-3dB point of the amplifier’s gain curve. The gain curve for our amplifier, under three different loadconditions, is shown in Figure 5.6. The gain curve shows relatively little deviation from the target
gain of 81.6 dB, especially for the 250 pF load, indicating that the amplifier bandwidth extends
beyond the target of 30 kHz. The amplifier was not tested above 30 kHz at 20 kVpp because the123
local feedback may not be fast enough to ensure even voltage distribution between the stages, anda single stage may be overvoltaged. However, tests at 10 kVpp show the -3 dB point to be beyond
40 kHz for all load capacitances tested.
Table 5.1: Technical parameters of the amplifier.
Parameter
Max input voltage range
Output voltage range
Gain
Load
Peak Current
Bandwidth
Noise
Harmonic distortionc
Supply voltage

Value
±1V
± 10 kV
12,000
up to 500 pF± 1.5 A
>30a or 23b √kHz
300 µV / Hz
1.4 %± 15 kVa

Calculated from gain fall-off
Calculated from THD measurements. Limit 5% THD
on 250 pF loadcMeasured at 10 kHz with a 500pF loadb82.5

140 pF250 pF500 pF

Gain (dB)

82.0
81.5
81.0
80.5 05

10 15 20Frequency (kHz)25

30

Figure 5.6: Measured gain of the amplifier. The solid horizontal line is located at 81.6 dB, which is
the target gain of the amplifier. The gain was measured using an input single-frequency sine wave
with a peak-to-peak amplitude of 1666 mVpp .

While the gain curve indicates a bandwidth greater than 30 kHz, the quality of the amplifier

124
output begins to deteriorate beyond 18 kHz. One measure of output signal fidelity for high-voltage
amplifiers is Total Harmonic Distortion (THD) [177]. THD compares the amplitude of the Fouriercomponent of the peak frequency against the amplitude of all higher-order harmonics, and indicatesthe distortion from an ideal, single-frequency wave. If Vn labels the nth harmonic amplitude, thenTHD is defined as:

v
u∞
X
1u
t
THD =
Vn2 .
V1

(5.2)

n=2

Distortion of the sine wave will appear “smooth” if the amount of power in the higher harmonics
decreases with increasing harmonic number. An example of two output waves with their Fouriertransforms is shown in Figure 5.7. Although the 30 kHz waveform shows a significant THD of
11%, the distortions appear smooth due to the decreasing power of the higher-order harmonics. An
analysis of the THD across the frequency range shows that the THD stays below 2% for frequencies
below 18 kHz. The THD then rises sharply for frequencies above 18 kHz to a final value of 11% at
30 kHz. For Stark deceleration, the primary requirement is that the amplifier reach the required
voltage and operate at the required frequency. Smooth distortions will slightly change the edgesof the Stark potential well, but are not likely to strongly affect the deceleration of the molecules,
particularly since these distortions occur when the molecules are moving at high speeds, where themolecular packet is less sensitive to non-ideal potentials.
Because of the smooth nature of the distortion and the primary reliance of Stark decelerationon the absolute amplitude of the signal, we will consider both the THD and the gain when determining the bandwidth of the amplifier. For applications where amplitude is a primary concern,
the bandwidth is greater than 30 kHz. For applications where waveform fidelity is of concern,a bandwidth of 18-20 kHz is more relevant. The relatively large amplitudes of the even-orderedharmonics indicate an asymmetric distortion between the positive and negative sides of the wave,
which is evident in the time-domain waveform. This is due to the asymmetric nature of the all-nchannel-MOSFET amplifier construction noted earlier.
The output voltage of the amplifier was tested at ±10 kV. The gain curve shown in Figure

125

Amplitude (V)Amplitude (kV)

4 kHz
10

30 kHz(a)(b) 10

0
10
0
103

0
250 500 750 0
Time ( s)

(c)

50
100
Time ( s)(d) 103

101

10 10

10

101
25 50
Frequency (kHz)0200 400 10
Frequency (kHz)1

Figure 5.7: Measured output sine waves and their respective Fourier transforms for 4 kHz (a, c)and 30 kHz (b, d) input sine waves on the 250 pF load capacitor with ±13 kV rails. The x-axes
are scaled such that there are the same number of periods (3) and harmonics (15) shown for eachof the frequencies. (a) The time domain and (c) frequency domain response for a 4 kHz input sine
wave have a calculated THD of 0.7 %. (b) and (d) are the same for a 30 kHz input sine wave, witha calculated THD of 11.0 %.

5.6 was taken with a constant amplitude input sine-wave of 1666 mVpp , and shows a near-constantgain of 81.6 dB, giving a constant output of 20 kVpp across all frequencies. As tested, the amplifier
reached a peak current of 860 mA, while driving the 500 pF load at 30 kHz. This is significantly
above the 500 mA needed to charge the 250 pF load of our Stark decelerator.
Additional tests were performed with a square wave to measure rise and fall times andtime delays. The results of these tests are summarized in Table 5.2. The values for rise and falltimes highlight the asymmetry introduced through the all-n-channel-MOSFET construction of theamplifier banks. While the fall time, controlled by the bottom bank sinking current from the load,
is dependent only on the capacitance of the load, the rise time is dependent on both the capacitanceand on the output voltage. This indicates that the output current that the top bank can source isdependent on how far the output voltage is from the rail voltage.

126

Table 5.2: Small-signal amplifier parameters. Rise and fall times, tr and tf , and delay d weretaken with a 1 kHz square wave with an output of V on a load capacitance of Cl . The rails were
held fixed at ±11 kV.
V
kVpp
10
12
10
12
10
12
a

Cl
pF
125
125
250
250
500
500

tr
µs
3.9
4.8
4.2
5.3
4.9
5.6

tf
µs
3.4
3.4
4.4
4.4
6.2
6.2

d
µs
2.8
2.8
3.2
3.2
3.9
3.9

Sa
V/µs
2590
2530
2320
2260
1630
1920

Slew rate is calculated from peak amplitude and thelarger of tr or tf .

127
Voltage Sharing

1.50

4 kHz
20 kHz
30 kHzVoltage Sharing Ratio

1.45

Amplitude (kV)

5.3.3

1.0
0.5
0.00

1.40

L
F9
50
Time ( s)

1.35

1.30
2

3

4
5
6
7
Amplifier Output (kVpp)

8

Figure 5.8: Ratio of voltage dropped between the final follower stage (F9) and the leader stage(L) on the bottom bank for three different frequencies. The voltage sharing for high frequencies
is poor at low voltages, but stabilizes as the output voltage increases. All data were taken withrail voltages of ±6 kV. The inset shows the waveforms for the voltage across the leader and final
follower at 30 kHz and at 8 kVpp . The point at which these data were taken is highlighted on themain plot with the red star.

Voltage sharing between the stages of the amplifier via the local feedback is critical to thestability of the amplifier in order to assure that no single stage is over-voltaged under any conceivable
operating conditions. In order to asses the quality of voltage sharing between stages of one bank, thevoltage across each stage is measured by separately probing the voltage at the source end and thenthe drain end of each stage and then subtracting the signals during post-processing. The sourceand drain ends of the stage need to be measured separately, or crosstalk between the measurement
probes’ leads can inject current into the stage and drastically alter the stage’s functionality.
The largest voltage difference occurs between the stage that is closest to the rails and the128stage that is closest to the output. For the bottom bank, these are the leader and ninth follower
stages, respectively, and vice-versa for the top bank. The behavior of the two banks is similar, andthe following discussion refers only to the bottom bank. The ratio between the voltage across theninth follower stage to the voltage across the leader stage is shown in Figure 5.8. Data were taken
at 4, 20, and 30 kHz, and at amplitudes from 2 kVpp to 8 kVpp . Higher amplitudes were not tested
because measuring voltages across stages requires probing inside the amplifier while it is running,which requires the potting material to be removed from the circuitry. This, in turn, decreases thestability of the amplifier, and increase the likelihood of corona effects at high voltage.
Figure 5.8 shows that while higher frequency signals cause the amplifier to share poorly at
low voltages, increasing the output voltage increases the stability of the local feedback network athigh frequencies. The voltage across the final follower stage reached about 1.33 times the voltage
across the leader. The inset shows a sine fit of the measured voltage on both stages. While theamplitude difference is clear, there is very little phase shift between the two signals.
The voltage sharing ratio is a measure of how well the voltage is distributed across the entire
amplifier bank. If the ratio is too large, the ninth follower stage could experience too large a voltage
drop, and could become overvoltaged. To determine if the measured sharing ratio of 1.33 is low
enough to allow the amplifier to produce a ±10 kV sine wave with ±13 kV rail voltages without
overvoltaging any stage, we consider the following calculation.
The mean voltage across a stage, V , is defined as one tenth of the voltage across an entirebank, and is the ideal case for the amplifier. A voltage sharing ratio different from unity indicatesthat the voltage across the leader and ninth follower are offset from V . Measurements of this offset,
Voffset have shown that it is symmetric about V for the leader and the ninth follower. Thus, thevoltage drops across the leader and ninth follower are VL = V − Voffset and VF 9 = V + Voffset . The
sharing ratio is then defined asR=

VF9
V + Voffset=.
VL
V − Voffset

(5.3)

129
The maximum value for the voltage across a single stage, Vmax , is set by the protection diodechain to be 3 kV. The ninth follower stage is at a higher voltage than the leader stage, and may
potentially rise above the diode threshold voltage. This sets a bound on the maximum allowable
voltage offset ofVoffset < Vmax − V .

(5.4)

Combining Equations 5.3 and 5.4 gives an upper bound on the acceptable value of the voltage
sharing ratio of

R<


−1
V
2
−1
.
Vmax

(5.5)

For the amplifiers to safely produce an ±10 kV sine wave with rail voltages of ±13 kV, eachbank must be able to withstand a maximum of 23 kV, which sets V to 2.3 kV. R must then beless than 1.875 in order for no stage to be overvoltaged during normal operating conditions. The
measured R value of 1.33 is well below this maximum value. Therefore, we do not anticipate thissmall voltage sharing error to limit the performance of the amplifier.

Amplitude (kV)

5.3.4

Chirped sine waves

10
0
10
0.0

0.2

0.4

0.6
Time (ms)

0.8

1.0

1.2

Figure 5.9: A linearly chirped voltage waveform from 30 kHz to DC at ± 10 kV. Fewer periods
than would be used for TWSD are shown for clarity, and three start-up periods are appended to
the front of the wave packet in order to prevent large start-up current spikes.

Ultimately, the amplifier will be used for TWSD and must be able to output a chirped
sine-wave voltage with uniform output amplitude across the frequency range. A sine-wave chirped

130
from 30 kHz to DC at ±10 kV output voltage is shown in Figure 5.9. Here, for clarity, a moreaggressive chirp is shown than would typically be used in TWSD. A typical deceleration waveformin our decelerator would have 78 periods in 6 ms. A DC hold is also demonstrated, as this would
be required for trapping the molecules. Additionally, a three period start-up sequence, where theamplitude is increased linearly to the operating voltage, is appended to the front of the waveform
to prevent the large current spikes necessary to start a sine wave at arbitrary phase from ground.
The high frequency part of the waveform shows distortions similar to those in Figure 5.7, while thelower frequency part is free of distortions.

5.4

Conclusion
A new type of Stark deceleration technique called traveling-wave Stark deceleration promises

to greatly increase the number and density of cold, slow molecules produced compared to traditional
pulsed-pin deceleration. The challenge to implementing TWSD lies in creating high-voltage analog
amplifiers with demanding specifications. The bandwidth, voltage, and current requirements needed
to bring a supersonic beam seeded in krypton down to rest in 1.25 m are not available in any
commercial high-voltage amplifier. The amplifier presented here is capable of output voltages up
to ±10 kV, instantaneous currents up to 1.5 A, and a frequency range from 30 kHz down to DC,
which will allow for deceleration of a molecular beam with an initial velocity of >450 m/s down
to rest. We have quantitatively measured the voltage sharing error between stages and the totalharmonic distortion. We demonstrated that despite small deviation from ideal performance, theamplifier can operate over the full design frequency range. Additionally, the flexibility of theseamplifiers can allow for not only traveling-wave Stark deceleration, but also efficient trap loading
and manipulation.

5.5

Individual amplifiers
Each individual amplifier setup consists of an amplifier box (which contains the two banks),a high-voltage probe, a breakout box, and a control board. The circuits for all these components

131
can be found in Appendix A. Figure 5.10 shows the amplifier, probe, and breakout box. The 20
kV 1500:1 probe is separate from the amplifier box and plugs into the amplifier via an Amphanolhigh voltage connector. The probe can be attached via screws so that it cannot be accidentally
removed. The amplifier is run by a control board, of which the front panel is shown in Figure 5.11.
Two control boards are mounted in each panel mounted box, and the left edge of the second control
box can be seen in the Figure. The control box converts the input commands and feedback signals
into drive signals for each amplifier bank. The inputs are a manual enable switch, TTL enable
input, control voltage (labeled VIN), and +12 V power for the amplifier fans. The two enable
signals dictate when the global feedback for the amplifier is active. The three monitors provide
low voltage output monitors for the output voltage (VOUT) and top and bottom bank current(ITOP and IBOT). Lastly, the control board also contains knobs for adjusting the proportional
and integral gain for the amplifier global feedback and eight indicator LEDs. From top to bottom
the error LEDs (red) indicate: fan error, fan error latched, rail error, and rail error latched. The
errors latch so that any failures that are too fast to observe by eye can still be caught. Once theamplifier detects an error it turns off until the error is no longer present and the clear button has
been pressed. Error monitors can be disabled via jumpers on the control board. The four status
LEDs (green) indicate: amplifier “ok”, amplifier enabled, standing current enabled, and tuning
mode. Each goes green if that state is true. The amplifier ok state indicates that there are no
detected errors.
A breakout box communicates between the control board and the amplifier/probe. It reads
in the voltage from the high-voltage probe, contains the probe compensation circuit, and separates
out the control and monitor signals signals from a 50-pin cable into three 8 pin connectors. Ethernet cables are used for the 8 pin connections because they are a convenient shielded cable andcommercially available in many styles. The three ethernet cables contain the control and monitor
signals for the top bank, bottom bank, and fans.
Each assembled amplifier must be tested and tuned on the bench before it is placed on the
decelerator. A picture of the testing setup diagrammed in Figure 5.5 is shown in Figure 5.12. For

132

Figure 5.10: A potted high-voltage amplifier with its probe (left) and unattached breakout box(top). Holes have been cut into the potting material to allow for placements of probes for current
tuning. The probe (left side) plugs into the amplifier via an Amphanol high voltage connector.
When in opperation, the probe is connected to the breakout box using a BNC cable (not shown).
On the right side of the amplifier box, two Amphanol high voltage connectors provide connections
to the positive and negative high voltage rails and two fans provide additional cooling. Three
ethernet cables (not shown) make the connections between the the breakout box and the amplifier.
The ethernet cables provide control signals for the top and bottom bank and carry power power tothe cooling fans.

Figure 5.11: The front panel of the amplifier control box. The manual enable switch, TTL enable
SMA input, and Vin SMA input are noted by red arrows. The manual enable switch and TTL
enable SMA input together control the output state of the amplifier. The desired chirped sinewave
control signal is set via the Vin SMA input.

bench testing, in addition to the amplifier, probe, breakout box and control box from Figure 5.10,
a low-voltage power supply, a high-voltage power supply, backing capacitors, arbitrary waveformgenerator (AWG), and a digital delay generator (DDG) are required. The low-voltage supply
provides the +12 V fan power, and the high-voltage supply and backing capacitors provide therail voltages for the amplifier. The AWG creates the sine-wave control voltages, which are fed
to the control board. The DDG triggers the AWG and creates the TTL amplifier enable signal.
The enable signal must begin ahead of the AWG trigger so that the standing current begins ahead

133

Figure 5.12: The high-voltage amplifier must be first tested on the bench to ensure equal sharing
between stages and faithful input/output voltages. For bench testing, in addition to the amplifier,probe, breakout box and control box from Figure 5.10, a low-voltage power supply, a high-voltage
power supply, backing capacitors, AWG, and a DDG are required. Since often the amplifier top is
open during testing so that probes can be place, the setup should remain as clean as possible.

of the sine-wave signal. An additional fan (not shown) plugged into the same power strip as thehigh-voltage supplies is often helpful as a audible reminder that the high-voltage is on. The power
strip should be switched off whenever the high-voltage supplies are turned off.

Figure 5.13: The amplifier can be carefully probed at both test point and at jumper connections.
Here two probes have been place in the jumper connections in follower 9 of the top bank. This is
not an ideal configuration since the probes are relatively close to one another (see text).

A special lid for the amplifier was created for individual testing so that probes could be
inserted into the amplifier (Figure 5.13). This setup allows access to the interior of the amplifier so
extreme care must be taken when testing. Testing should never be completed alone. The test bench

134should remain as clean as possible since the amplifier lid is often open. Each amplifier stage canbe probed in test points (labeled TPx) and at jumper connections (labeled Jx) where x represents
the component number which is different on each stage. To probe test points, a Tektronic P6015A
1000X probe is connected to a high-voltage clip cable, which can be attached to the test point.
To probe a jumper connection, the Tektronic probe is connected to a stiff high voltage wire thatmatches the gauge (19 SWG) of the jumper connector. Since the wire that runs between theprobe and board is not insulated, cross-talk can occur and change the measured signal. Thus it isimportant to keep the high voltage wires from crossing and away from other cables. Cross talk canlead to incorrect measurements, and it is important to remember that probing the amplifier circuit
can easily change its behavior. While multiple probes can be placed on the amplifier as shown in
Figure 5.12, care must be taken as to where these probes are placed because what is measured may
not be what is actually happening due to the probe impedance changing the normal behavior of
the amplifier. For a full step by step procedures for tuning and testing see sections 6.5.2.1 and 6.5.3of [95] respectively.

5.6

Insulation

5.6.1

Amplifier bank

The original amplifier design presented in [95] is prone to current instabilities at output
voltages larger than ±6 kV. In addition to the oscillation caused by the voltage limiters discussed
in section 5.8, two other types of oscillations show up. The first kind is persistent and occurs on
the falling edge of the current oscillation. It was found on all sixteen amplifiers that have been
built. The second type of oscillation causes a dramatic dip in the output current 10-20 µs wide,
but only occurs sporadically.
The first persistent current oscillation is dependent only on the output voltage and not on
the voltage across a stage (number of enabled stages) or current (load capacitance). For example
it will appear with ±8 kV output voltage using ten stages on each bank but not at a ±4 kV output

135
voltage using five stages on each bank regardless of the output load. It is frequently observed on thefalling edge of the current oscillation which corresponds to the positive peak output voltage of theamplifier, as shown in Figure 5.14a. This oscillation is most easily seen in pictures of the oscilloscopesince infinite persistence traces are very difficult to save to data files. Infinite persistence is used
to capture all the different current oscillation behaviors and to show that the oscillation does notoccur in the same location in time on each shot. It is also useful when debugging the amplifier,since it will catch spurious behavior that occurs only in a small percentage of the iterations of theoutput.

(a) Current oscillations issue(b) With the addition of SF6 the current oscillation issue is almost entirely suppressed.

Figure 5.14: ±8 kV output without (left) and with (right) the amplifier box filled with SF6 . The
output voltage is shown in green and the output current as measured across the sense resistor isshown in blue.

Figure 5.15 shows a close-up on the type of oscillations seen in Figure 5.14a. This type ofoscillation had a very repeatable frequency character and examinations of multiple oscillations at
different amplitudes all resulted in similar frequency responses. The oscillations begins with a fastand quickly decaying 130-140 MHz oscillation follow by a 12 MHz slower decay.
In each shot of the output, only a few oscillations occur. The picture in Figure 5.14a contains
97 shots of the experiment and many oscillations are overlaid. Although the oscillations do notalways appear in the same place in time on each shot, they remain contained to the positive fallingedge of the current. The largest oscillations always occur on the first one or two periods of theoutput current sine wave. This was true even at different output frequencies. There is also a

136

Figure 5.15: A close-up of the persistent oscillations seen in Figure 5.14a. The oscillations have
two characteristic frequencies, an initial fast response at 130-140 MHz and a slow response at 12
MHz.

137
smaller oscillation that appears on the negative rising edge, but since it does not grow significantlywith the output voltage, we were not very concerned about it. These oscillations typically started
at a threshold output voltage of ±6-8 kV and their behavior had some hysteresis. As the output
voltage was slowly increased there would not be oscillations below a threshold voltage. Once theoscillations began, if the output voltage was adjusted to be below the previously observed thresholdthe oscillations would remain. However, if the amplifier was turned off for a few minutes and thenturned on again at a voltage below the threshold there would be no oscillations.
Although both of these types of oscillations were not previously reported in the version of theamplifier in [95], these instabilities occur frequently on all sixteen of the amplifiers that have been
built. These oscillations do not appear to affect the output voltage at moderate output voltages(±6-8 kV), but since they grow in amplitude at a faster rate than the output current amplitude
we have chosen to address them before they caused significant problems. It is suspected that thesecurrent instabilities are caused by corona discharge. In a very dark room, a few faint blue corona
spots could be seen particularly at the corners of the vertical FET wall.
Originally, the amplifier circuit boards were coated with Super Corona Dope (MG chemicals),a one-part insulating coating. However, this did not improve the corona discharge situation. It also
made repairing the amplifier boards more difficult. A soldering iron can burn through the clear
and hard cured Super Corona Dope, but this had to be done in a very well ventilated area. In
discussions with the manufacture, we learned that although it has a rating of 4100 V/mil, this is
not linear and does not build with thickness. The coating was also designed for coils and not PCB
boards so it was not suited for our applications. We also tried Silicon Conformal Coating 422B
(MG Chemicals) to address the corona discharge, but again found no improvements.
While in the initial design it was suitable for the circuit board to just be in air inside thespecially designed box, an insulating gas or potting material significantly improved the performanceof the amplifier and greatly reduced the current oscillations. Two dielectric mediums that are often
used in high-voltage circuit breakers and switches are oil and SF6 gas. We did not test oil due tothe difficulty of containing it and making repairs to anything that has been submerged in oil. SF6

138

Figure 5.16: 50 shots at a 1 Hz repetition rate of ±12 kV output at 5 kHz using an amplifier filledwith SF6 . The output voltage is shown in green and the output current as measured across thesense resistor is shown in blue.

has a much higher dielectric strength then either air or dry nitrogen. The amplifiers were tested in
SF6 and it dramatically reduced the oscillations. It did not make the oscillations disappear entirely,
but this may have been due to the difficulty of keeping the amplifier boxes gas tight.
Figure 5.14b shows an amplifier with the same output voltage and current as Figure 5.14a,but with the addition of SF6 . For this ±8 kV output, the current oscillation issue is almost entirely
suppressed and indicates that corona discharge and other high-voltage insulation and isolation
issues are the cause of this type of current oscillation. Thus with improved insulation, the current
oscillation should be suppressed. With SF6 the amplifier was able to go up to our design specificationof ±12 kV without significant current oscillation issues (Figure 5.16).
SF6 was tested in two configurations, initially by placing the amplifier in a sealed glove bagand later by sealing the box shut with tape and adding a tube to evacuate the inside of the amplifier
and fill it with SF6 . Neither of these methods produce very gas tight seals, but the SF6 remains in
the amplifier box long enough (a few minutes) to make measurements. The tape method produces
an weaker seal, but it was a easy modification, used less SF6 , and allowed for better access. In the
glove bag configuration, in order to limit the number of wires and tubes that entered and exited thebag, the entire breakout box, all ethernet connectors, and the probe were also place inside. If the
setup was left for several hours, oscillations would usually return, indicating that SF6 had leakedout and had been replace by air. All tests with SF6 were run with the entire test setup was placed

139
Table 5.3: RTVS 3-95-1 properties
Viscosity
Pot life 25◦ C
Cure time 25◦ C
Share A hardness
Thermal conductivity
Dielectric strength

10,000 cps
1.5 h
24 h
65
1.25 W/(m K)
500 V/milin a fume hood.
While SF6 showed promising results for solving the oscillation issues, it its not a practicallong-term solution. The amplifier box design requires two high-voltage inputs, two high-voltage
outputs, and two ethernet connections, which carry the low-voltage control signal, and one more
ethernet to power the fans and monitor their status. Due to the difficulty of constructing a gas-tightbox that can accommodate these connections, in addition to the cooling requirements, we chose touse a potting material to encapsulate the amplifier banks instead of SF6 gas. The requirements forselecting a potting material were high dielectric strength, high thermal conductivity, and low viscosity. We selected Insulcast RTVS 3-95-1, which has the bonus feature that the silicone compound
does not bond with most materials and can be removed for repairs without damaging the electricalcomponents. This means potting is not permanent and allows for repairs, which are tedious but
possible. When removing the potting material, care must be taken to not rip up any components(most typically the test points). Although the material does not bind to any of the components,
it does seep under anything that is not soldered down. Thus, if it is removed in large chunks, thecomponents can be ripped off the board. The only material that we found that RTVS 3-95-1 did
not easily release from was glass. It also does not cure properly when it comes into contact withvarious adhesives. The properties of mixed RTVS 3-95-1 are listed in Table 5.3.
Initially, only a thin coating of RTVS 3-95-1 was used on each amplifier bank (Figure 5.17).
However, with just a thin layer on the banks the oscillations did not diminish. Placing the thinly
potted banks back into a sealed box, and adding SF6 improved the behavior of the current indicatingthat there was not sufficient insulation. In the end, the banks were potted into bricks (Figure 5.18).

140

Figure 5.17: A thin layer of RTVS 3-95-1 potting material on one amplifier bank. This was notenough potting material to stop the oscillations and adding SF6 gas to the box improved theinsulation(a) Potted amplifier bank immediately after it isreleased from the mold.

(b) Potted amplifier bank with high voltage connection points cut out.

Figure 5.18: Two fully potted amplifier banks. Cut out high-voltage connection points can be seenon the front-left corner of the picture on the right.

This has the added benefit of stabilizing the optoisolators, which have very fragile solder connections
due to the very fine (45 gauge) wires, and which must support to ethernet communication receptacle.
At this point, adding SF6 to the amplifier box no longer had any affect. Although the fully potted
amplifier did not perform quite as well as the amplifier in SF6 , it was still a significant improvement
over a non-potted amplifier.
RTVS 3-95-1 is a two part room-temperature-vulcanizing silicone. Part A (red) and part B

141(clear) are mixed in a 20:1 ratio. A new can of Part A always arrives slightly separated and must be
well mixed (at least 10-15 minutes) before weighting out the two parts. Part B does not require any
premixing. When first mixed, the material has the consistency of thin honey and takes 24 hours tocure, though a bit longer to reach the final stiffness. Mixing introduces many air bubbles, so the
mixture is evacuated in a bell jar. this produces a smooth finished product. The evacuated mixture
must be poured into the mold slowly to ensure that no air bubbles are trapped in the underside of
the circuit board. Once released from the mold, the finished potted amplifier bank is very smooth.
Any wrinkles or soft spots indicate large air bubbles underneath, these can be repaired by cutting
open the air pocket and filling it again with RTVS 3-95-1.
The amplifier boards are potted while attached to the outside wall via ‘L’ shaped brackets
and nylon screws. A mold is constructed of PVC and polycarbonate pieces and held together withmodeling clay and double sided tape. This allows the mold to be easily released, wiped down, andused again. Although the tape causes the corners of the mold not to cure, any soft corners or edges
can easily be shaved off with a razor blade once the mold is removed. Small plugs were placed in
the high-voltage rail and output connection points before pouring in the potting material in orderto keep the connectors clean from the silicon. After the silicon cures, the plugs are cut out andremoved (Figure 5.18b). This can be done fairly easily with a small razor blade.
Potting the amplifier banks helped to eliminate many of the first type of oscillation but asecond type of sporadic oscillation was still present. The second type of oscillation was found tooccur when the pink high-voltage wire that comes with the Amphenol Alden high-voltage connectorleans against polycarbonate. This insulated wire (pink) is 22 AWG and rated up to 30 kVDC.
However, the connector (white) is only rated to 25 kVDC. While the first type of oscillation was ahigh frequency and symmetric oscillation, this one has a high frequency spike followed by a muchslower dip, Figure 5.20. The dip always followed the direction the current was already going, butwith a steeper slope. Whenever this oscillation occurred, a simple rearranging of the high-voltage
wires inside the amplifier box or output cable could resolve this issue. Keeping the length of pinkhigh voltage wire inside the amplifier relatively short reduces these oscillations because there is less

142
wire to accidentally curl up and touch the interior polycarbonate box.
This oscillation with a dip also occurs when pressure is placed on the output cable thatconnects the amplifier and the load. For the input and output cable on the amplifier, we use
in-house built cables made from Amphanol Alden A401QX and A800QX connectors, the QX wirethat comes with the Amphanol connectors or other 30 kVDC HV wire, additional insulation, anda ground shield. Figure 5.19 shows a cross section of the cables used with the TWSD setup. The
high-voltage wire is placed inside 3 mm wall Tygon tubing. The cable is then surrounded by groundbraid, which shields against noise and pickup and provides protection should all insulators fail. The
left cable in Figure 5.19 has been used for high-voltage switching in our PPSD experiment withgood success. However, with the sine-wave voltages from the amplifier output, there are occasional
current and voltage dips. These can usually be eliminated by adjusting the angle of the output
cable, which suggest that the issue again stems from the position of the interior high-voltage wire.
To remedy this, the space between the Tygon tubing and wire is filled with the same RTVS 3-95-1
potting material as the amplifier circuit board (right cable Figure 5.19). The input cables to theamplifiers that just sit at the high-voltage rails are not potted.
The increased insulation adds extra capacitance of 20-40 pF/ft to the cable. The amplifiers
are mounted such that they are as close as possible to the vacuum electrical feedthroughs, but are
still mounted practically. Each cable from the amplifier to the decelerator is ∼2 ft. From Figure
5.6, even with the additional capacitance and current draw, this will not significantly affect the
behavior of the amplifier.
The high-voltage probes are also potted, which further reduces current noise. While someprobes were potted with RTVS 3-95-1, we found it easier to pot them with Hysol ES1001 since it
is easier to prepare and has a lower viscosity. The high-voltage probes are very reliable once built
and all tunning is done externally, thus potting them with a non-removeable material is not an
issue.

143

Figure 5.19: Cross section of the custom high voltage cable used in the TWSD setup. A RTVS
filled cable (right) is used if it carries an AC voltage, non-potted cables (left) are used to carry DC
voltage, such as from the Spellman voltage supplies to the amplifier.

Figure 5.20: Current (blue) dips caused by proximity to polycarbonate. Usually current oscillations
do not affect the voltage (green) on the decelerator, but when the current issues are severe enoughthey also cause droops and bumps in the output voltage.

5.6.2

Amplifier walls

High voltage isolation is not only a concern for the amplifier circuit board, but also for theamplifier box. The two layer box consists of an interior primarily polycarbonate box for electricalisolation and an exterior grounded aluminum box. Two sides of the polycarbonate box not only had
to provide voltage isolation, but also cooling for the IXTF1N400 FETs. A piece of boron nitride, athermally conductive, but electrically insulating ceramic, is set into two sides of the polycarbonate
wall to allow for heat exchange between the FETs and the exterior aluminum walls, which are watercooled. Although Super Corona Dope was found to be not useful for the amplifier boards, it wasused to seal the space between polycarbonate and boron nitride in the FET walls of the box. It
serves as a dielectric glue that holds the boron nitride in place. Figure 5.21a shows a picture of just144
the polycarbonate and boron nitride wall. It is then affixed to the aluminum cooling wall by screws
through the aluminum wall and into blind tapped holes in the polycarbondate. These screws should
not be any more then finger tight, tightening them will flex the polycarbonate wall and cause cracks
in the Super Corona Dope seal. Thermal paste is applied between the walls to facilitate thermal
conductivity. Building these walls is a tedious process that involves filling the gap between theboron nitride and polycarbonate in many steps. The boron nitride and polycarbonate have a step
cut into it in order to increase the path length between the FET wall and the grounded exteriorwall. Due to the small space that needed to be filled, the surface tension of the Super Corona Dopecauses many air bubble to form, thus it must be applied in thin layers and the bubbled popped
each time before it cures. Each layer must begin to cure (∼6 hours) before the next layer can beapplied. This is most easily done with a 23-25 gauge hypodermic needle so that the bubbles canbe released as each layer is applied. While this method creates wall that are able to sustain a 20
kV difference for at least 5 minutes, there are probably filling materials for this application which
could be easier to use. If the walls were to be remade, the electrically insulating but thermallyconductive panel could possibly be made out of the same RTVS potting material used to insulate
the amplifier instead of boron-nitride. However, this would make them incredibly fragile and othermore rigid potting materials should be explored.

Figure 5.21: The interior insulating polycarbonate wall with boron nitride inserts. Each side walluses two boron nitride pieces (A). The black scorch mark on the right-hand side shown a point
where the wall failed. A close up of the inset boron nitride (B) shows the step that increases thepath length between the aluminum wall and the back plane of the FET.

145
Once assembled, the walls must be tested to ensure that they can withstand 20 kV. It iseasiest to test the walls without thermal paste initially. This way the walls are much easier andless messy to repair. Once the walls have passed the isolation test, thermal paste should be applied
and the wall tested one last time. The test set up should use no backing capacitors and have a low
current limit. The outside wall MUST be grounded at all times. The voltage should be increased
slowly so that if the wall fails, it fails at the lowest voltage possible.
Wall failures are audible and visible if the lights are low. Once the wall is no longer athigh voltage, the failure point should be visible when the polycarbonate wall is removed from thealuminum wall. The failure point will usually leave a fairly noticeable scorch mark on the step
portion of the boron nitride and a small mark on the aluminum wall. Occasionally the Super
Corona Dope will turn yellow and brittle at the point of failure. Wall failures are almost always
caused by air bubbles in the Super Corona Dope. While from the surface there may not appear tobe air bubbles near the failure point, once the top layer of Super Corona Dope has been removed,
there almost always will be an air bubble underneath. Wall failures can be repaired by carefully
removing the Super Corona Dope in the vicinity of the failure and refilling the opening.

5.6.3

Optoisolator Failures

Even with the potting material, the amplifiers still encountered some unfortunate high-voltage
issues. In all but one of these events, the negative high voltage rail shorted to the ground plane on
the ethernet board via the current monitoring optoisolator D21/Q52. This would usually annihilate
Q2, Q13, and Q14 and the surrounding resistors. Figure 5.22 shows the result of one of these failures.
Each optoisolator consists of a transmitting LED and a receiving phototransistor. Although
the OPI120 optoisolator comes in a package, each of these subcomponents is listed separately on
the circuit diagram. Q51/Q11 is the optoisolator for driving the leader circuit and D21/Q52 is
the optoisolator for monitoring the amplifier current. Although the component Q51 is a LED, it islisted as a ‘Q’ transistor component because of a historical error. We keep it as Q51 so that it iscompatible with [95] and because the D51 is already a different component (one of the TVS diodes

146

Figure 5.22: A side on (left) and top down (right) view of an amplifier that had a short to ground.
Potting material has been removed for visual access to the damaged portions of the board. The sideon view shows how the board was bent in the explosive event. The top down view shows several of
the scorched components.

in the protection chain).
These failures always destroyed D21/Q52 and occasionally Q51/Q11. Since it appeared that
D21 was the culprit in these failures, the bottom bank current monitoring circuit was removed fromthe circuit by shorting the planes at TP4 to TP7. This is most easily accomplished by connecting
the -HV rail (TP7 and TP8) connection points to the MASTER SOURCE plane (TP4) via thepads originally designated for the brass shield (J20), Figure 5.23. This results in D21 conducting nocurrent and both leads constantly sitting at the negative rail voltage. Even with this modification,
D21/Q52 would occasionally fail at rail voltage greater than ±10 kV, even though it was within thespecifications of the optoisolator, which is rated to ±15 kV and possibly higher if encapsulated. Oneof these failures occurred on the test bench and not on the decelerator. This was less destructive
due to the smaller backing capacitor (1 µF instead of 5 µF) used on the bench and thus less energy
was dissipated through optoisolator and circuit board. In this case, only D21/Q52 failed andcaused minor damage to Q51/Q11 and no damage to the board. After replacing both optoisolators
the amplifier returned to normal operation. Although previous amplifier failures were violent anddestructive, this suggests that D21/Q52 was the source of the trouble and all other damage wascollateral.
The OPI120 has an input-output isolation voltage rating of ±15 kVDC and if suitably encapsulated it can be increased to ±25 kVDC. While the top bank optoisolator must isolate between

147

Figure 5.23: The current monitoring optoisolator is shorted out by connecting the -HV rail (TP7 andTP8) connection points to the MASTER SOURCE plane (TP4) via the pads originally designatedfor the brass shield (J20).

ground and the oscillating output voltage, the bottom bank optoisolator always isolates between
ground and the negative high-voltage rail. The bottom bank optoisolator is always the one thatfails even though it is the one sitting at DC, while the top bank optoisolator oscillates. The next
iteration of these amplifiers will replace the OPI120 with OPI150, which has an input-output isolation voltage rating of ± 50 kVDC. This will require some modifications to the driving cascodecircuit due to the lower gain of the OPI150 and physical modifications to the amplifier mounting
system to account for the increased height of the OPI150.
One amplifier failure did not result in the a short to the ethernet ground plane and was barely
audible. Instead, it was only marked by a rail error on the control board. When disassembled,
all 1/2 W 10 Ω resistors on the drain end of the big FETs on the bottom bank were destroyed.
It seems that this failure traveled up the chain of follower stages instead of to the ethernet board
ground plane. This failure mode was not investigated in depth since it occurred only once.

148

Digital Timing

Decel Command Voltages x8

Trap Command Voltages x8

Decel Amp Enable

ARB8T Enable

ARB8d Enable

Trap Amp Enable

SMA Cable(s)Ethernet Cable(s)SCSI 2 50 Pin Cable(s)BNC Cable(s)Custom High Voltage Cable(s)DB25 Cable(s)Ribbon Cable(s) 50 Pin
Twisted Pair Cable(s)Decel Control Signal(s) x8
Decel Amp Bus
Trap Control Signal(s) x8
Trap Amp Bus+HV Supply Interface

Fan Power/
RPM Monitor

Amp Control

Decel Amp Bus(to other control boards)

8 for the decelerator electrodes
8 for the trap electrodes-HV Supply Interface

Top Bank Drive
Bottom Bank Drive

Start Trigger

Digital Timing

Sample/Hold

High Voltage Amplifier

Figure 5.24: A simplifier schematic of the amplifier electronic and control connections. Modified from Figure 6.43 in [95]. One amplifier contains everything inside the red-dashed rectangle.
Everything required to run one amplifier is contained inside the blue-dashed rectangle.

149

5.7

Operating multiple amplifiers
In order to run the full decelerator, eight amplifiers, each with their own control, feedback

probe, and breakout box, must be connected properly to the decelerator and computer control
system. The full control system for running TWSD is shown in Figure 5.24. Components inside
the amplifier box itself are contained in the red dashed rectangle. Inside the blue dashed rectangle
is everything required to run one amplifier. This selection of parts must be repeated for the numberof amplifiers being used. Only one of all parts outside of the blue dashed rectangle are required.
Working approximately left to right, a computer generates the analog and digital signals to run
the decelerator. The digital signals control when each component of the experiment turns on andthe analog signals control the amplifier waveforms. A digital delay generator is the master clock
for the experiment and controls the frequency at which the decelerator runs. A master interlock
box checks for errors and only allows the amplifiers to output high voltage only if everything elsein the experiment is running properly. Lastly, two ±15 kV Spellman SL (SL 2000) power supplies
and are backed by two 5 µF backing capacitors provide the rail voltages to all amplifiers.

5.7.1

Digital and analog signals

Control of the experiment is accomplished via a PC running LabVIEW and with two GaGe
8152 (eight channel arbitrary waveform generators with ±1 V outputs) cards and a Viewpoint
Systems DIO64 (64 channel FPGA-based digital I/O) card. The computer calculates two sets oftiming sequences, one analog and one digital, based on the user inputs for the desired experiment.
The analog signals are produced by the GaGe boards and control the amplifiers. The GaGe boards
produce up to a ±1 V output. With a gain of 12,000 on the amplifiers, this is sufficient to drive
any desire output on the amplifiers up to ±12 kV. The digital sequence sets the timings for themolecular beam valve, enabling and starting the amplifier waveforms determined by the analog
boards, detection lasers, and TOFMS voltage switches. Similar to the PPSD experiment, thedigital control outputs are optically isolated and buffered with 50 Ω line drivers to help reduce

150interference from high-voltage noise and to prevent damage to the computer should there be a highvoltage failure.
The full amplifier control system is designed to support 16 analog amplifier control signals
produced by two eight channel GaGe arbitrary waveform generators. Eight of these channels are
dedicated to the amplifiers attached to the decelerator and eight are dedicated to the amplifiers
for the trap. Since we perform only deceleration and not trapping in the experiments in thisdissertation, only one of the GaGe boards is used. Figure 5.24 includes all connections required
for trapping, however if trap amplifiers are not going to be used, these portions of the setup canbe ignored. While theoretically any eight rings of the decelerator can be used as a trap for a shortamount of time, if trap times longer than ∼10 ms are required, it is best to use rings that areelectrically isolated from the decelerator so that the entire decelerator does not need to be heldat the trap potential during trapping. Using separate amplifiers also means that there is more
flexibility when trap loading since as the molecule approach the trap, there are actually 16 ring
electrodes that can be at 16 different potentials, which increases the trap loading possibilities.
The computer calculates the full deceleration waveform (Equation 2.14) required for a given
initial and final velocity. However, this full sequence may not always be used. In order to detectmolecules ahead of the timing molecule, the laser must fire before the full deceleration sequenceis completed. The decelerator cannot be on when the laser fires because the resulting ions will besteered by the strong fields from the electrodes at the end of the decelerator. The electric field of the
TOFMS plate voltages, which steers the ionized molecules to the MCP detector, will be modified
by the decelerator. To avoid this, the deceleration sequence is abbreviated and the decelerator
grounded right before the detection laser fires. The full calculated waveform is referred to as thedeceleration sequence, while the actual, possibly abbreviated sequence, is referred to as the GaGe
output.
The entire experiment is timed off of a digital delay generator (DDG), which provides themaster clock. The DDG triggers the DIO board, which sets when to enable the amplifiers and whento start the GaGe boards. The majority of the TWSD experiments are run at 5 Hz. Although the151experiment was designed to run at 10 Hz, running at 5 Hz reduces the duty cycle on the amplifiers
and increases the time for the backing capacitor bank to fully recharge. If the capacitor bank does
not fully recharge on each cycle, the rail voltage will not be maintained. The amplifier output willthen be distorted, and the master interlock may kick in and turn off all amplifiers.
Figure 5.25 shows the digital timings to run a decelerator experiment as described in section
2.5. Here, all times indicated with a upper case T are times referenced to the beginning of thetiming sequence, while times indicated with a lower case t are referenced to another trigger. T0
represents the time when the DIO64 board is triggered by the DDG. Two triggers are required for
the Nd:YAG that pumps our dye laser, one for the flash lamps and one for the q-switch. There is a
set delay between the flash lamp trigger and the q-switch trigger, tq . The q-switch trigger occurs at
T1 and all other timings are referenced from it. The main time that will be varied in a deceleration
experiment is the detect time of the molecules, tdetect . The valve is fired at a time T1 -tdetect andthe rest of the experiment is timed off the valve. For optimal deceleration, molecules loaded into
the decelerator should have an initial velocity that matches the initial velocity of the chirped sine
wave. This means the decelerator should turn on after a time t = vdi where d is the distance fromthe valve to the decelerator entrance and vi is the initial mean velocity of the molecular packet.
Although this time can be calculated, it will not be accurate since there is a delay between the timethe valve is triggered and when the valve actually opens, and as a result, this delay is determined
experimentally. This delay is called tGaGe since it is the time in which the GaGe board is triggered
after the valve.
Although the GaGe output is not a digital signal, it is shown in Figure 5.25 since it is used
to calculate the amplifier enable signal. The GaGe output is a sine wave signal that controls theamplifier output. Only one GaGe channel is shown here but in practice there is one GaGe signal
per amplifier. The GaGe output is triggered on the rising edge of the GaGe enable signal. It
continues until either the end of the deceleration sequence or until T1 , whichever comes first. In
Figure 5.25, we have shown what would be the entire deceleration sequence, but since it ends after
T1 , the sequence is truncated. The portion of the sequence shown with the dashed line would be at

152
ground. If tdetect were increased to a point where the entire deceleration sequence occurred before
T1 , then the GaGe output would go to ground after it finished its sequence.
While all other digital signals trigger systems that begin on a rising edge, making the exact
pulse length not crucial, the length of the amplifier TTL enable signal is very important. Thissignal sets when the amplifier has its global feedback and standing current on. It must turn on
before the desired sine-wave output and remain on until after the sine-wave output ends in orderto ensure that the amplifier maintains linearity. Typically, the amplifier is enabled 1 ms before
the desired output and is kept on for an additional 1 ms after the output has finished. The lengthof the amplifier enable signal is determined by the actual GaGe output signal and not by the fullcalculated deceleration sequence. Therefore, if the GaGe signal is prematurely cutoff due to a shorttdetect , the amplifier enable signal ends 1 ms after T1 (as shown in Figure 5.25). If on the other
hand, the GaGe output ends before T1 , the amplifier enable signal ends 1 ms after the GaGe output
ends.
Picking the time for T1 is not critical except that it must be sufficiently after T0 to ensuresthat the amplifier enable signal does not need to occur before T0 ,T1 > 1ms − tGaGe + tdetectmax .

(5.6)

Here tdetectmax is the maximum detect time that will be used in the experiment. All triggers arereferenced from T1 , the time that the q-switch fires because the pulsed YAG laser must run at 10
Hz. If all timings were referenced from the time that the valve fires or when the decelerator turns
on, the laser frequency would change each time the detect time for the experiment changes. In
order to keep the laser as stable as possible, it is best to have all timings referenced to the laser
flash lamp or q-switch triggers.
For the case of running the experiment at 5 Hz, the laser must still fire at 10 Hz. In Figure
5.25, two extra triggers are added to the flash lamp and q-switch triggers in order to trigger thelaser a second time during the 5 Hz experimental cycle. The triggers are placed 100 ms after the
initial triggers to maintain the 10 Hz laser repetition rate. There is a ∼30 ns jitter in the DIO64

153

Figure 5.25: A schematic of the digital timings. T is the time referenced to the DDG and t is relative
time between triggers. Although it is an analog and not digital sequencey, one GaGe output isshown at the bottom. The timing of the GaGe sequence is dependent on the digital sequence.

board between receiving the start trigger and beginning its sequence, thus it is best to have thelaser q-switch and flash lamp triggers on the DIO64 board instead of the DDG to eliminate thejitter from the experiment. However, if pressed for channels on the DIO64 board, the triggers forthe laser can be run off of the DDG. In this case, the DDG is run at 10 Hz and the DIO sequenceis extended to be longer than 100 ms even if the experimental sequence is significantly shorter than
100 ms. By extending the timing sequence, the DIO board will be triggered only once every othertime the DDG sends a trigger.

5.7.2

Master Interlock

The signals from the GaGe boards are passed to the master interlock box, which serves as theglobal control of whether the amplifiers are enabled. Under normal operation, the master interlock
passes all the analog signals from the computer to each amplifier control board and monitors forany errors. Once it detects an error, all signals to the amplifier control boards are halted until theerror is addressed. The master interlock monitors the status of each amplifier, external conditions
such as the rail voltage and water pressure, and offers access to additional utility functions of thepower supplies.

154
While each individual amplifier monitors its own rail and fan error, the master interlock
checks each control board via a daisy chain bus communication scheme. Each amplifier has aunique binary address (0000-1111). The master interlock cycles through the range of amplifier
addresses using a 555 timer (U25) and a sequential 4-bit counter (U24). Each control board reads
the instantaneous address and if it matches that of the control board, then that particular board
communicates any errors to the master interlock. If any amplifier has an error, the master interlock
will ground all analog control signals and display which amplifier has an error via four LEDs on thefront panel. Like much of the amplifier design, the bus communication is carried on an ethernet
line. In addition to the four pins required for the address and one for the error bus, the otherthree pins of the ethernet daisy chain from the master interlock to the control boards contain theenable signal, +HV RAIL and -HV RAIL signals. The last two signals communicate the Spellman
voltages to the amplifier.
The master interlock contains a sample-and-hold ability to sample the desired end trap voltage
and hold for a time longer than the GaGe board can output. The GaGe boards do not have enoughmemory to generate both a fast chirped sine wave (30-0 kHz in ∼6 ms) and then hold a constantvalue for seconds as required for trapping. The sample and hold functionality is performed by
an SMP-04 4-channel sample-and-hold IC on channels 8-15 on the master interlock board. The
sample-and-hold function can be enable with digital signal from the DIO board. This function was
not used for the experiments described in this dissertation since no trapping was performed. Withno sample-and-hold control signal into the master interlock, the eight trap channels can be usedexactly like deceleration channels. Although the master interlock is designed to have amplifiers 0-7
run as the decelerator amplifiers and amplifier 8-15 run as the trap amplifiers, it is possible to swap
the amplifiers around. It is permissible to plug an amplifier with an address between 0 and 7 into
the trap bus or to use the trap channels to control decelerator rods. The master interlock does notcheck the decelerator/trap bus against the amplifier addresses.
In addition to the amplifier error signals, the master interlock monitors the flow and pressureof the cooling water. It also communicates with the two Spellman voltage supplies and interlocks the155
voltage supplies to the water cooling. If the cooling water does not have adequate flow or pressure
due to a clog, leak, or building issue, the Spellman supplies will be shut off. This indirectly grounds
the amplifier input signals since the sagging rails voltages will cause a rail error on each individual
control board. Turning off the Spellmans to turn off the amplifiers is not a suggested method ofturning off the amplifier except in unusual or emergency circumstances.
The master interlock also includes a few options for controlling the Spellman supplies including disabling front panel voltage and current control (so that the Spellmans can be controlled bya separate analog signal) and the ability to link the two supplies together so that the -HV supply
always follows the +HV supply. Although this is useful for ensuring that the output of the amplifier
stays at zero when the supplies are first turned on, it is not recommended to use this function of
the master interlock box. We found that due to the long cables required to connect the masterinterlock and Spellman supplies in our current setup, slaving the Spellmans together leads to a
voltage sag on the -HV supply and is not recommended unless the 25-pin cable (yellow in Figure5.24) can be greatly shortened.

5.7.3

Enabling amplifiers

In order to output a voltage, each individual amplifier must be enabled and have a control
signal from the GaGe board. The enable signal turns on the global feedback, and provides theamplifier with the standing current explained in Section 5.2. To enable an amplifier, the manualenable switch on the control box must be in the on position and the amplifier must receive a
TTL enable signal (Figure 5.11). This TTL enable signal can come from the front panel enable
SMA input (typically used when testing individual amplifier) or through the ethernet daisy chain(typically used when running amplifiers on the decelerator). Only when both of these signals arehigh does the amplifier fully enable and begin amplifying the control signal. The enable LED(second from the top in the green LED stack) will be on when both signals are high. Under normal
operation when the amplifier is enabled for 5-8 ms, the blinking is easily seen by eye.
While testing the amplifier, the easiest and fastest way of turning the amplifier on and off

156
is via the manual enable switch while keeping the TTL enable signal and control signal active.
While this is an acceptable method of testing one amplifier it is not the optimal method of running
multiple amplifiers attached to the decelerator. Instead, when running the decelerator, all amplifiers
should be manually enabled before any control signal is sent. This ensures that global feedback is
enabled any time voltage can be applied to the decelerator. Even if only one rod of the decelerator
has a voltage on it, all amplifiers on all other rods should have their feedback enabled and output
forced to ground. This prevents any decelerator rods from being at an undefined potential. For
example if AMP1 is applying voltage to rod 1 and AMP2, connected to rod 2, does not have its
feedback enabled, rod 2 will capacitively couple to rod 1 and will float up to an arbitrary potential
between ground and the voltage on rod 1. However, if the feedback on AMP2 is enabled and thecontrol signal grounded, AMP2 will actively try to keep rod 2 at ground. Since there is a limited
bandwidth to the feedback, rod 2 has residual oscillations when its control signal asks it to be at
ground.
Figure 5.26 shows the voltage on a rod when the control signal for the amplifier is at ground,while the amplifier has the feedback both on and off, and an adjacent rod is oscillating at ±1 kV.
The red traces shows when feedback is never enabled, and the black trace shows when the feedback
is enabled starting at 0. The drift away from 0 V when the amplifier feedback is off is due to small
amplifier stage sharing error. When global feedback on an amplifier is not enabled, voltage sharing
across the two banks is predominantly dictated by the resistor divider chain and there may be small
differences between stages since the chain in created by ten 1% resistors. Without the amplifier
feedback enabled, the rod, which is supposedly at ground, swings ∼150 V and is centered near 0
V. With the amplifier feedback on, the voltage on the rod swings by ∼100 V centered around 0 V.
In order to limit the voltage swings on the rods when some amplifier are on and others areoff (such as when first turning on the decelerator), a software turn-on procedure was implemented.
Instead of using the manual enable switch to control which amplifiers are outputting a non-zerovoltage, a software control is used. The amplifier output should be controlled via the GaGe board.
The recommended procedure is:157(1) Calculate desired digital control signals and TTL enable timings(2) Update DIO board with calculated TTL sequence(3) Set all GaGe outputs to ground (via LabVIEW)(4) Turn on Spellman high voltage supplies(5) Manually enable each amplifier using the manual enable switch and make sure that theoutput voltage remains near 0 V using the Vout monitor(6) On the computer, change the GaGe board output to desired control signal
This procedure was started because there were concerns that current from the decelerator
rod could be pushed onto the bottom bank of disabled amplifiers. While all the followers maybe
able to share any excess current or voltage via passive feedback, the leader would not. The baseof the control BJT in the leader is not connected to the feedback chain so the leader turns on only
when it is given a control signal. Since it does not have an active control signal, the leader cannot
adjust the voltage across it and could conceivably be over voltaged. This was considered to be one
potential cause for the bottom bank optoisolator failures discussed in section 5.6.3. While this nolonger appears to be a possible cause, this procedure is maintained since it is an overall safer way
to run the amplifier and decelerator.
Lastly, on the decelerator, each amplifier is turned on with a three period ramp up sine
wave (Figure 5.9). The turn on waveform is prepended to the deceleration waveform such thatthe amplifier turns on smoothly from 0 V. This eliminates any current spikes that will occur if acapacitive load is forced to an arbitrary voltage, as would be the case if each rod was forced to therequired voltage (from ground) at the moment the timing molecule enters the decelerator.

158

Figure 5.26: The voltage on a decelerator rod, measured with a high-voltage probe, when theamplifier control signal in grounded, but the adjacent amplifier has an oscillating voltage. The
adjacent rod has a voltage oscillation of ±1 kV. On and off refer to whether the manual enableswitch, and thus the feedback is on or off. In the case of the feedback being on (black), when it isenabled at t=0 the output becomes centered near 0 V and remains there until the feedback turns
off. Additionally having the feedback on reduces the amplitude of the oscillation of the “grounded”
rod. Offsets from 0 V when the amplifier is not enabled occur because of small deviations in theresistor chain.

5.8

Amplifier Changes
Several changes have been made to the amplifier design since [95]. Here, we detail why

various component have been added, changed, or removed. Updated circuit diagrams for thecomplete amplifier circuit and a concise list of changes can be found in Appendix A.

5.8.1

Component value changes

The Tables 5.4, 5.6, and 5.5 give the changes to specific component values on the amplifierboard, control board, and breakout board respectively. These component have remained in place,and only their value has changed.
On the amplifier board (Table 5.4) two resistors have been replaced, R21 (on the leader rightabove the local power supply) and R159 on the small optocoupler board. This change to R21 only
needs to be made if the voltage limiter on the leader is to be used. For reasons detailed below,
we no longer use the voltage limiters (Q7 and Q8). If the voltage limiter is used, R21 sets when159
Table 5.4: Changes to amplifier boards resistor values. The change to R21 is optional if Q8 or Q7
are not installed, see the text for an explanation.
Component number
R21
R159

Original value
470 Ω
300 Ω

Updated value
430 Ω
100 Ω

the voltage limiter begins to conduct. With Q8 and Q7, removed the value of R21 becomes rather
insignificant since it is in series with half of R6, which is 2.5 MΩ. On the original circuit diagrams,
the part number for the protection diodes on big and little FETs (D1, D12, D22, D23, D40...) are
not listed, we use MMSZ4701.
On the amplifier breakout board (Table 5.5), C4 and C6 are part of the high-voltage probe
compensation circuit. This circuit is individually tuned for each probe following the procedure
outlined in section 6.5.1 of [95]. Although this is done primarily via the trimcaps C5 and C7, 470
pF and 100 pF are more useful places to start for C4 and C6 respectively. If these values still do
not produce a faithful square wave, the next two most likely changes are to increase C4 by adding
an additional 68 pF or 100 pF capacitor in parallel or to reduce the value of C6+C7 by removing
C6.
On the master interlock the 10 kΩ resistor before the ADG613 switch (R34, R56, R59...) wasremoved and replace with a 0 Ω resistor. Additionally pin 3 of the op-amp (U22, U60, U64...) wastied to ground using a 1 MΩ resistor.
On the amplifier control board (Table 5.6), R13 was changed to have the correct input
impedance from the master interlock box, which has a high impedance output. On the other hand,
if running without the master interlock box and directly from the GaGe boards then a 50 Ω input
impedance is required. However, the master interlock should only be bypassed when testing on the

Table 5.5: Changes to amplifier breakout boards
Component number
C4
C6

Original value
330 pF180 pF

Updated value
470 pF100 pF

160
Table 5.6: Changes to control boards
Component number
R13
R35
R38
R166
R167
R168
R170
R171
R173

Original value
51 Ω
200 kΩ
200 kΩ
100k Ω
10k Ω
5.11k Ω
10k Ω
100k Ω
5.11k Ω

Updated value
1M Ω
390 kΩ
390 kΩ
10k Ω
7.5k Ω
7.5k Ω
7.5k Ω
10k Ω
7.5k Ω

bench and not when the amplifiers are connected to the decelerator. R35 and R38 are part of the
optocoupler LED drive circuit and help set the standing current. They were adjusted so that we
could set 10 mA as the typical standing current. The remaining changes on the control board are
to resistors that set the rail proximity limit and must be adjusted to fit the power supply beingused.

5.8.1.1

Rail Proximity Monitor

The rail proximity limit sets how close the amplifier output voltage can get to the rail voltages
before the amplifier errors. The circuit for this section of the control board is given in Figure 5.27.
R166, R167, R168, R170, R171, and R173 can be adjusted to adapt for various power supplies
output voltage monitors and desired rail proximity limits. The Spellman supplies that we use in
our lab have an output monitor voltage of 0-10 V where 10 V is the maximum output of a particularsupply. Thus on a 15 kV supply, 5 V on the output monitor would mean the supply is at 7.5 kV,
but if it were a 20 kV supply, 5 V on the output monitor would mean the supply is at 10 kV.
On the control board, U5 and U41 are set up as differential amplifiers that determine how
far the output is away from the rail voltage. In order to function properly, the correct scaling
between the output monitor and the rail monitor is required. Taking the positive high-voltage
rail differential amplifier as an example, U5 and it’s surrounding resistors, R165-168 must have thecorrect ratio of resistances to provide the proper scaling of +HV RAIL, OUTPUT MONITOR, and161

OUTPUT_MONITOR

8

R172
10k

2
3

7

OUTPUT_MONITOR

R180
10k

+HV_RAIL~0.34V

5

R171
10k

R168
7.5k

U41

+V1

+

7
2

1

-V1

4

3

R165
10k

R167
7.5k

R170
7.5k R173
7.5k

R179
330

C47

R31
10k

0.1uF

-HV_RAIL
10V for -15kV output
0V for 0kV output

LF356M

6

+V1

R17
1k

5

R18
10k

D2
10.0V
LM4040

1

U33

+V1

7
-

4

+

-V1

** (+HV_RAIL - VOUT)/2 [0-10V]*** ( -HV_RAIL+VOUT)/2 [0-10V]

7

6

2
3

7

+V1

5

R166
10k

U5
1

-V1

4

+

6

2

3

1

U57

-V1

+
4

8
5
-

+V1

LF356M***

RAIL_PROXIMITY

6
LF356M

6

6

7

**

LM311DR

3
2

5

6

7

+5V

R60
10k

LM311DR

4

4

U58
74LVC1G332
1
A
4
3
Y
B
6
C

RAIL PROXIMITY MONITOR

+V1

1

U55

8
5
+
4

-V1

+5V

R71
10k

5

CLEAR_ERRORSRAIL_ERROR

+5V

3

CLK

D
1

U26
Q

4

3

74LVC1G175

3

2

1

TOO_CLOSE_TO_RAIL

JILA ELECTRONICS LAB
HV Amplifier Control

DRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

RAIL_PROXIMITY_MONITOR
H

1

5/2/2013 SHEET 6 OF 7

VERSION:DATE:

N. Fitch

R177
10k

jump to enable rail proximity monitoring
J28

RAIL_ERROR_LATCHED

U31
74LVC1G332
1
A
4
3
Y
B
6
C

el
ectronics

DESIGN BY:

2UPDATE: 2/26/2018
DN: LEW0099

2

5
VCC
CLR
6

D

C

B

A

8

1

GND
2

H
D

C

B

A

Figure 5.27: Control board rail monitor circuit.

162
the output. The input at R167 is the output monitor from the Spellman supply, which is scaled by
1 V/1.5 kV. The input at R165 is the output monitor voltage from amplifier. The output voltageof the differential amplifier is given by
Vout =(R166 + R165) R168
R166
VOUTPUT MONITOR −VHV RAIL .
(R168 + R167) R165
R165

(5.7)

Since a ±5 kV supply has the same scaling as our output monitor (1 V/1.5 kV) on the control
board, both coefficients in front of VOU T P U T M ON IT OR and VHV RAIL should be one. This resultsin R165 = R166 and R167 = R168. We set R165 = R166 = 10 kΩ and R167 = R168 = 7.5 kΩ.
The rail monitor is set by the voltage at RAIL PROXIMITY. We set the error limit at 500 V.
Although ideally the output will remain at least 1 kV and preferably 2 kV away from the rail, thisgives some buffer for noise pickup on the control board, which can sporadically cause the rail error
to go off. Thus the rail monitor errors only when the amplifier is forced to go significantly above its
operational limits. The scaling of the OUTPUT MONITOR voltage is 1 V/ 1.5 kV, which meansa rail limit at 500 V corresponds to 0.34 V at RAIL PROXIMITY.
If 20 kV Spellman supplies are used instead, the coefficient in front of VHV RAIL should be
4/3. This means R168 needs to be twice as large. So when working with 20 kV Spellmans R168
an R173 must be changed to 20 kΩ.

5.8.2

Parts not in use anymore

The voltage limiters, bottom bank current monitors, and the brass shields on both banks
were eliminated from the original amplifier design. The voltage limiters where removed because
the NPN transistors were easily damaged under regular operation. Once damaged, they would
cause a small, fast current oscillation at the exact same location on every period of the current sine
wave. It is unclear what was causing the damage to the transistor. While the oscillations remained
small, this component was removed due to its propensity to break. Since each stage contains one,or two in the case of the leader, transistor as part of the voltage limiter, this make 22 possible
failure points on each amplifier.

163
The bottom bank current monitors were disabled because they were the most common pointof failure while running the amplifiers (see Section 5.6.3). Since the optoisolator also provides
support for the ethernet connector, the component was not removed but instead shorted out. Thisis accomplished by connecting the plane at TP4 to TP7, see Figure 5.23. In order to prevent thisissue, one option is to replace the OPI120 with OPI150 optoisolators, which have an input-to-output
isolation voltage of ±50 kVDC. However, this would not be just a single component swap. Dueto the difference in current transfer ratio, the driving portion of the leader circuit will need to bemodified. This modification is currently being investigated.
The brass shield (connected at J20), which was originally placed over the leader stage control
circuity that is located on the bottom of the amplifier board, was removed because it caused an
asymmetry in the positive half of the current on the amplifier. The board pictured in Figure 5.23
originally had a shield and had been coated in super corona dope. The super corona dope did
not flow into the area covered by the shield and an outline indicates where the shield use to be.
In addition to the improved output current, not having the shield makes it significantly easier toreplace Q10, Q12, and the optoisolators, which are one of the most likely components to needrepair.

Chapter 6

Electrostatic trapping of OH

Collisions between cotrapped hydroxl radical (OH) and rubidium present an interesting studyof cold molecule and ultra-cold atom interactions. The cotrapped hydroxyl-rubidium (OH-Rb)
system has the potential for sympathetic cooling of OH (hundreds of millikelvin) by rubidium(hundreds of microkelvin). Sympathetic cooling is the process of making one sample cold by placing
it in thermal contact with a different sample that is even colder. It is a technique that has beenused with ions [178] and atoms [179]. Sympathetic cooling of neutral molecules by ultra-cold atoms
is a goal within the cold molecule community, and could help make the transition from millikelvinto microkelvin for direct cooling techniques.
Sympathetic cooling will be possible only if elastic collisions dominate over inelastic collisions.
Elastic collisions, where momentum is exchanged, will cool down a sample, but inelastic collisions,where internal states are changed, will knock trapped molecules into untrapped states. In orderfor efficient sympathetic cooling to occur, there should be at least 10-100 elastic collisions for every
inelastic collision [180].
Theoretical calculations suggest that the OH-Rb system has elastic cross sections that could
be large enough compared to inelastic collision for sympathetic cooling to occur; however, background gas limited lifetimes and significant inelastic cross sections could prevent sympathetic cooling [181, 182]. These calculations have also indicated that optical or microwave dipole traps andalternating current traps would be more suitable for observing sympathetic cooling of OH by rubidium than an electrostatic trap, since the lowest energy state can be trapped. By trapping the165lowest energy state, inelastic collisions are limited since there is no lower energy state to fall into.
They find that improved candidates for molecular sympathetic cooling should have high centrifugal
barriers to supress inelstic collision channels, a weak coupling of the electron to the internuclear
axis (ie. Hund’s case (b)), and a closed-shell atom to produce more isotropic potential energy
surface [181, 182]. This suggests that a system with Li, Sr, or Ca and NH or CaH maybe better
suited for sympathetic cooling. The CaF-Li and CaF-Rb systems have been modeled and shows
promiss toward sympathetic cooling down to 100 µK [183].
Nevertheless, the OH-Rb system is interesting to study due to the behavior of OH in electricand magnetic fields. OH has both an electric dipole moment (1.67 Debye) and a magnetic dipole
moment (2µb , where µb is the Bohr magneton). This gives rise to complex and interesting behavior
in the presence of crossed electric and magnetic fields. This is opposed to a molecule such as
ammonia, which has almost no magnetic dipole moment and thus would not have strong interactions
with a magnetic field. OH exhibits both Stark and Zeeman effects and can be control with fields
achievable in the laboratory. In the presence of combined fields, a complex energy landscapeemerges with many avoided crossings that may shift significantly as the strength of the fields andthe crossing-angle changes.
We proposed to study cotrapped OH and rubidium using a quadrupole electrostatic trap
for OH and and quadrupole magnetic trap for rubbidum. One goal will be to measure collisioncross sections between electrostatically trapped OH and magnetically trapped rubidium. Althoughcollision cross sections may not be favorable for sympathetic cooling, experimental measurements
are still important, since small changes to the potential energy surfaces can lead to larger changes
in the collision cross sections, making accurate predictions very challenging.
This study will compliment the many theoretical and experimental studies of cold OH thathave already been performed. This includes theoretical studies of cold OH collision in a magnetic
field [184] and a slow helium atomic beam colliding with trapped OH [185]. This second system has
also been studied experimentally [92]. Cold OH has also been used in studies of the measurementof fundamental constant [10] and precision spectroscopy [186]. The effects of energy level crossings

166
cause by electric and magnetic fields on trapped OH have been observed experimentally in magnetic
traps with electric bias fields and overlayed magentic and electric quadruoples [34, 187, 188].
In any study of trapped molecules, nonadiabatic losses are a concern. In the Stark deceleration
calculations and experiments we have conducted thus far in this dissertation, we have made theassumption that the potential energy of the molecules is dependent only on the electric field strengthand that the molecule remains in one quantum state. We take it for granted that as the fields change,
the molecule reorients itself to follow the new axis and the potential that it is traveling on alsochanges smoothly. However, if the molecule changes quantum state at some point, the potentialthat it experiences would also change. Transitions to different quantum states are likely to occur
if the rate of quantum state energy change is fast compared to the time it takes to traverse theregion with small energy splitting. If a state change occurs, this can lead to transitions to a strongfield-seeking state and immediate trap loss or to more weakly trapped weak-field-seeking states foreventual trap loss. If the trap depth becomes shallower due to the new quantum state having a
different Stark or Zeeman shift, molecules with large kinetic energies will be lost.
Studies of nonadiabatic loss of molecules from a trap have been completed using 12 CO and13 CO [122] and for ammonia in an Ioffe-Pritchard type electrostatic trap [189]. Studies of nonadia-

batic transitions inside a Stark decelerator found that losses are small for the decelerated group ofmolecules [190]. In this same study, they calculated that nonadiabatic transitions in decelerated OH
are unlikely due to the large Λ-doubling splitting between the strong-field and weak-field seeking
states and the linearity of the Stark shift at small fields.
In this chapter, we presents the beginnings of an experiment working toward an OH-Rb cotrapped system, which will measure elastic and inelastic collision cross sections. We have measured
electrostatically trapped OH distributions and discuss considerations regarding electrostaticallytrapped OH in a uniform magnetic field. Although the final OH-Rb trap configuration will have
OH in a quadrupole electrostatic trap and Rb in a quadrupole magnetic trap, examining OH in aquadrupole electrostatic trap with a uniform magnetic field is a step toward building up the fullexperiment and model for the OH-Rb system. Additionally, it provides the opportunity to explore

167
configurations could potentially improve the density of trapped OH.

6.1

OH experimental setup
In order to slow down and trap OH molecules, we used our pin decelerator operating at ±12

kV and a four electrode electrostatic trap at ±10 kV. While the experiment operates in much thesame fashion as described in Section 2.5, a few modifications have been made to accommodate thecreation of OH and to slightly increase the deceleration and detection efficiency. OH is created
via a discharge of 1% H2 O seeded in krypton. The gas mixture is pulsed into the chamber usinga PZT valve with discharge plates mounted on the end, Figure 6.1. The discharge is formed
between the two stainless steel plates (gray) which are separated by Macor disks (white). The
resulting supersonic expansion produces a beam that is internally and translationally cold. The
OH molecules are primarily in their rovibronic ground state with a mean longitudinal velocity of∼415 m/s. The pin decelerator is used to slow down the molecular packet to a mean velocity of 34
m/s. The detection region (Figure 6.2) has an electrostatic trap and two detection lasers for 1+1’
REMPI of OH. The four trap electrodes are shown in blue and the two detection lasers, at 281 nm
and 118 nm, counterpropagate between the two central electrodes.

Figure 6.1: The gas mixing system, valve, and discharge plates for creating a supersonic beam of
OH. This figure is modified from Figure 3.16 in [155].

168

Figure 6.2: The detection region configuration for detecting trapped OH includes the last two setsof pins in the decelerator (gray), four trap electrodes (blue), 281 nm beam (red), and 118 nm beam
(green). Taken from [153].

The pulsed-pin decelerator is operated in a hybrid mode that has presumably better transverse confinement and is referred to as mixed deceleration. In this method, a select number of S=3
deceleration stages are mixed into a timing sequence consisting of predominantly S=1 deceleration
stages. The number of S=1 deceleration stages is chosen such that the deceleration phase angle isnear φ0 =50◦ and that the total number of remaining unused stages is even. φ0 =50◦ is chosen here
because due to transverse-lontiduinal coupling, higher phase angles can lead to improved decelerator efficiency up to a phase angle near φ0 =50◦ [140]. The unused stages are then spliced into the
S=1 sequence to form S=3 deceleration stages. One stage in a S=3 deceleration stage is three times
longer than an S=1 stage. Thus, there must be an even number of unused stages in order to extend
a sequence from S=1 to partially S=3, since two additional stages are required per switch time. In
the mixed mode, the S=3 deceleration stages are used as every third stage until they are all used
up. The sequence is then followed by all S=1 deceleration stages until the end of the decelerator.
The sequence is typically calculated by selecting the number of desired S=3 stages and thenchecking the phase angle for the remaining number of deceleration stages. Figure 6.3 shows thetime each stage lasts as a function of the stage number for one mixed deceleration timing sequence.

169This sequence is for a timing molecule with an initial velocity of 447 m/s, a final velocity of 108
m/s, and a phase angle of φ0 = 54.9◦ . Here, 20 S=3 stages are used. This results in a total of
109 deceleration stages of which 20 are S=3 and 89 are S=1. The underlying curve, without the
spikes, is the S=1 sequence for 109 stages. Each stage lasts longer than the previous stage since
the timing molecule slows down and takes longer to traverse subsequent stages. Every third stage
for the first 60 stages is an S=3 deceleration stage and has been extended to be three times longer
than the typical S=1 stage. This operation mode was recommended by David Reens and Hao Wu
and yields a factor of two more signal. The success of this sequence was determined experimentallyand careful 3D molecular dynamics simulations have not yet been performed to characterize thedynamics that cause this increase.

Figure 6.3: The length in time versus the stage number for one mixed deceleration timing sequence.
This sequence has 20 S=3 stages and an initial velocity of 447 m/s, a final velocity of 108 m/s, anda phase angle of φ0 = 54.9◦ .

After the OH molecules are decelerated, they are loaded into an electrostatic trap. The
flexibility of the four electrode trap allows for various trap loading schemes. The Stark potential
hills in the ‘half on’ and ‘trap on’ (Figure 2.20) configurations of the trap can be used as additional
deceleration hills after the decelerator and before turning on the trap [155]. Figure 6.4 shows two
examples of trap loading schemes. The optimized loading scheme (blue) was constructed so thatthe timing molecule is brought to a stop at the center of trap. The non-ideal loading scheme

170(orange) does not bring the timing molecule to a stop, instead the timing molecule is located partway up the longitudinal potential energy hill when the trapping configuration is turned on for thelast time. This results in greater average energy of molecules in the trap, which is normally notdesired. However, there may be certain experiments where trapped molecules with greater energy
are desired (see Section 6.4).
With ±10 kV on the trap electrodes, the trap depth for OH is 700 mK in the z direction and
250 mK in the x and y directions. The molecules are held in the trap for a set amount of time before
they are released and detected via a 1+1’ REMPI scheme. To detect the OH molecules, the 281 nm
photon is created by a dye laser and the 118 nm photon is created by frequency tripling 355 nm lightfrom a Nd:YAG (Section 6.5). The 281 nm beam is focused using a cylindrical lens so that it can
fit between the two central electrodes of the trap and is uniform across the vertical (y) axis of the
trap. The 118 nm beam is focused on the detection region using a f=25 cm lens. Two picomotors
are mounted to the last steering mirror for the 355 nm beam. This allows for both horizontal andvertical movement of the 355 nm beam, which in turn steers the 118 nm beam. By moving the 118
nm beam, the vertical density profile of the entire trapped sample can be mapped out. The 281
nm beam is approximately uniform over the entire trapped sample so that there is a fairly uniform
extraction efficiency vertically across the trap. On the other hand, the horizontal density profile
cannot be easily detected since the 118 nm beam has limited mobility in the horizontal direction
due to the trap electrodes. Additionally, the extraction efficiency of the TOFMS is dependent on
the horizontal position of the detection laser making the extraction non-uniform in this direction.
Once the OH molecules have been ionized, they are accelerated to the MCP detector usinga TOFMS configuration of [2,2,1,0] kV on the four trap electrodes. This is slightly different thanprevious work in our lab [95,155,191], which always used [1,1,0,0] kV. It was found that the [2,2,1,0]kV configuration give a more uniform extraction efficiency as the 118 nm beam position is scannedin the vertical direction.

171
Final
Decelerator Rods

Trap Geometry
Trap Electrodes

0.5 Trap On

Longitudinal Potential Energy (cm-1)

0.0
Optimized
Non-Ideal

Trap Off0

0.5 Trap On

0.0
Trap Off0

0.5 Trap Half On

0.0
0.5 Trap On

0.0
-15

-10

-5

0

Distance (mm)510Figure 6.4: A diagram of two different OH trap loading schemes. The top panel shows the location of
the last pair of pins in the decelerator and the four trap electrodes. The subsequent panels illustrate
two trap loading schemes. Blue (optimized) and orange (non-ideal) lines show the location of thetiming molecule when the potential is switched from one configuration to another. Both schemes
use the same sequence of configurations: on, off, on, off, half on, and on, but switch at different
times. Figure taken from [153]

172

6.2

OH REMPI Detection
OH has only four bound electronic states: X2 Π, A2 Σ+ , B2 Π, and C2 Σ+ [192]. The B←X andC←X transitions lie in the vacuum ultraviolet (VUV) range where there are few tunable sourcesof laser light. Thus the A←X transition is the most promising one for state selective detection of
OH. OH has an ionization potential of 13.017 eV. While it has been detected using 2+1 [193, 194]
and 3+1 REMPI schemes [195], the observed ion signals have been weak. LIF on the A2 Σ+ −X2 Πtransition is readily used in many OH experiments [87, 101, 108, 188], but as discussed in Section
2.5.2, REMPI provides the added ability to map out the density distribution of trapped molecules.
The A2 Σ+ excited-state electron configuration of OH is (1σ)2 (2σ)2 (3σ)1 (1π)4 , while theground-state electron configuration of OH+ is (1σ)2 (2σ)2 (3σ)2 (1π)2 . This suggests that a onephoton process between these two states should be forbidden since two electrons must change
orbitals. However, a 1+1’ REMPI process, which makes uses of an autoionizing Rydberg statethat converges on a higher ionization limit, has been experimentally demonstrated by Beames etal. [196]. This scheme has subsequently been used in other OH studies [152,153,197]. This REMPI
scheme makes use of one 281 nm and one 118 nm photon. The 281 nm photon is typically generated
via a doubled dye laser. The tunability of a dye laser is useful in this case so that different excitedstates can be used as the intermediate. The second, 118 nm, photon is generated by frequency
tripling the third harmonic (355 nm) of an Nd:YAG in a gas cell. This procedure is discussed indetail in Section 6.5.
Figure 6.5 shows the relavent OH energy levels for REMPI detection with the transitions
used in this experiment in bold. From a strictly energy stand point, 118 nm light is able to ionize
OH from any rotational level in the excited A2 Σ+ , v = 1 manifold. However, careful choice ofthe excited state will make a significant difference in the resulting ion signal. The trapped OH
molecules are in the upper Λ-doublet of the rotational and vibrational level (J=3/2, v=0) of theground X2 Π3/2 electronic state. The strongest A ← X LIF transition is Q1 (1.5), but ionizationfrom the (J=3/2, p=-) state yields minimal ion signal. In a supersonic beam of OH, the largest

(A 3Π, 3d)173

118 nm

7
2
5
2

-

5
2
3
2

+
+

3
2
1
2
1
2

A 2Σ+ (ν = 1)+J

281 nmQ1(1.5)

3

2

+

-

Q21(1.5)

R21(1.5)

X 2Π3/2 (ν = 0)

J p

Figure 6.5: An energy level diagram of OH showing the relevant states for 1+1’ detection. Theenergy levels are not to scale. Q1 (1.5) is the typical LIF transition, Q12 (1.5) is the strongest
transition between the X2 Π3/2 and A2 Σ+ states, and R12 (1.5) is the transistion used in the 1+1’
REMPI scheme for OH. Figure taken from [153].

ionization signal is achieved on the Q12 (1.5) transition [152]. However Q12 (1.5) originates fromthe lower Λ-doublet, which is not decelerated and trapped. Instead ionization from the R21 (1.5)
transition is used in this work. A 118 nm photon from the (J=5/2, p=-) state is resonant with theA3 Π, 3d autoionizing state which helps to enhance the ion signal.

6.3

OH 1+1’ REMPI with 118 nm photons
The advantage of using REMPI detection over LIF is the ability to scan the laser over the

sample and map out the density distribution using a setup such as the one described in Section
6.1. Although decelerated OH is commonly detected using LIF [75, 108, 116, 188], the 1+1’ REMPI
scheme opens the doors to improved signal-to-noise and data analysis methods. There are many
limits to 118 nm light generation, but enough 118 nm power can be created to make the difficulties
of setting up a REMPI scheme for OH worth it. Below, we show a few measurements that can only
be performed by scanning the detection beam and would not be possible using only LIF since LIF

174
requires detecting the entire trapped sample at once. An expanded beam, which illuminates theentire trapped sample, is used in LIF. While the beam could be made smaller, the signal-to-noise
become impractically low and a localized LIF beam is not a practical detection method.
In the case where two different trap loading schemes have been used (see Figure 6.4), andeach results in different density distributions in the trap [153], differences in the central density andwidth of the trapped molecules can be observed via 1+1’ REMPI. These measurements would not
be possible with LIF detection where the entire sample is illuminated and detected at once. Figure
6.6 shows measurements of the central OH density in both the experiment and simulations. In the
optimized loading scheme, where the timing molecule is stopped at the center of the trap, more
molecules are found near the center of the trap. On the other hand, in the non-ideal case, where
the trap turns on when the timing molecule is part way up one side of the longitudinal potential,
there is lower density at the center and many more molecules orbit at large radii about the centerof the trap. The density distribution at different times can be used to determine the full-width
half-maximum (FWHM) of a trapped sample over time, Figure 6.7. Larger changes in the width
can be seen in non-ideal loading (Figure 6.7b) than in optimized loading (Figure 6.7a). This is
expected since, on average, the molecules in the non-ideal loading scheme have a greater residual
oscillations.
The FWHM of the cloud the vertical (y) direction is determined by recording vertical density
scans at set detect times and then fitting the distributions. The FWHM is then extracted byfitting these scans. 3D Monte Carlo molecular dynamics simulations of molecules in the trap
produce similar width modulations as seen in the experiment. Such modulations can be used todiagnose issues with the detection laser alignment or with the trap loading scheme. Since trap
loading sequences are determined based on the final velocity of the timing molecule, if the resulting
decelerated molecule packet does not have the same average velocity and position as the timing
molecule, the resulting molecule signal in the trap can be very low. By iterating through trap
loading sequences or adjusting the position of the 118 nm beam, it can be determined whether thetrap was loaded well or not.

175
1 0

E x p e r im e n t
S im u la tio n

O H C o lu m n D e n s ity ( a r b . u n its )

(a )

2 0
1 0

5

-1 0
-2 0

0
2 0

(b )

1 0

5

z V e lo c ity ( m /s )

0

0
-1 0
-2 0

0
3 .5

4 .0

4 .5

5 .0

5 .5

6 .0

6 .5

-2

-1

0

1

2

z P o s itio n ( m m )T im e ( m s )Figure 6.6: Experimental (solid) and simulated (dashed) measurements of the central density OH
in the trap for the two different loading schemes depicted in Figure 6.4. (a) the optimized loading
scheme shows smaller oscillations when loading and an overall greater density at the center of thetrap once the oscillations damp out. (b) the nonideal loading scheme has larger loading oscillations
and a lower central density once the oscillations damp out. The difference in the central density canbe seen in phase-space plots of the simulations. In the optimized case, the majority of molecules
are at the center of the trap. In the nonideal case the molecules are primarily at large orbits about
the center of the trap. Figure from [153].
2 .0

(a )

E x p e r im e n t
S im u la tio n

1 .5

F W H My a x is ( m m )

1 .0
0 .5
0 .0
2 .0

(b )
1 .5
1 .0
0 .5
0 .0
4 .3

4 .4

4 .5

4 .6

4 .7

4 .8

4 .9

5 .0

T im e ( m s )Figure 6.7: The FWHM of trapped OH over time for a) optimized loading and b)non-optimized
loading. Both simulations (solid lines) and experimental measurements (squares) are shown. In
both cases, the simulations reproduce the modulation of the cloud after it is trapped as seen in
the experiment. The statistical uncertainty is on the order of the point size or smaller. Figure
from [153].

Lastly, the ability to map out the density distribution allows for the measurement of the176effective temperature of the trapped molecules. The density profile can be measured at various
times after the trap is turned off. From these measurements, the FWHM can be extracted and thechange in width used to determine a temperature. Figure 6.8 shows one of these measurements.
Here, OH was trapped using the optimized loading scheme and held for 15 ms before being released
from the trap. A fit to this expansion gives a Vrms (root-mean-square velocity) of 5.5 ± 0.2 m/s
and 6.2 ± 0.2 m/s for the experimental and simulated results respectively [153].
The difference in the initial size of the cloud in the simulation and experiment can likely be
attributed to uncertainty in the initial distribution of molecules in the trap. In the simulations, anassumption is made about the initial distribution in a Stark deceleration experiment, particularlythat its position and velocity distribution are Gaussian. The Gaussian molecular packet propagates
through the decelerator and trap loading potentials. Deviations between the packet in the experiment compared to the simulation will propagate through the simulations and lead to differences
between the observed molecule signal and the simulated signal. It is important to remember herethat this is not a true temperature since the trapped molecules do not have enough collisions tothermalize. Instead, this is a measurement of the average energy of the trapped molecules.
These measurements in Figures 6.6, 6.7, and 6.8 demonstrate some of the ways in which
the dynamics of trapped molecules can be observed and characterized. While these dynamics haveoften been investigated using simulations, they are not often observed experimentally. This methodof observing OH molecules using 1+1’ REMPI demonstrates the advantage of using an ionization
detection technique even though it is more complicated than LIF, since it requires two lasers.

177
1 .2

y a x is ( m m )0 .8

F W H M

1 .0

0 .4

0 .6
S im u la tio n
E x p e r im e n t

0 .2
0 .0
0

5 0

1 0 0

F r e e E x p a n s i o n T i m e ( µs )1 5 0

Figure 6.8: The width of the OH cloud as it expands after the trap is turned off. Figure from [153].

6.4

OH in electric and magnetic fields
With a reliably operating electrostatic trap and a REMPI detection scheme that allows us

to map the vertical density distribution in the trap and fully understand and characterize thetrapped OH molecules, we can now examine trapped OH under the influence of other fields andparticles. To perform cotrapped OH-Rb experiments, the ultra cold rubidium will be preparedseparately in a rubidium cell that is attached to the trap chamber. A MOT of rubidium is loaded
into a magnetic trap. The coils for for the magnetic trap are mounted on a translating track. The
magnetically trapped rubidium is then transported from the rubidium cell into the trap chamberof the decelerator experiment and centered on the electrostatic trap. This procedure is an almost
identical to the one used in [94], but with a slightly different geometry.
Given this coil setup, we also have the ability to apply a uniform magnetic field to theelectrostatically trapped OH. The two coils, which are external to the vacuum chamber, can beplace in a Helmholtz configuration to apply a uniform magnetic field to the trap. Figure 6.10 shows
this setup where a uniform magnetic field is applied along the y axis. The coils have 24 turns eachand can carry a current up to 500 A. In the Helmhotlz configuration, this gives a maximum field of
800 G at the center of the trap. Figure 6.9 shows a plot of the the electric fields in the longitudinal

178
and transverse directions with ±10 kV on the trap electrodes. Near the bottom of the trap, thegradient in the longitudinal and transverse directions are 123 kV/cm2 and 62 kV/cm2 respectively.
This configuration will be used to study electrostatically trapped OH in a uniform magnetic field.

(a) Longitudinal(b) Transverse

Figure 6.9: The electric field in the trap along (a) a line along the z axis and (b) a line along they axis. The asymmetry in the longitudinal direction is due to the grounded decelerator electrodesthat are upstream of the trap.

Figure 6.10: The electrostatic trap with Helmholtz coils to produce a uniform magnetic field at thecenter of the trap. While the trap and decelerator are located in the UHV chamber, the coils are
external to the chamber. This is almost the same setup as in Figure 6.2, but with the addition of
the coils.

179
6.4.1

Hamiltonian for OH in electric and magnetic fields

With the ability to apply a uniform magnetic field, we must now examine how the OH spinorbit and rotational states behave in crossed electric and magnetic fields. The strong coupling of
L and S in Hund’s case (a) means the internuclear axis will want to follow both the magnetic andelectric field lines. Here we summarize the treatment of the 2 Π3/2 ground state of OH in crossed
fields.
The same convention as in [198] is used, the magnetic field B is restricted to one axis andthe electric field E forms and angle β with B. The Hund’s case (a) basis |J, M, Ω, i is used. The
Hamiltonian for the ground state of OH in crossed electric and magnetic fields is [34, 199]
√
 ∆ 6
3
3
− 2 − 5 µb B

0

0

0


0
−∆
− 25 µb B
0
0
2

2

+
µ
B
0
0
0
−∆
2
5 b


0
0
0
−∆
+ 65 µb B2 − 3 µE cos β − √3 µE sin β
0
0
5
 √5
 − 3 µE sin β 1 µE cos β
2
µE
sin
β
0
 5
5
5
√

0
− 2 µE sin β − 1 µE cos β − 3 µE sin β
5

0

5
√

0

√5

− 53 µE sin β − 53 µE cos βµE cos β− 5 µE sin β

0

0



− 25 µE sin β001µE cos β5− 25 µE sin β






.






5√
− 53 µE sin β√− 15 µE cos β − 53 µE sin β√− 53 µE sin β − 35 µE cos β00∆− 65 µb B
2

0

0

0

0

∆
− 25 µb B
2

0

0

0

0

∆
+ 25 µb B
2

0

0

0

0

∆
+ 65 µb B
2(6.1)
The state ordering from left to right and top to bottom begins with |J, M, Ω, i=| 23 , − 32 , 32 , ei andends with | 32 , 32 , 23 , f i, where first M is increased and the .
The fully stretched states do not experience any actual or avoided crossings in the crossed
fields. At large E or B fields the states approach the case for E-field only or B-field only. However,at intermediate values of E and B with certains values of β, there are level crossing and avoided
crossings. Additionally, in combinations of strong electric and magnetic fields neither fields provides
a suitable quantization axis. However good quantum numbers can still be detemined using a ‘Hund’scase-X’ [171].
The Hamiltonian in Equation 6.1 can be used for the uniform magnetic field case discussed
above since the magnetic field, B is always in the same direction. The changing magnitude of theelectric field is represented by E and the changing direction of the electric quadrupole with respect
to the y-axis is represented by β.

180
Figures 6.11-6.13 each show how the various states of the 2 Π3/2 ground state of OH evolve
under different magnetic and electric fields. Each figure has a constant magnetic field of 90, 500,
and 800 Gauss. These values correspond with 50, 300, and 500 A in our coils. 50 and 500 A are
achievable in our setup, however, 300 A is not due to power dissipation limitations on the current
driving MOSFETs. Despite this, 500 G (300 A) has been plotted to give a better sense of how theenergy surfaces evolve by changing angle and field. The electric field range on the x axis covers therange found in the center of quadrupole electrostatic trap. The maximum electric fields in the trapare 30 kV/cm and 16 kV/cm in the longitudinal and transverse directions respectively. Withineach figure, β, the angle between E and B, takes on the values of 0, π/16, π/8, π/4, 3π/8, and π/2starting from the top left and moving across each row.
Small uniform magnetic fields (ie. B=90 G, Figure 6.11) do not significantly change the trap
depth at any angle. However, crossing and avoided crossing between the various states Zeeman
and Stark shift states begin to emerge. At large uniform magnetic fields (ie. B=800 G, Figure6.13), the maximally stretched state | 23 , 32 , + 32 , f i (blue) changes slope with changing angle, β. Thismeans that trap depth will be modified with a large uniform magnetic field.

6.4.2

Electrostatically trapped OH with a uniform magnetic field

As the molecules traverse the trap in the presence of a strong magnetic field, they willencounter a different potential energy landscape than in the no-field case. If they are in a statethat has an avoided or actual crossing with another state, they will follow either adiabats or diabatsdepending on the energy gap and molecule velocity. This will alter either the trap depth that themolecule encounters or it may cause the molecule to fall into an untrappable state.
In the case of the electrostatic trap with a strong uniform magnetic field, the trap depth isslightly weaker than in the purely electrostatic trap. Molecules out of the decelerator will be in the|f ; + 23 i state. Once in the trap, they should predominantly remain in the | 32 , 32 , + 32 , f i state. Asa quick estimate, we take the case where the minimum energy gap between the | 32 , 32 , + 32 , f i state
and any other state is less than 10 MHz to have any probability of a diabatic transition. This only

181

Figure 6.11: OH energy levels in a uniform 90 G magnetic field with varying β and electric field.

182

Figure 6.12: OH energy levels in a uniform 500 G magnetic field with varying β and electric field.

183

Figure 6.13: OH energy levels in a uniform 800 G magnetic field with varying β and electric field.

184
occurs at electric fields greater than 6 kV/cm and β = π/2 (See Figure 6.13). In our trap, thesetwo conditions occur only in the x-z plane and far away from the trap center. Figure 6.14 shows a
cut in the x-z plane of our trap with the regions where the electric field is greater than 6 kV/cm
colored in red. This create a “zone of death” that is a sheet, but with a hole at the center of the
trap.

Figure 6.14: The region in the x-z plane (y=0) of our trap where he electric field is greater than 6
kV/cm is shown in red. For a uniform field of 800 G in our electrostatic trap this is the only planein which trapped OH molecules encounter any avoided crossings with another fine structure stateand have a chance of falling out of the trap.

This is compared to the case of no magnetic field, where there is a degeneracy between the
MJ Ω = -9/4 and -3/4 states when E=0 at the center of the trap. Molecules traveling on trajectories
that come close to the trap center have a chance of crossing from the MJ Ω = -9/4 state to the
MJ Ω = -3/4 state. In the MJ Ω = -3/4 state, molecules are more weakly trapped. This can lead totrap loss if the kinetic energy of the molecule can over come the trap potentials. Over the course of
the background gas limited trap lifetime (1-2 s), the molecule may traverse this crossing hundredsof times. Taking the same approach as in [188], the transition probably when the molecule crosses
through an energy minimum between two states can be calculated from the Landau-Zener hopping
probability, P ,2

P = e−πa /2~Ġ ,(6.2)

where a is the coupling between the two states in question and Ġ is the rate of approach. In one

185
dimension only, Ġ can be found via
Ġ = vz

dG
.
dz

(6.3)

Simulations in which multiple molecules evolve on more than one potential energy surface and thecrossings between MJ Ω = -9/4 state to the MJ Ω = -3/4 state have been calculated using Equation
6.2 are needed in order to understand theses trap losses in both the electrostatic trap with nomagnetic field. Once completed these simulations will be compared with measured experimental
trap life times for both the uniform magnetic field case and no field case.

6.4.3

Future work

In the uniform magnetic field case, it appears that trap losses will occur only at large radii.
If a molecule distribution in the trap has a greater average energy, with many molecules orbitingat large radii, it may experience greater trap loss than one that has a a lower average energy, withthe majority of molecules orbiting near the trap center. We have already demonstrated that two
trapped samples such as this can be prepared and measured (Figure 6.6) [153]. Poor trap loading
will lead to larger average energies in the trap and molecules that orbit the trap at larger radii. If
molecules can be intentionally loaded into the ‘zone of death,’ trapped molecules in the non-ideal
loading scheme will have shorter trap lifetimes.
After characterizing the electrostatic trap with a uniform magnetic field, the electrostatic
trap with a quadrupole magnetic trap and OH-Rb collisions wil be examined. For the OH-Rb
system, there is a quadrupole electric trap with a quadrupole magnetic trap, and in this case there
will not be perpendicular electric and magnetic fields. However, since the gradients between the
two traps are different, the angle between the electric and magnetic fields (which will be < 90◦
will still change. A similar electric and magnetic field model to above will still be needed to study
this system. The Hamiltonian for the system cannot be taken to just be in Equation 6.1, since themagnetic field is not uniform along one axis. Instead, a lab frame Hamiltonian will be required.
Once this has been characterized elastic and inelastic collision cross sections can be measured in
the OH-Rb system.

186

6.5

118 nm light
118 nm (10.5 eV) photons fall in the vacuum ultraviolet (VUV) range. While VUV photons

are very useful as ionization sources in mass spectrometry, few table-top high flux VUV sources
exist. The majority of VUV light used in experimental physical chemistry comes from synchrotrons,
but the complexities, scale, and location of theses sources limits the number of experiments that canuse these sources. When generating table top VUV, either an excimer laser or a gas cell containing
a nonlinear media is used. VUV light cannot be generated inside a crystal because crystals become
opaque around 200 nm.
To create the 118 nm light required for OH REMPI detection, we triple the third harmonic
output of a Nd:YAG (355 nm) in a xenon-argon gas cell. 118 nm is the third harmonic of 355 nm,
which is an easy to obtain wavelength from commercial YAG lasers. A tripling process is chosen
since the isotropic nature of gases limits the nonlinear process to only odd-orders. In order foreven numbered processes to occur in a gas, a symmetry breaking field such as a strong electric or
magnetic field must be applied. At 118 nm, xenon is negatively dispersive and xenon acts as thetripling medium. Xenon is the only rare gas that has a negative dispersion at 118 nm. Argon ispositively dispersive at 118 nm and acts as the phase matching medium. The phase-matching gas isrequired so that the fundamental light (355 nm) and third-harmonic light (118 nm) maintain a fixedphase relationship and 118 nm light created at slightly different locations build coherently. While
krypton or neon could also be used as the phase-matching gas, as will be seen below, krypton is lessefficient than argon, and neon requires significantly higher total pressures, which adds experimental
challenges.
The 118 nm photon can be used in a single or multi-photon ionization molecular detection
technique. As seen in Section 6.2, 118 is well suited for 1+1’ REMPI of OH due to the auto ionizing
state that can be accessed from the A2 Σ+ , v = 1 excited stated. Additionally, for molecules witha lower ionization potential, 118 nm photons can be used for single photon ionization. This isespecially useful when constructing a 118 nm detection system, since it can be tested using a

187
molecule such as ammonia or propyne, which have ionization potentials below 10.5 eV. The xenonargon 118 nm system has been used for various molecule detection schemes including hexane [200],
methanol [201], and OH [152, 196].
The sensitivity of the 1+1’ REMPI detection technique for OH is limited by the flux of
118 nm photons, since there is significantly lower 118 nm power than the first 281 nm photon.
The conversion efficiency from 355 nm to 118 nm is low and an additional suppression factor
occurs at moderate xenon pressures (>20 torr), which limits the overall efficiency of this detection
method. Here, we give an overview of 118 nm light production and explore the suppression at
higher pressures. More details on the mechanisms and calculations for the tripling process can befound in [155, 200, 202, 203].

6.5.1

Creating 118 nm light

The power at the third-harmonic, P3ω , for an incident fundamental power Pω , where both
powers are in watts, is given by [202, 203]P3ω =8.215 × 10−2 (3) 2 3
χef f Pω |F1 (b∆k)|2 .
(3λ)4

(6.4)

(3)

Here λ is the third-harmonic wavelength in cm and χef f is the macroscopic nonlinear coefficient.
F1 (b∆k) is a dimensionless function, ∆k is the wave-vector mismatch between the fundamental
and third-harmonic, and b is the confocal parameter. The confocal paramter is a measure of how
tightly a beam is focused. It is equal to twice the Rayleigh length. Since we are discussing only
118 nm light production, λ is set and there are three free parameters left that can be varied(3)

experimentally: the peak powers in the fundamental, the macroscopic nonlinear coefficient χef f ,and the phase matching function F1 (b∆k).
The peak power in the fundamental is limited only by the output power of the Nd:YAG laser
and the resulting power density on any optics in the beam path. Thus, to create as much 118
nm light as possible, Pω should be as large as possible. Independent maximization of the last two(3)parameters is impossible because both χef f and F1 (b∆k) are dependent on N , the atomic number

188
(3)

density of the gas. χef f is given by(3)

χef f = N × χ(3)
a ,

(6.5)

(3)

where N has units of number/cm3 and χef f is in esu.
The last factor, F1 (b∆k), is the phase-matching function. It is an integral over the reduced
longitudinal coordinates of the gas cell and generally evaluated numerically. However, since thenonlinear medium is much longer than the confocal parameter of the focused fundamental beam(b  L), F1 (b∆k) in this tight-focusing limit can be solved to give [203, 204]

|F1 (b∆k)|2 =π 2 (b∆k)2 eb∆k∆k < 00∆k ≥ 0.

(6.6)

Figure 6.15 show a plot of Equation 6.6 for b = 1. This function has has a maximum at ∆k(λ0 )max =− 2b . This means in order to maximize 118 nm light production, ∆k should be adjusted based on
the confocal parameter, which is set by the lens used to focus the 355 nm light into the gas cell.

Figure 6.15: Plot of |F1 (b∆k)|2 in the tight-focusing limit and for b = 1. The function has amaximum at ∆k(λ0 )max = − 2b .

∆k in Equation 6.6 is related to N through the index of refraction,∆k =2π[n1 − n3 ] .
λ

(6.7)

In this notation, n1 and n3 are the index of refraction at the third-harmonic wavelength λ and thefundamental wavelength 3λ, respectively. For a gas, the effective macroscopic index of refraction,

189n, is given byn(λ) = 1 + N χ(1)a (λ),(1)

where χa(6.8)

is the atomic linear susceptibility at wavelength λ. Now ∆k can be related to N andexpressed as∆k = CN ,

(6.9)

where
C=

i
2π h (1)χa (λ) − χ(1)
(3λ)
a
λ

(6.10)

is a constant describing the microscopic dispersive properties of the gaseous medium. ∆k, and thus
F1 (b∆k), can be optimized by simply varying the pressure of the gas.
As can be seen from Equation 6.6, ∆k must be negative to generate third-harmonic light.
This occurs only in media that exhibits anomalous dispersion (i.e., n3 > n1 ). Xenon was chosen as
the nonlinear medium for THG of 118 nm because it is the only rare gas that exhibits anomalous(3)

dispersion at this wavelength. With only a negatively dispersive gas, ∆k and χef f are both depen(3)dent on N and χef f and |F1 (b∆k)|2 in Equation 6.6 cannot be varied independently. If instead(3)

a positively dispersive gas with negligible nonlinearity is added, ∆k and χef f can be decoupled.
Argon is typically used as the positively dispersive gas for THG of 118 nm light. For a mixtureof the two gases, the total wave-vector mismatch at the nominal third-harmonic wavelength λ0 is
given by summing over the partial pressures of each gas,∆k(λ0 ) = NXe CXe (λ0 ) + NAr CAr (λ0 )= NXe [CXe (λ0 ) + RCAr (λ0 )](6.11)(3)

NAr
where R = N
is the pressure ratio of the two gases. With the addition of argon, χef f (Equation
Xe6.5) can be adjusted using NXe , while ∆k (Equation 6.11 can be adjusted using NAr ).
In order to maximize F1 (b∆k) and find the optimum phase-matching ratio of the two gasesin the tight-focusing limit, Eq. 6.11 must equal − 2b , the value of ∆k(λ0 )max at the maximum of
Eq. 6.6. After changing the number density, N , to pressure, P, via the ideal gas law, this gives an190optimum ratio of


NAr
NXe


=−
opt

1
2
CXe (λ0 )−.
b NXe CAr (λ0 ) CAr (λ0 )(6.12)(3)

For large xenon pressures, which are desirable for increasing χef f and thus P3ω , the optimum ratio
Xeapproaches the constant value of C
CAr and is independent of the value of confocal parameter b.

Using the values CXe (118.2 nm) = −6.12 × 10−17 cm2 and CAr (118.2 nm) = +5.33 × 10−18 cm2from Mahon et al., [205] this ratio is 11.48.

6.5.2

Experimental setup

The experimental setup for the gas cell used to create 118 nm light is shown in Figure 6.16.
The gas mixing cell (tan) is ∼ 40 cm long and is constructed of three 2-3/4” standard stainlesssteal ConFlat crosses. It is important that the cell diameter not be too small at any point. This
restricts gas flow and leads to inconsistent gas mixing and variable 118 nm signal. For example, we
found that when we attached a section of 1/4” tubing to the gas cell, xenon, the first gas placedin the cell would become trapped in the narrower section and diffuse out over time. This would
significantly change the gas ratio as a function of time and decrease 118 nm light production. The
input of the cell is sealed with a UV fused silica window. It is important to make sure that thepower density of the 355 nm beam at the window is low enough that it does not burn. 355 nm light,
produced by a Continuum Inlight III-10, which is internally tripled, is focused into the gas mixing
cell with a 50 cm focal length lens. The second lens in the system is a 25 cm focal length MgF2lens and focuses the 118 nm beam in between the TOFMS electrodes. This lens sits in a custom
conflat holder [155] so that it can also act as a seal between the gas mixing cell and the detection
chamber. MgF2 was chosen for this lens because of its VUV transmission and hardness, since many
optics are not transmissive in the VUV. A Macor iris (not shown) is placed after the MgF2 lens on
the detection chamber side, which blocks the excess 355 nm light that was not converted to 118
nm light.
Once the 118 nm photons are created, they are difficult to detect since they cannot propagate
through air. Here, we use ionization of a uniform molecular cloud in order to detect the 118 nm

191

Figure 6.16: A diagram of the 118 nm gas mixing cell and the ionization and detection region. The
335 nm beam (red) is focused into a gas cell containing xenon and argon (tan). 118 nm light isformed at the focus of the 355 nm light via THG if the gas cell contains the correct ratio of xenon
to argon. The 118 nm light (purple) is focused into the detection chamber (light blue). Inside thedetection chamber four electrodes (dark blue) accelerate ions formed at the focus of the 118 nm
beam toward the MCP detector. The detection chamber can either be flooded with a low pressure
gas or a decelerated beam can be loaded into the trapping region. The blue arrow in the detection
chamber indicates the molecular beam axis of the decelerator. Slow OH molecules enter the trap
along the arrow.

photons. This is easier than using a molecular beam since the arrival time of the molecules in thedetection region is not a factor. This is accomplished by flooding the detection chamber with ND3 ,a molecule that can be ionized with a single 118 nm photon. Typically, the detection chamber isfilled to a partial pressure of ∼ 9 × 10−8 torr. Since the ND3 pressure in the detection chamber is
kept constant, the ND3 ion signal acts as a proxy for the 118 nm photon flux. The number of ND+
3ions created will then be proportional to the number of 118 nm photons that reach the detection
region. The resulting ND+
3 ions are accelerated by a TOFMS to an MCP detector as described in
Section 6.1.

6.5.3

Limitations to 118 nm light production

As seen in Equation 6.6, increasing the xenon pressure and the corresponding phase-matchingargon pressure should result in more 118 nm light production. However, this is not the caseexperimentally. Figure 6.17 shows the 118 nm flux for various pressures of xenon gas and a constant

192
355 nm input power. Each colored curve shows a constant pressure of xenon gas with varying
pressures of argon gas. The peak of each curve is the phase-matched mixture for the given pressureof xenon. For PXe > 15 torr the phase-matched pressure is 11.5 as predicted by Equation 6.12.
Each curve is recorded by adding a set amount of xenon gas to the mixing cell, then argon is added
slowly while monitoring the ionized ND3 signal. As argon is added, the gas mixture will take time
to mix. This may take 1-15 minutes depending on how the gas is let in to the mixing cell, thegeometry of the cell, and if any active mixing, such as a mixing paddle or a cold bath, is utilized.
Once the signal has reached a platau, the signal at the platau is taken to be the 118 nm flux forthe given mixture. Each phase-matching curve is then construced from the value at each platau.
Each peak of each phase-matching curve represents the phase-matched mixture for the given xenonpressure. At each peak F1 has been maximized and Pω3 is constant. Equation 6.6 indicates that as(3)

3 should increase as the square of the xenon pressure. Instead,PXe increases, and thus χef f , P3ω

the 118 nm flux reaches a maximum at 24 Torr of xenon. At the peak of the phase-matching curvefor 24 Torr of xenon, it is estimated that there are 10s of nJ of 118 nm light. At higher pressures,
instead of increased 118 nm signal, the flux decreases until very little 118 nm light is observed. Thissame turnover in 118 nm light production versus total pressure was observed in Shi et al. [201].
The large discrepancy between the predicted and measured yields of 118 nm light at high pressuresindicates that some process is significantly limiting the conversion efficiency. If this process can beunderstood and counteracted, then signal in molecular detection techniques that use 118 nm could
be greatly enhanced.
The decrease in 118 nm flux is accompanied by the observation of a fluorescence streak(Figure 6.18) near the focus of the 355 nm light. The streak follows the propagation axis of the 355
nm light. The streak could be observed and studied through a ConFlat window located above the355 nm light focal region. The streak became brighter as the 118 nm signal decreases with higher
xenon pressures.
A photo diode and an Ocean Optics USB2000 spectrometer were used to examine the fluorescence streak. During phase-matching measurements with xenon pressures greater than 20 torr,

193

Figure 6.17: Phase-matching curves at different pressures of Xe. While theory indicates that thephase-matched peak heights should increase as the square of the xenon pressure, this is not thecase, and 118 nm signal reaches a peak at a phase-matched mixture with 24 torr of xenon.

Figure 6.18: A picture of the fluorescence streak that appears near the 355 nm focal point.

the streak intensity is correlated with 118 nm production. Figure 6.19 shows the fluorescence signal
closely following the shape of the phase-matching curve. This indicates that 118 nm photons playa role in the creation of the fluorescence streak. Additionally, when examining a phase-matchedmixture (a constant 1:11.5 ratio of Xe:Ar with different total pressures) the intensity of the streak
increased with increasing xenon pressures (Figure 6.18). The fluorescence intensity increased linearly at a threshold xenon pressure (∼20 torr), which is near the peak of the 118 nm photon flux.
The intensity of the fluorescence increases linearly as 118 nm photon flux decreases.

194
In order to further understand the fluorescence streak, we examined 118 nm photon production with a different phase-matching gas, krypton. Krypton is positively dispersive at 118 nm
just like argon. It has a measured phase matching ratio of 1:4.6, which agreed with the krypton
dispersion calculated in Mahon et al. [205]. The same measurements that were conducted with thexenon-argon mixture were also conducted using xenon-krypton. The red curves in Figure 6.20 show
the measurements for krypton. This mixture did not yield more 118 nm light than the Xe/Ar mixture and the fluorescence streak was still present. The overall 118 photon flux for phase-matchedmixtures reaches a lower peak at a lower xenon pressure than for the xenon-argon mixture. And
similar to the xenon-argon case, a fluorescence streak appeared starting with ∼20 torr of xenon.
The xenon-krypton mixture did not have any advantages over the xenon-argon system due to thedecrease in the observed 118 nm signal.

Figure 6.19: A phase-matching curve,with PXe =50 torr, taken while monitoring both the 118 nm
flux and the fluorescence intensity. The fluorescence signal is correlated with the presence of 118
nm light.

Figures 6.19 and 6.20 suggest that 118 nm light is being created, but is being consumed bysome mechanism before it is able to reach the detection region. This is supported by the fact that

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Figure 6.20: A comparison of the 118 nm signal (solid markers) and fluorescence streak (openmarkers) signal at different xenon pressures for a phase-matched mixture with Ar (green, Xe:Ar =1:11.3) and Kr (red, Xe:Kr = 1:4.6).

the fluorescence streak does not occur when 355 nm light is focused into a cell containing only
xenon or only argon. With only one gas, there is the same 355 nm power, Pω3 , but no 118 nm
light should be produced due to the lack of a phase-matched mixture. Since no fluorescence streak
appeared in this situation, 118 nm light is a prerequisite for the formation of the streak.
The mechanism for this decrease in 118 nm flux above PXe =20 torr must include a runaway
or positive feedback process since 118 nm signal continues to decrease with increasing fluorescence.
If the 118 nm signal did not turnover, but instead reached a plateau, the mechanism would haveto be a regulating or a negative feedback process. A plateau indicates that the process requires a
threshold amount of 118 nm light to begin, but would stop once it depletes the 118 nm light below
the threshold. Instead, we observe a turnover, this indicates that once the mechanism is initiated it“runs away” and consumes as much a 118 nm light as possible. As we increase the xenon pressure
for a phase-matched mixture, more 118 nm light should be produced. However, once the florescencestreak appears, increased pressure leads to a decrease in 118 nm flux.
To gain additional information about the fluorescence streak, a spectrum of the streak was

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Figure 6.21: A spectrum of the fluorescence streak created in a xenon-argon mixture. The locationof Xe I (Ar I) spectral lines are indicated in green (red).

taken with an Ocean Optics USB2000 spectrometer. The spectral lines from the streak are similarin shape and intensity to those observed in a xenon arc lamp indicating that the fluorescence ismost likely from electron-ion recombination in xenon. Figure 6.21 shows the recorded spectrum
and the location of the most prominent Xe I and Ar I lines. The spectrum shows predominantly
Xe I spectral lines and very weak Ar I spectral lines. Although xenon is present in a much lower
concentrations in the gas mixture, it is preferentially ionized over argon. This suggests that aphoton above the IP of xenon and below the IP of argon (15.76 eV) [206] is present in the system.
118 nm (10.51 eV) light is not enough energy to ionize xenon, which has an ionization potential(IP) of 12.13 eV [206].
A spectrum was also recorded for xenon-krypton system, Figure 6.22. While there are some
Kr I lines in the spectrum, again Xe I lines are the most prominent. Since krypton is not ionized
here, this limits the theory for the secondary process in the cell to a xenon only ionizing process,which should fall between the IP of xenon (12.13 eV) and krypton (14.00 eV).

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Figure 6.22: A spectrum of the fluorescence streak created in a xenon-krypton mixture. The
location of Xe I (Kr I) spectral lines are indicated in green (red).

6.5.4

Possible explanations for the limitations

Despite the data on the fluorescence streak and the 118 nm flux turnover, the mechanism
behind this effect is not well understood. Limitations to the conversion efficiency could arise fromlinear one-photon absorption as well as other non-linear processes not considered in the basic
theoretical model discussed in Section 6.5.1. The mechanism for signal decrease must provide an
explanation of all observed properties of the fluorescence streak including:(1) the predominance of Xe I lines with few Ar I/Kr I lines,(2) correlation of the fluorescence streak intensity with the phase matching curve,(3) and increased fluorescence with decreased 118 nm production (ie. a positive feedback
process not a negative feedback process.)
Non-linear processes including the Kerr effect and bandwidth limitations were discussed in[155], but did not sufficiently explain the magnitude and character of the observed decrease. The

198
spectra in Figures 6.21 and 6.22 suggest that a higher energy photon, possibly from higher-orderharmonics, is present. This criterion eliminates the possibility of efficient higher-order harmonic
generation (such as fifth-harmonic generation at 17.48 eV) since that photon would ionize bothxenon and argon. In that case, more Ar I spectral lines would be expected since argon is morethan 11 times more prevalent in the sample. Higher-order harmonic processes are also alreadyunlikely since the gas mixture is not phase matched for these processes. We consider two possible
mechanisms, linear absorption of 118 nm light and sum-frequency generation of 88 nm light, thatcan be tested experimentally.

6.5.4.1

Linear absorption of 118 nm light

Linear reabsorption of 118 nm light by the xenon-argon gas mixture could be an explanation
for the decrease in 118 nm flux. Although the 118 nm light is detuned from any transition inxenon or argon, absorption can still be possible in the wings of resonance lines. The most likely transitions for linear absorption of 118 nm in xenon is the (2 P3/2 )5d 23 line at 119.203 nm. There isan additional (2 P3/2 )7s line at 117.043 nm, but it is less likely to contribute due to its smaller, by afactor of 4, oscillator strength. The nearest argon line is at 106.66 nm, which is significantly further
away and even less likely to contribute to 118 nm light absorption. A more detailed description
and calculation of 118 nm linear absorption in a xenon-argon mixture can be found in [155].
To test for linear absorption of 118 nm light, a short absorption cell was placed in between
the 118 nm generation cell and the UHV detection chamber. Figure 6.23 shows a schematic of thissetup. A MgF window is placed after the MgF lens. The area between the window and lens serves
as the absorption cell. By filling this volume with various pressures of xenon and comparing theresulting signal, we can examine the possibility of 118 nm linear absorption by xenon. The 118 nm
generation cell, including the sealing MgF lens has been shifted away from the detection region by∼2 cm. To account for this change, the 355 nm lens on the outside of the vacuum chamber can be
adjusted such that the 118 nm light remains focused at the center of the TOFMS. Additionally,
this adjustment slightly changes the Rayleigh range of the focused beam. However, since this test

199

Figure 6.23: A cartoon of the 118 nm gas mixing cell, absorption cell, and ionization and detection
region. The absorption cell is sealed off using a MgF2 lens and window. The gas cell remains thesame length as in Figure 6.16, but has been shifted ∼2 cm away from the detection chamber.

was performed using NH3 as the detection ion, the single-photon process is less dependent on thefocus of the beam.
Preliminary studies using the absorption cell suggest that linear absorption is unlikely to be
the cause of the decrease in 118 nm flux [154]. Adding xenon, the most likely linear absorption
candidate, to the absorption cell did not decrease the observed 118 nm flux. Instead the flux
increased. The addition of various other gases (argon, nitrogen, air) to the absorption cell also
caused an increase in the observed signal. While the increase in signal could be due to a systematiceffect, it is unlikely that there is also linear absorption occurring simultaneously.

6.5.4.2

Sum-frequency generation

A second possible explanation for the decrease in 118 nm light production is sum-frequency
generation (SFG) from 355 nm and 118 nm photons. This would produce an extreme ultraviolet(EVU) photon at 88 nm (14 eV), which satisfies criteria (1). Although SFG is a χ(2) processes,
which is normally forbidden in atomic gases, second-harmonic and sum-frequency effects havebeen observed in several atomic gases and metal vapors. These processes were first observed
using external electric [207] or magnetic [208, 209] fields to break the symmetry of the gas and200
permit second-harmonic generation (SHG). SHG in an atomic gas without an external field was
subsequently observed in thallium by Mossberg et al. [210]. Additionally, SHG in gases without anexternal field has also been observed in metal vapors of sodium [211] and zinc [212], and atomic
gases of xenon [213, 214] and hydrogen [215]. Lastly, one case of Sum-frequency generation in an
atomic gas has been observed in sodium [216].
Various processes have been proposed to explain these normally χ(2) processes in atomic gases.
Primarily these processes include symmetry breaking components that allow for normally forbidden
process to proceed. The symmetry breaking processes fall into two categories: those that involve
photoionization and those with only neutral atoms [217]. The first category includes models wherecharge separation occurs as a result of multiphoton ionization of the gas. A symmetry breaking
electric field is formed due to the separation of the ion and electron. This occurs either from theradiative forces exerted by the pump light or the resulting kinetic energy of the ionization process.
The second category includes models that take into account the dipole-forbidden second-ordersusceptibility of the medium. By including contributions from higher-multipole orders, such as theelectric quadrupole and magnetic-dipole of the non-linear medium, χ(2) maybe non-vanishing [216].
Here, we concentrate on only the first category since Bethune [217] found that only ionization could
produce a strong SHG signal.
In previous atomic SHG experiments, it was not always possible to determine which of theexact mechanisms caused SHG in the non-metallic gases. However, there are two conditions thatalways made SHG more probable [213–215]. The first is ionization of the atomic gas that causes
charge separation. The electric field between the ion and electron is sufficient to break the symmetry
and allow for SHG. The second condition is a resonant two-photon allowed transition in the atom
at the wavelength of the SHG light which helps to enhance the creation of SHG light.
Both of these conditions can be fulfilled in the xenon-argon 118 nm system and could explain
the decrease in detected 118 nm flux. In SHG in a single atomic gas, the atom provides both theelectric field, usually through multiphoton ionization, and the resonant transition. However, in ourcase, xenon and argon each provide one of these components, and together aid in the generation

201
of 88 nm light. The initial electric field may come from 118 nm ionization of contaminants in
the gas system that have lower ionization potentials. Once a small field is present one of the
3p5 3d ← 1S0 transitions in argon, which are in the 87-89 nm range, can provide the resonant twophoton transition to help enhance SFG. Now that both conditions that make SHG more probable
are present, 88 nm light can be created. As soon as 88 nm light is present in the system, it would
ionize xenon and increase the symmetry breaking electric field. This mechanism meets criteria(2) and (3). With more 118 nm production there is a higher chance of 88 nm light and thus thefluorescence streak. It also contains a positive feedback loop of which both xenon and argon play arole. The loop is depicted in Fig. 6.24. Although more 118 nm light is created at higher pressures,
more EUV light is also created at higher pressures. If the SFG process dominates over the THG
process, it can explain the observed florescence increase and VUV decrease.
All the measurements with krypton are consistent with this mechanism since there are many
more potentially resonant transition in krypton than in argon. Since the SFG photon (14 eV) isright at the ionization potential of krypton (14.00 eV), there could be many high lying excitedstates of krypton that could assist in SFG.

Figure 6.24: Diagram depicting the feedback mechanism of electric field induced SFG. Symmetryis broken by an electric field caused by ionization of contaminants, which leads to SFG of 88 nm
aided by a near resonant transition in argon. The 88 nm light ionizes Xe, which causes a larger
electric field and more 88 nm light.

At this point it is uncertain which 3p5 3d ← 1S0 transitions in argon would be the one toenhance the SFG process, but the 3p5 3d [5/2]2 state appears to be the most likely. Using the same
argument as in Shi et al. [214], the highest laying J=0 or 2 state that also has an efficient onephoton coupling, should have the most efficient SFG process. Although in Shi et al., they examined

202
second-harmonic generation, the arguments should still relevant here. For 88 nm light and argon,
this would be the 3p5 3d [5/2]2 state at 113425.964 cm−1 (88.165 nm) coupling to 3p5 5s [3/2]1 at
113643.26 cm−1 (87.995 nm), which is 217.3 cm−1 away.
A possible experimental test of the SFG theory could be completed with a xenon-neon cell.
THG in a phase-matched mixture of xenon-neon has the potential to avoid any resonant transitions with SFG light. The first excited state of neon (16.62 eV) and the IP of neon (21.56 eV)
are sufficiently large enough that there are no resonant states to increase the efficiency of SFG
production at 88 nm (14 eV). To test a xenon-neon system, measurements would ideally be takenwith PXe > 24 torr. However, a phase-matched ratio of xenon-neon containing 50 torr of xenon
would have a total pressure around 20 bar. This is not achievable in the current experimental setup
since conflat components are not designed to hold positive pressures. Instead, a reinforced highpressure cell would have to be constructed, and special considerations would be required for thesealing lens since it would encounter even greater pressure differentials.
One other option for testing the SFG mechanism could be changing the pump laser wavelength. A tunable dye laser around 355 nm could be used instead of a Nd:YAG. If 118 nm lightyield is dependent on the pump laser wavelength, specifically if resonances are observed, this would
support the SFG mechanism. It would also help to determine which transition in argon is assistingin the SFG process. The pump beam could then be tuned so that the SFG wavelength is sufficiently
far away from the resonant 88 nm argon transition. While all the tests to determine whether SFG isthe cause of the decrease in 118 nm light signal are experimentally difficult to perform, if completed
they would significantly further our understanding of the 118 nm suppression mechanism. If it ispossible to overcome the suppression mechanism then many chemical studies that use 118 nm lightfor ionization and molecule detection would benefit greatly.

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[192] A.J.C. Varandas and A.I. Voronin. Calculation of the asymptotic interaction and modellingof the potential energy curves of OH and OH+ . Chemical Physics, 194(1):91 – 100, 1995.

216[193] Esther de Beer, M. P. Koopmans, C. A. de Lange, Yumin Wang, and W. A. Chupka. (2+1)
resonanceenhanced multiphoton ionizationphotoelectron spectroscopy of the OH radical. The
Journal of Chemical Physics, 94(12):7634–7639, 1991.
[194] Margaret E. Greenslade, Marsha I. Lester, Dragana . Radenovi, Andr J. A. van Roij, andDavid H. Parker. (2+1) resonance-enhanced ionization spectroscopy of a state-selected beamof OH radicals. The Journal of Chemical Physics, 123(7):074309, 2005.
[195] R. Forster, H. Hippler, K. Hoyermann, G. Rohde, and Lawrence B. Harding. REMPI mass
spectrum of the OH radical in the gas phase. Chemical Physics Letters, 183(6):465 – 470,
1991.
[196] Joseph M. Beames, Fang Liu, Marsha I. Lester, and Craig Murray. Communication: A newspectroscopic window on hydroxyl radicals using UV + VUV resonant ionization. The Journalof Chemical Physics, 134(24):241102, 2011.
[197] Amy M. Green, Fang Liu, and Marsha I. Lester. UV + V UV double-resonance studiesof autoionizing Rydberg states of the hydroxyl radical. The Journal of Chemical Physics,
144(18):184311, 2016.
[198] Manuel Lara, Benjamin L. Lev, and John L. Bohn. Loss of molecules in magneto-electrostatic
traps due to nonadiabatic transitions. Phys. Rev. A, 78:033433, Sep 2008.
[199] M. Bhattacharya, Z. Howard, and M. Kleinert. Ground-state OH molecule in combined
electric and magnetic fields: Analytic solution of the effective hamiltonian. Phys. Rev. A,
88:012503, Jul 2013.
[200] Nicholas P. Lockyer and John C. Vickerman. Single photon ionisation mass spectrometry
using laser-generated vacuum ultraviolet photons. Laser Chem, 17:139–159, 1997.
[201] Y. J. Shi, S. Consta, A. K. Das, B. Mallik, D. Lacey, and R. H. Lipson. A 118 nm vacuum
ultraviolet laser/time-of-flight mass spectroscopic study of methanol and ethanol clusters in
the vapor phase. The Journal of Chemical Physics, 116(16), 2002.
[202] R Miles and S Harris. Optical third-harmonic generation in alkali metal vapors. Quantum
Electronics, IEEE Journal of, 9(4):470–484, 1973.
[203] Gary C Bjorklund. Effects of focusing on third-order nonlinear processes in isotropic media.
Quantum Electronics, IEEE Journal of, 11(6):287–296, 1975.
[204] JF Ward and GHC New. Optical third harmonic generation in gases by a focused laser beam.
Physical Review, 185(1):57, 1969.
[205] R. Mahon, T. McIlrath, V. Myerscough, and D. Koopman. Third-harmonic generation inargon, krypton, and xenon: Bandwidth limitations in the vicinity of lyman- α;. IEEE Journalof Quantum Electronics, 15(6):444–451, Jun 1979.
[206] A. Kramida, Yu. Ralchenko, J. Reader, and and NIST ASD Team. NIST Atomic Spectra
Database (ver. 5.3), [Online]. Available: http://physics.nist.gov/asd [2016, January 29].
National Institute of Standards and Technology, Gaithersburg, MD., 2015.

217[207] R. S. Finn and J. F. Ward. dc-induced optical second-harmonic generation in the inert gases.
Phys. Rev. Lett., 26:285–289, Feb 1971.
[208] A. Flusberg, T. Mossberg, and S. R. Hartmann. Optical difference-frequency generation in
atomic thallium vapor. Phys. Rev. Lett., 38:59–62, Jan 1977.
[209] M. Matsuoka, H. Nakatsuka, H. Uchiki, and M. Mitsunaga. Optical second-harmonic generation in gases: ”rotation” of quadrupole moment in magnetic field. Phys. Rev. Lett.,
38:894–898, Apr 1977.
[210] T. Mossberg, A. Flusberg, and S.R. Hartmann. Optical second-harmonic generation in atomic
thallium vapor. Optics Communications, 25(1):121 – 124, 1978.
[211] Kenzo Miyazaki, Takuzo Sato, and Hiroshi Kashiwagi. Spontaneous-field-induced opticalsecond-harmonic generation in atomic vapors. Phys. Rev. Lett., 43:1154–1157, Oct 1979.
[212] W. Jamroz, P. E. LaRocque, and B. P. Stoicheff. Resonantly enhanced second-harmonic
generation in zinc vapor. Opt. Lett., 7(4):148–150, Apr 1982.
[213] Michelle S. Malcuit, Robert W. Boyd, William V. Davis, and Kazimierz Rza¸ewski. Anomaliesin optical harmonic generation using high-intensity laser radiation. Phys. Rev. A, 41:3822–
3825, Apr 1990.
[214] Y. J. Shi, W. Al-Basheer, and R. I. Thompson. Two-photon resonant second harmonic
generation in atomic xeon. The Journal of Chemical Physics, 130(9), 2009.
[215] L. Marmet, K. Hakuta, and B. P. Stoicheff. Second-harmonic generation in atomic hydrogen
induced by a charge-separation field. J. Opt. Soc. Am. B, 9(7):1038–1046, Jul 1992.
[216] Donald S. Bethune, Robert W. Smith, and Y. R. Shen. Sum-frequency generation via aresonant quadrupole transition in sodium. Phys. Rev. A, 17:277–292, Jan 1978.
[217] D. S. Bethune. Optical second-harmonic generation in atomic vapors with focused beams.
Phys. Rev. A, 23:3139–3151, Jun 1981.

Appendix A

Circuit Diagrams

This appendix contains the full updated circuit schematics, updated from [95] for the amplifiers discussed in Chapter 5. The circuits are included in the following order (circuit titles arefound in the lower righthand corner of each circuit):• Control board: this board creates the driving signals for both banks of one amplifier. The
PID feedback loop for each amplifier is located on this board.
• Amplifier bank: this is one half of one amplifier. One bank consists of four circuit borad
the main board containing the follow and nine slaves, a high-voltage FET wall, a resistordivider wall, and a protection diode wall. Two banks make up one amplifier.
• Amplifier breakout: this board interfaces between the amplifier (via ethernet cables) andthe control board (via a HPDB50 cable).
• Master interlock: this board conducts global error monitoring including cooling water,
power supplies, and amplifiers (through the error bus)
• Master interlock breakout: this board converts between two DB25 connectors for the Spellman high-voltage supplies and two ethernet error bus connectors to one 50 pin ribbon cablethat connects to the master interlock

A

B

C

D

8

8

J50-10J50-12

J50-5

J50-7

J50-9

J50-11

FAN1_TACH+5V

J50-20J50-19J50-47

J50-49BB_CATHODE

BB_ANODE
J50-50J50-48

J50-46

J50-42

J50-40J50-44

J50-41-V1

J50-45

J50-39BB_CURRENT

J50-38

J50-43

J50-37

J50-36

J50-35+V1

J50-34

J50-32

J50-30J50-29J50-33

J50-28J50-27

TB_ANODE

J50-26

J50-25

J50-31

J50-24

J50-23+V1

TB_CURRENTTB_CATHODE

J50-22

J50-21-V1

J50-18J50-17-V1

J50-16

J50-15

HV_MONITOR

J50-14J50-13

J50-8

+V1

7

J50-4

FAN_GND

J50-3

FAN_GND

FAN2_TACH

J50-6

J50-2

FAN_PWR

J50-52

J50-51

J50-1

FAN_PWR6

6

adapts to 50 pin HPDB50 (half-pitch DB connector) on board mounted on rear panel

50 pin ribbon cable output connector

7

A1
A2
A3
AMP_ERROR_BUS

2345+HV_RAIL-HV_RAIL

7
8

6

A0

1

J9

5

+HV_RAIL

7
8-HV_RAILAMP_ERROR_BUS
AMP_ENABLE

5
6

A3

A2

3
4

A1

A0

2

1

extra RJ45 for daisy chaining

J3

Bus Signals to/from Master Interlock
shielded ethernet, shield carries ground

5

100k
R4

TTL High = Enable

4

1V in = 12kV out

J1

+5V

+5V

J6

R16
10k

pin 1 grounds on pushpushbutton, NO

S1

Manual Enable/Disable Switch
up = enabled

pin 3 NC

AMP_ENABLE

4

R76
1k

S4

R13
1M

100k
R67

3

C153
1uF

CONTROL

CLEAR_ERRORSMANUAL_ENABLE

FP_ENABLE3electronics

RAIL_ERROR

DN: LEW0099

2

R61 1kR49 1k

R47 1k

R46 1k

R44 1kDRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 1 OF 7

HINPUTS_AND_OUTPUTSHV Amplifier Control

JILA ELECTRONICS LAB

VERSION:DATE:

N. Fitch

All 4 red

LED2
LED_STACK_4HIGH

1k

1k

R15 1kR9

R6

LEDs monitor error status whether that interlock
monitor is enabled or not

RAIL_ERROR_LATCHED

4

3

2

6

5

1

8

7
RPM_ERROR

All 4 green

LED1
LED_STACK_4HIGH

RPM_ERROR_LATCHEDUPDATE: 2/26/2018

DESIGN BY:

43ENABLE_STANDING

2

6

5

1

8

7

TUNE

1

Bottom Bank Current
1V/A

Top Bank Current
1V/A

Vout Indicator
1V/1.5kV

ENABLE

J8
1V/A

J14

J7

AMP_OK

BB_CURRENTTB_CURRENTOUTPUT_MONITOR

2

H

A

B

C

D

219

A

B

C

U49
74LVC1G332
1
A
4
3
Y
B
6
C

MANUAL_ENABLE

8

FAN_ERROR

7

TOO_CLOSE_TO_RAIL

U61

74LVC1G11
4

J5

R12
10k

U11
74LVC1G332
1
A
4
3
Y
B
6
C

+5V

jump to tune optocoupler gain
TTL_ENABLE

TTL enable signal can come from the master interlock board (rear panel ethernet)
or from front panel sma (for testing)

AMP_ENABLE

FP_ENABLE3
6

1

AMP_OK

1

D

2

7

6

2

1
4
74HC1G00

U50

TUNE

U63
74LVC1G332
1
A
4
3
Y
B
6
C

Enables feedback
ENABLE6

AMP_ERRORAMP_OK

4

5

4

Enable Standing Current if:
1) Tuning Mode is selected OR
2) Normal operation switch + high logic on "Amplifier Enable" input

ENABLE_STANDING

5

A3

1
2
3
4

74HC86

U2-D

74HC86

U2-C

3

8

3

11

74HC86

U2-B

74HC86

U2-A

ADDRESS_MATCH

AMP_ERROR

13

12

10

A2

AMP_A395

AMP_A2

4

A1

2

1

AMP_A1

A0

AMP_A0

S5

6

2

4

U19
74LVC1G125

low if match2electronics

DN: LEW0099

2

UPDATE: 2/26/2018

ADDRESS_MATCH

1H

DRAWN BY:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 2 OF 7

VERSION:

BUILT FOR:LOGIC

HV Amplifier Control

JILA ELECTRONICS LAB

U16
74LVC1G332
1
A
4
3
Y
B
6
C

DATE:

N. Fitch

AMP_ERROR_BUS

U12
74LVC1G332
1
A
4
3
Y
B
6
C

U4
74LVC1G332
1
A
4
3
Y
B
6
C

AMP_A3
AMP_A2
AMP_A1
AMP_A0DESIGN BY:

sets board bus address R19 R40 R41 R58
0-7 Decelerator Amps 100k 100k 100k 100k
8-15 Trap Amps

8
7
6
5

+5V

3

1

8

H

A

B

C

D

220

1500:1

6

R1
2.21k

15kV = 10V
12kV = 8V

6

R10
2.21k

LF356M
R8
100

-

-V1

4

3 +

2

7

+V1

R2
221

6

5

AD825AR

U1

20K
R5

CW

proportional gain adjust

OUTPUT_MONITOR

D

R3
2k

C4
DNI
R7
221

4

7
-

-V1

4

3 +

2

+V1

ENABLE63
5

C65 15nF

S2

C66 12nF

7

VCONTROLelectronics

N. Fitch

If the output voltage is greater than the requested input value,
Vcontrol > 0, which willturn the Bottom FET Bank on, and the Top Bank off.

Feedback Gain Sign:

C61 0.1uF

C62 68nF1

2

C71 47nF

C63 33nF

3

C64 22nF

5
4

6

C68 6.8nF

10

13

C69 4.7nF

11

C67 10nF

C70 3.3nF

12

8

U22-A

* MAX4510

9

6*Analog switch positions shown for 0V input

AD825AR

U3

R11
2.21k

R70
100

2

JILA ELECTRONICS LAB

1

H

C

D

3

DN: LEW0099

2

UPDATE: 2/26/2018

DESIGN BY:

DATE:

H

DRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 3 OF 7

VERSION:

FEEDBACK_LOOPHV Amplifier Control

A

7

AD825AR65

HV_MONITOR-V1x(-8), 1V in = 12kV desired = -8V out

-V1

4

U6

U8
1

3

Integral gain adjustable on front panel via 12 position rotary switch
S2 position 1 disables integrator

4

A

8

-

3 +

2

7

R14
500

-

2
4

+

3

7

+V1

5

B

CONTROL

R20
1k

+V1

R21
7.5k

HV_MONITOR

6

B

C

7

CW rotation increases integral gain
GH7105_12POS_ROTARY

D

8

221

A

B

C

bank gain balance

R23
10k

8

D5
10.0V
LM4040

R25
1k

+V1

C24

0.1uF

+VREF

Bottom Bank is on for Vcontrol > 0V.

VCONTROL

R30
5.1k

R27
5.1k

7

7
-

R26
1k

-V1

6

6
AD825AR

U14

D10
BAV19W-7

R36
10k

AD825AR

U9

C25
0.1uF

-V1

4

3 +

-

7

+V1

-V1

4

3 +

2

2

D6
10.0V
LM4040Top Bank is on for Vcontrol < 0V.

+V1

D7
BAV19W-7

R33
10k

D14
BAV19W-7

-VREF

R28
5.1k

+VREF

*

6

R29
5.1k

ENABLE

Negative Output

ENABLE

6

5

R53
10k

3
6

*

3

5

U29-A
MAX4520

R97
10k

*

5

MAX4510
U30-A

R34
5.1k

*

R35
390k

5

MAX4510
U24-A

MAX4510
U37-A

-VREF

*

5
ENABLE_STANDING

3

U23-A
MAX4520ENABLE_STANDING

Positive Output

D13
BAV19W-7

6

5
6

D

CW

3
3

7

3

6
5
6

5
6

8

*

R37
5.1k

MAX4510
U10-A

7
-

R38
390k

6
AD825AR

U13

-

7

+V1

-V1

4

3 +

2

C21
100pF

R48
5.1k

6

TP1

CW

R57
10k

R64
250
1/4W

AD825AR

U18

D12
BAV19W-7

CW

R52
10k

4

*Analog switch positions shown for 0V input

-V1

4

3 +

2

+V1

D9
BAV19W-7

C18
100pF

R43
5.1k

4

R66
250
1/4W

TP2

inverting half-wave rectifier with buffer in feedback
optoisolator LED acts as the second diode in this circuit

3

TB_CATHODE

TB_ANODE

3electronics

DN: LEW0099

2

1

DRAWN BY:BUILT FOR:

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5/2/2013 SHEET 4 OF 7

H

OPTOCOUPLER_LED_DRIVE

HV Amplifier Control

JILA ELECTRONICS LAB

VERSION:DATE:

N. Fitch
UPDATE: 2/26/2018

DESIGN BY:

BB_ANODEBB_CATHODE

2

A

B

C

D

H

222

A

B

8

7

C120
0.1uF

FAN2_TACH

D4
2.048V
LM4040

R132
1k

+V1

10

C102 R110 C100
47nF 100k 1uF

R109
10k

R108
470
+5V

+5V

FAN_REF

C105
C103
47nF R117 1uF
100k

R113
10k

R112
470
+5V

FAN_REF

6

want Vout > 2.5V to indicate normal operation
fout = Vcc * fin * C105 * R110

U36
LM2917R118
10k

FAN_REF+5V

want Vout > 2.5V to indicate normal operation
fout = Vcc * fin * C102 * R110

FAN_REF

+5V

11
12

FAN1_TACH

U34
LM2917
R111
10k

6

8

GND

+5V

1

FAN_REF
12
GND
C+

CCP1
2

9
V+
OP+

C
E

C+
1

+
4
1

U42

8
5
6

5

2

3

+
4
1

U43

8
5
-

+5V

4

7

LM311DR

7

LM311DR

R54
10k

+5V

R59
10k

+5V

Y

4

74LVC1G332
U44

6
C
3
B
1
A
4

FAN RPM MONITOR

6

FAN2_FREQ

2

3

+5V

FAN1_FREQ5

RPM_ERROR

CLEAR_ERRORS

1

3

+5V

3

CLK

D

3

VCC

OPCP2
3
11

5
CLR
6

5

C-

Q

U17

GND
2

C

7

74LVC1G175

4

DN: LEW0099

2

1

H

DRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 5 OF 7

VERSION:

FAN_MONITOR

HV Amplifier Control

JILA ELECTRONICS LAB

R141
10k

FAN_ERROR

jump to enable fan monitoring
J19

DATE:

N. Fitch
UPDATE: 2/26/2018

DESIGN BY:

electronics

U25
74LVC1G332
1
A
4
3
Y
B
6
C

RPM_ERROR_LATCHED

2

1

4
10

CP1
2

8
C

9

OPCP2
3

V+
OP+
4

E
5

2

D

8

H

A

B

C

D

223

A

B

C

OUTPUT_MONITOR

8

R172
10k

3

2

1

U33

-V1

4

+

-

7

+V1

5

R18
10k

D2
10.0V
LM4040

R17
1k

R31
10k

-HV_RAIL

7** (+HV_RAIL - VOUT)/2 [0-10V]*** ( -HV_RAIL+VOUT)/2 [0-10V]

3

2

R165
10k

R167
7.5k

R170
7.5k R173
7.5k

R179
330

R180
10k
~0.34V

C47
0.1uF+HV_RAIL

10V for -15kV output
0V for 0kV output

LF356M

6+V1

OUTPUT_MONITOR

1

U41

-V1

4

+

-

7

+V1

5

R171
10k

R168
7.5k

1

U5

-V1

4

+

-

7

5

6

LF356M

6

6

2

3

-V1

+
4
1

U57

8
5
-

+V1

LF356M***

RAIL_PROXIMITY

3

2

+V1

R166
10k

6
7
LM311DR

**

5

+5V

-V1

+
4
1

U55

8
5
-

R71
10k

2

3

+V1

6
LM311DR

7

R60
10k

+5V

4

U58
74LVC1G332
1
A
4
3
Y
B
6
C

RAIL PROXIMITY MONITORRAIL_ERROR

CLEAR_ERRORS

1

3

+5V

CLK

D

VCC

4

5
CLR
6

5

Q

U26

GND
2

6

3

74LVC1G175

4

3

DN: LEW0099

2

HV Amplifier Control

DRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 6 OF 7

H

RAIL_PROXIMITY_MONITOR
VERSION:DATE:

N. Fitch
UPDATE: 2/26/2018

DESIGN BY:

TOO_CLOSE_TO_RAIL

1

JILA ELECTRONICS LAB

R177
10k

jump to enable rail proximity monitoring
J28

electronics

U31
74LVC1G332
1
A
4
3
Y
B
6
C

RAIL_ERROR_LATCHED

2

1

7

2

D

8

H

A

B

C

D

224

A

B

C

2

3

+-RTN

-15V/-12V IN

8

1

J4
POWER IN

+15V/+12V IN

C20
10uF

+

C12

C23

S9

IN

S6

1

2

GND

OUT

LM7805CT
U7
3

7

+

C48

GRN
D11

R45
C40 2.21k
10uF

+5V

FAN_PWR

2+V1

FAN_GND

1

GRN R425.1k
D8(12V, 4.16A)

J2

R24
5.1k

from fan transformer

-V1

C19
10uF

+

+V1

C28

GRN
D15

0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C9

+5V
C60
0.1uF
0.1uF

C154

6

0.1uF

C159
0.1uF

C135

C7

C125
C15

C101

C104
C121 C123

C13

C17

C10

C11
C42

C38

C45

C41

C137
C139

C49

4

C141 C143

C84

C80
C82

C146 C151

3

C46

C8

-V1

C1

5

C3

C26
C30

C31
C138

C142 C144

C81

C150 C152

-V1

4

-V1

-V1

3

-V1

el
ectronics

DN: LEW0099

2

-V1

V2 4

1

DRAWN BY:BUILT FOR:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 7 OF 7HPOWER_CONNECTIONSHV Amplifier Control

JILA ELECTRONICS LAB

VERSION:DATE:

N. Fitch

-V1

V2 4

UPDATE: 2/26/2018

DESIGN BY:

-V1

V2 4

V2 4

V2 4

V2 4

U10-B
1 MAX4510
V+

U30-B
1 MAX4510
V+

U29-B
1 MAX4520
V+

U37-B
1 MAX4510
V+
V2 4

+V1

+V1

+V1

+V1

C16

U23-B
1 MAX4520
V+

C32

+V1

C83

U24-B
1 MAX4510
V+

C85

GND

+V1

C50

GND

U22-B
1 MAX4510
V+

C140

2

GND

+V1

C35

C6
0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C2
0.1uF

0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C14

+V1

0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C136 C5

GND

D

1

1

5

GND

6

GND

7

GND

8

H

A

B

C

D

225

226
C

D

B

A

1

1

1

2

S1_DIVIDER

1.5M

2.5M
3

R6
HV_RESISTOR(S)2

TP2

Q7 and Q8 make up the voltage limiter
Installation is optional

R1
10
1/2W
D2 1
3kV 3

C9
220pF
6.3kV

Q8

Q1
IXTF1N400

3

D1
15V

C3
5pF
6.3kV

GREEN
D37

100

2

C2
47pF
6.3kV

R21
430

R23

3906

R3
100

R8
51k

R7
400k

4

S1_SOURCE

+12V
3

R2
510k

Q10
3904 Q11

C1
1nF

R15
10k

6-9V
R22
10M

Q7
3904
R18
1k

4

R16
100

Q12
3906

+6V

R34
51k

D4
3.0V
MAX6009A

C4
1uF

D5
3.0V
MAX6009A

C5
1uF

D6
R17
3.0V
100
MAX6009A

C6
1uF

D7
3.0V
MAX6009A

C7
1uF

+

C8
10uF

4

Q2
NJT4031N

Q9-A

Q9-B

R19
5.11k

R5
3
1/2W

5
R9
2k

5

R10
1k

0V

TP4
D11
1N4007D21

D157
1N4007

Current Sensor

6

1

MASTER_SOURCE

1/2 OPI120

D13
1N4007Q13
NJT4031N

Q14
NJT4031N

TP1
TP3
TP9
TP10

2-56
M1

J20
to outside wall (shield)

2-56
M2

6

for bottom shield

TP5
R20
10
1/2W

R4
300
1/2W

ILED = Iout/30

TP6

7

8

TP7

7

TP8

To Output and Bottom Bank (Top Bank)To -HV (Bottom Bank)el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIERDESIGN BY: N. Fitch / T. Brown

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN:

8MASTERDATE:D

H DRAWN BY: N. Fitch

5/2/2013 SHEET 1 OF 9

C

B

A

227
C

D

B

A

1

1

2

2

OPTOCOUPLER CONNECTIONS(elevated off board)

ANODE

3
Q51

ANODE

1

CATHODE

2

J19

3

3

CATHODE

4+V
CURRENT-V

5shielded ethernet from breakout board

6
7
8

4

4
+V
+V

Ic = 0.1*IledIc = Iout/300
5mA max

R161
1M

4
Q52
3

5

R160
100k

R159
100

*

C175
0.1uF

5
-

LM8261

+
2

R61
100

1

U65

C17
0.1uF

CURRENT

represents bank current
1V + 1V/A

5-V

10:1 receiver current ratio*V = (Iout/30)*(1/10)*300 = Iout
+ ~1V of DC offset

OPI120 phototransistor is insensitive to LED currents below ~250uA
Since the LED drive is Iout/30, the current sensor is insensitive to Iout less than 7.5mA or so

6

6

OPI120 phototransistor case (shield) is connected to the collector
OPI120 LED case (shield) is connected to the anode
Common collector configuration chosen so that phototransistor body/shield is a low impedance point

7

8

7

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIERDESIGN BY: N. Fitch / T. Brown

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

8

OPTOCOUPLERS

DATE:

D

H DRAWN BY: N. Fitch

5/2/2013 SHEET 2 OF 9

C

B

A

228
C

D

B

A

1

1

S3_SOURCE

S3_DIVIDER

D12

R51
510k

1 J3
1462X

Jump to disable stage

IXTF1N400

2

C23
220pF
6.3kV

R48
2M

Q21
2N6660

4

C28
47pF
6.3kV

R44
100

Q19

D43
3.0V
MAX6009A

C22
1uF

D42
3.0V
MAX6009A+
C27
D41
10uF 3.0V
MAX6009A

C21
1uF

D44
3.0V

C25
1uF

C26
1nF

R14
1k

2

3

Q3
C20
1uF
3904
R11
270

D
R45

G

S2_DIVIDER

100

S

4

D40 15V
R49510k

S2_SOURCE5

R31
HV_RESISTOR(S)

3

2.5M

1 J1

D22

R25
510k

3kV 3
C18
220pF
6.3kV

2

Q16
2N6660

7

R27
2M

C19
1nF

D

D26
3.0V
MAX6009A

C12
1uF

D27
+
3.0V
C16
10uF MAX6009A

C13
1uF

D28
3.0V
MAX6009A

C14
1uF

D29
3.0V

C15
1uF

R29
1k

1462X

1 J2
C11
5pF
6.3kV

R26
100

D3 1

5

D25
GREEN

Q15
IXTF1N400

R32
400k

R33
51k

R24
10
1/2W

1462X

Jump to disable stage

TP11

1.5M

2

C10
47pF
6.3kV

Jump to disable stage

1

M6
2-56

TP15
for testing voltage sharing

1

2

J21

6

1 J4
C29
5pF
6.3kV

4

3

D38
GREEN

R40
51k

R53
400k

Jump to disable stage

3kV 3

TP13

1.5M

1462X

R39
10
1/2W

D8 1

2

2

R52
HV_RESISTOR(S)

3

2.5M

4

1

2

6

Q4

3904

R12
270

R30

G

100

S
D23 15V
R28
510k

S1_SOURCE

S1_DIVIDER

7

TP12
J22

8

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIER8SLAVE1:2

DESIGN BY: N. Fitch / T. Brown
DATE:

D

Q3 and Q4 make up the voltage limiter
Installation is optional

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

for testing voltage sharing

1

H DRAWN BY: N. Fitch* Sets slave voltage limit, Vlimit = 0.6*Rbias/Rlimit

5/2/2013 SHEET 3 OF 9

C

B

A

229
C

D

B

A

1

1
S5_SOURCE

2

R74
100
R81
510k

Q29
2N6660

+

C46
1nF

R78
2M

C47
10uF

D

C42
1uF

D72
3.0V
MAX6009A

C41
1uF

D71
3.0V
MAX6009A

C40
1uF

D74
3.0V

C45
1uF

R35
1k

100

S
D70 15V
R79
510k

S4_SOURCE

J24

3904

S4_DIVIDER

4
TP21

R67
HV_RESISTOR(S)

3

2.5M
TP16

5

1.5M

1 J5

5

1 J6

IXTF1N400

D52

3kV 3

2

C33
220pF
6.3kV
Q25
2N6660

C39
5pF
6.3kV

R59
100

Q23
D10 1

R66
510k

R63
2M

+

C36
1nF

C37
10uF

D
G

100

D55 15V
R64
510k

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIER

DATE:

D

C31
1uF

D56
3.0V
MAX6009A

C30
1uF

D59
3.0V

C35
1uF

6

Q6

3904

R36
270

S3_DIVIDER

7
TP18
for testing voltage sharing

1

8

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

D57
3.0V
MAX6009A

R37
1k

Q5 and Q6 make up the voltage limiter
Installation is optional

SLAVE3:4

DESIGN BY: N. Fitch / T. Brown

C32
1uF

S3_SOURCE

J23

el
ect roni cs

D58
3.0V
MAX6009A

2

C38
47pF
6.3kV

R60

S

7

R68
400k

D53
GREEN

R55
51k

R54
10
1/2W

1462X

Jump to disable stage

R13
270

for testing voltage sharing

1

1

M7
2-56

8

3

Q5

R75

G

4

D73
3.0V
MAX6009A

Jump to disable stage

D67

3kV 3

2

2

C48
47pF
6.3kV

1462X

IXTF1N400

2

D9 1

C49
5pF
6.3kV

1462X

1 J8

Q27

C43
220pF
6.3kV

6

2

4

1 J7

R83
400k

D68
GREEN

R70
51k

R69
10
1/2W

1462X

Jump to disable stage

TP19

1.5M

Jump to disable stage

2

3

R82
HV_RESISTOR(S)

3

2.5M

4

1

S5_DIVIDERH DRAWN BY: N. Fitch

5/2/2013 SHEET 4 OF 9

C

B

A

230
C

D

A

1

S7_SOURCER112
HV_RESISTOR(S)

3

2.5M

2

1

S7_DIVIDER

D24 1

1462X

1 J12

3kV 3

C69
5pF
6.3kV

R104
100

Q35
IXTF1N400

D97

R111
510k

2

R108
2M

C63
220pF
6.3kV
Q37
2N6660

+

C66
1nF

C67
10uF

D

D103
3.0V
MAX6009A

C62
1uF

D102
3.0V
MAX6009A

C61
1uF

D101
3.0V
MAX6009A

C60
1uF

D104
3.0V

C65
1uF

1462X

Jump to disable stage

2

C68
47pF
6.3kV

R41
1k
Q17

3904

R38
270

R105

G

100

S
D10015V
R109
510k

S6_SOURCE

S6_DIVIDER

4

4

TP27
for testing voltage sharing

1

2

R97
HV_RESISTOR(S)

3

2.5M
TP22

1.5M

R98
400k

4

J26

1

M8
2-56

D83
GREEN

R85
51k

6

Q31

D30 1

IXTF1N400

3kV 3

C59
5pF
6.3kV

R89
100
D82

R96
510k

2

C53
220pF
6.3kV
Q33
2N6660

R93
2M

+

C56
1nF

D
100

R94
510k

J25

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIER

DATE:

D

D86
3.0V
MAX6009A

C50
1uF

D89
3.0V

C55
1uF

Q18

6
3904

R42
270

S5_DIVIDER

TP24

7

for testing voltage sharing

1

8

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

C51
1uF

R43
1k

Q17 and Q18 make up the voltage limiter
Installation is optional

SLAVE5:6

DESIGN BY: N. Fitch / T. Brown

D87
3.0V
MAX6009A

S5_SOURCE

7elect roni cs

C52
1uF

2

C58
47pF
6.3kV

5

R90

G
S
D85 15V

8

C57
10uF

D88
3.0V
MAX6009A

1462X

1 J10

R84
10
1/2W

1462X

Jump to disable stage

5

1 J9

2

3

Jump to disable stage

3

D98
GREEN

R100
51k

R99
10
1/2W
1 J11

R113
400k

Jump to disable stage

TP25

2

1.5M

4

1

B

H DRAWN BY: N. Fitch

5/2/2013 SHEET 5 OF 9

C

B

A

231
C

D

B

A

1

1

S9_SOURCE

2.5M

1.5M

2

D31 1

C89
5pF
6.3kV

R134
100
D127

R141
510k

C83
220pF
6.3kV

R138
2M

Q45
2N6660

+

C86
1nF

C87
10uF

D
G

R135

S 15V

100

D130

4

R139
510k

D133
3.0V
MAX6009A

C82
1uF

D132
3.0V
MAX6009A

C81
1uF

D131
3.0V
MAX6009A

C80
1uF

D134
3.0V

C85
1uF

S8_SOURCE

2

C88
47pF
6.3kV

R47
1k

3kV 3

1462X

1 J16

Q43
IXTF1N400

2

Jump to disable stage

1 J15

R143
400k

D128
GREEN

R130
51k

R129
10
1/2W

1462X

Jump to disable stage

TP31

3

2

3

2

R142
HV_RESISTOR(S)4

1

S9_DIVIDER

3

Q20

3904

R46
270

S8_DIVIDER

4

TP33
for testing voltage sharing

1

5

2

1.5M

5

D32 1
3kV 3

R119
100

Q39
IXTF1N400

D112

R126
510k

2

C73
220pF
6.3kV
Q41
2N6660

R123
2M

+

C76
1nF

C77
10uF

D

C72
1uF

D117
3.0V
MAX6009A

C71
1uF

D116
3.0V
MAX6009A

C70
1uF

D119
3.0V

C75
1uF

R56
1k

2

C78
47pF
6.3kV

6

Q22

3904

R50
270

R120

G
S 15V

100

D115
R124
510k

7

D118
3.0V
MAX6009A

1462X

1 J14
C79
5pF
6.3kV

Jump to disable stage

1 J13

R128
400k

D113
GREEN

R115
51k

R114
10
1/2W

1462X

Jump to disable stage

TP28

6

R127
HV_RESISTOR(S)

3

2.5M

4

J28

1

M9
2-56

S7_SOURCE

S7_DIVIDER

7
TP30

J27

8

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIERSLAVE7:8

DESIGN BY: N. Fitch / T. Brown
DATE:

D

1

Q20 and Q22 make up the voltage limiter
Installation is optional

8

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

for testing voltage sharing

H DRAWN BY: N. Fitch

5/2/2013 SHEET 6 OF 9

C

B

A

232
C

D

B

A

1

1
HV

To +HV (top bank)
To Output (bottom bank)

2-56
M4

TP37 TP38 TP39

2-56
M5

2

2
HV

D143
GREEN

R145
51k

1 J18

D33 1
3kV 3

R149
100

Q47
IXTF1N400

C99
5pF
6.3kV

D142

R156
510k

2

C93
220pF
6.3kV
Q49
2N6660

5

R153
2M

+

C96
1nF

C97
10uF

D

D148
3.0V
MAX6009A

C92
1uF

D147
3.0V
MAX6009A

C91
1uF

D146
3.0V
MAX6009A

C90
1uF

D149
3.0V

C95
1uF

R58
1k

C98
47pF
6.3kV

2

Jump to disable stage

1 J17

R158
400k

1462X

4

1.5M

R144
10
1/2W

1462X

Jump to disable stage

TP34

3

2

R157
HV_RESISTOR(S)

3

2.5M

4

1

3

4

Q24

3904

R57
270

R150

G

100

S
D14515V
R154
510k

S9_SOURCE

S9_DIVIDER

5

TP36
for testing voltage sharing

J29

1

6

6

7

7

8

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIERDESIGN BY: N. Fitch / T. Brown
DATE:

D

8

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

Q24 is the voltage limiter
Installation is optional

SLAVE9H DRAWN BY: N. Fitch

5/2/2013 SHEET 7 OF 9

C

B

A

233
C

D

1

Input

+HV BR20

Input
BR18

2

Input
BR16

Input
BR14

3

Input
BR12

Input
BR10

4

Input
BR8

Input
BR6

Input
BR4

5

Input
BR2

1

B

A

R1090
150k

R1080
150k

R1070
150k

R1060
150k

R1050
150k

R1040
150k

R1030
150k

R1020
150k

R1011
150k

R1002
150k

R1091
250k

R1092
250k

R1093
250k

R1094
250k

R1095
250k

R1096
250k

R1097
250k

R1098
250k

R1099
250k

R1100
250k

R1101
150k

R1081
150k

R1071
150k

R1061
150k

R1051
150k

R1041
150k

R1031
150k

R1021
150k

R1012
150k

R1003
150k

R1102
250k

R1103
250k

R1104
250k

R1105
250k

R1106
250k

R1107
250k

R1108
250k

R1109
250k

R1110
250k

R1111
250k

R1112
150k

R1082
150k

R1072
150k

R1062
150k

R1052
150k

R1042
150k

R1032
150k

R1022
150k

R1013
150k

R1004
150k

2

1
2

1
2

1

R1113
250k

R1114
250k

R1115
250k

R1116
250k

R1117
250k

R1118
250k

R1119
250k

R1120
250k

R1121
250k

R1122
250k

R1123
150k

R1083
150k

R1073
150k

R1063
150k

R1053
150k

R1043
150k

R1033
150k

R1023
150k

R1014
150k

R1005
150k

R1124
250k

R1125
250k

R1126
250k

R1127
250k

R1128
250k

R1129
250k

R1130
250k

R1131
250k

R1132
250k

R1133
250k

R1134
150k

R1084
150k

R1074
150k

R1064
150k

R1054
150k

R1044
150k

R1034
150k

R1024
150k

R1015
150k

R1006
150k

2

1
2

1

R1135
250k

R1136
250k

R1137
250k

R1138
250k

R1139
250k

R1140
250k

R1141
250k

R1142
250k

R1143
250k

R1144
250k

R1145
150k

R1085
150k

R1075
150k

R1065
150k

R1055
150k

R1045
150k

R1035
150k

R1025
150k

R1016
150k

R1007
150k

2

1

R1146
250k

R1147
250k

R1148
250k

R1149
250k

R1150
250k

R1151
250k

R1152
250k

R1153
250k

R1154
250k

R1155
250k

R1156
150k

R1086
150k

R1076
150k

R1066
150k

R1056
150k

R1046
150k

R1036
150k

R1026
150k

R1017
150k

R1008
150k

R1157
250k

R1158
250k

R1159
250k

R1160
250k

R1161
250k

R1162
250k

R1163
250k

R1164
250k

R1165
250k

R1166
250k

R1167
150k

R1087
150k

R1077
150k

R1067
150k

R1057
150k

R1047
150k

R1037
150k

R1027
150k

R1018
150k

R1009
150k

R1168
250k

R1169
250k

R1170
250k

R1171
250k

R1172
250k

R1173
250k

R1174
250k

R1175
250k

R1176
250k

R1177
250k

R1178
150k

R1088
150k

R1078
150k

R1068
150k

R1058
150k

R1048
150k

R1038
150k

R1028
150k

R1019
150k

R1010
150k

R1179
250k

R1180
250k

R1181
250k

R1182
250k

R1183
250k

R1184
250k

R1185
250k

R1186
250k

R1187
250k

R1188
250k

R1189
150k

R1089
150k

R1079
150k

R1069
150k

R1059
150k

R1049
150k

R1039
150k

R1029
150k

R1001
150k

R1000
150k

2

1
2

1
2

1
2

BR19

2

Ouput

1

BR17

2

Ouput

1

BR15

2

Ouput

R1191
250k

R1192
250k

R1193
250k

R1194
250k

R1195
250k

R1196
250k

R1197
250k

R1198
250k

R1199
250k

2

1

BR13

2

Ouput

1

BR11

2

Ouput

1

BR9

2

Ouput

1

BR7

2

Ouput

1

BR5

2

Ouput

1

BR3

2

Ouput

1
2

R1190
250k

1

1

3

4

5

BR1

Ouput Master Source

66

1.5M bias resistor for each stage
Average voltage across each resistor is 1.5kV (with +/-15kV rails)
Hence 1.5W average power dissipation
If 30kV across either bank (output is railed), then 9W power dissipated per resistor network

7

8

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIER

8

BIAS_RESISTORDESIGN BY: N. Fitch / T. Brown

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

7

DATE:

D

H DRAWN BY: N. Fitch

5/2/2013 SHEET 8 OF 9

C

B

A

234
C

D

B

A

2

C

A
A

C

A

A

C

A
A

C

A

C

A

A

C

A

C

A
A

A

D34
*

C

A

C

D19

Ouput

1

BR24

2

Ouput

1

BR26

2

Ouput

A

C

C

A

C

A
A

C
C

C

A

D18

D48
*

D35

C

A

C

D62
*

D49

D36

C

A
A

C

A

C

A
A

C

A

C

A

A

C

A
A

C

C

C

D17

A

C

A

C

A

C

C

A

C

A

C
C

A
A

A

A

D16

A

C

A

C

A

C

A

C

A

C

A

C
C
C
C

A

A

C

A

C

A

C

A

C
C

A

C

A
A
A

C

A

A

D15

D39

D76
*

D63

D50

BR22

2

D20
*

1

BR28

2

Ouput

1

BR30

2

Ouput

1

BR32

2

Ouput

1

BR34

2

Ouput

1

BR36

2

Ouput

1

BR38

2

Ouput

2

3

4

5

6
1
2

BR40

Ouput Master Source*P6SMB550A
550V TVS
600W peak
495V working voltage * 7 = 3.46kV total

7

8

A

C

D14

D45

C

1

D46

D51

A

6

D47

D54

C

2

D60

A

1

D61

D90
*

D77

D64

1

D99
*

D91

D78

D65

D111
*

D105

D92

D79

D66

D114

D106

D93

D80

D69

C

Input
BR37

D75

D120

D107

D94

D81

C

C

D84

D121

D108

D95

C

C

D96

2

D122

D109

C

C

D110

2

2

D123

A

D124

A

D125
*

2

1

A

C

D126

2

Input
BR35

Input
BR39

D129

C

5

D135

C

1

A

Input
BR33

C

1

D136

A

Input
BR31

D137

C

1

D138

C

Input
BR29

D139
*

A

1

D140

A

Input
BR27

2

D141

A

1

D144

A

Input
BR25

2

D150

A

1

D151

A

Input
BR23

D152

C

4

2

C

3

1

C

Input

+HV BR21

2

C

1

C

1

el
ect roni cs

JILA ELECTRONICS LAB
HIGH VOLTAGE AMPLIFIER

8TVS_DIODE(S)DESIGN BY: N. Fitch / T. Brown

BUILT FOR: Lewandowski

UPDATE: 2/26/2018 VERSION:
DN: <DN>

7

DATE:

D

H DRAWN BY: N. Fitch

5/2/2013 SHEET 9 OF 9

C

B

A

8

7

6

5

4

4

3

3

el
ectronics

N. Fitch

1

JILA ELECTRONICS LAB

2

H

C

D

12/13/2013
DN: <DN>

UPDATE:DESIGN BY:

2

DATE:

VERSION:

5/2/2013 SHEET 1

H DRAWN BY:

BUILT FOR:

1

N. Fitch

Lewandowski
OF 1

THERMAL_PADS

Outside WallA

S9_SOURCE

S8_SOURCE

S7_SOURCE

S6_SOURCE

S5_SOURCE

S4_SOURCE

S3_SOURCE

S2_SOURCE

S1_SOURCE

MASTER_SOURCE

5

A

1

1

1

1

1

1

1

1

1

1

6

B

J10

J9

J8

J7

J6

J5

J4

J3

J2

J1

7

B

C

D

8

235

A

B

C

D

8

8

6

J16-28J16-29J16-30FAN2_TACH
FAN1_TACH
+5V

J16-3

J16-4

J16-5

J16-34-V1

J16-9

J16-17

7

J16-50

BB_ANODE

J16-25

6

J16-52

J16-51

J16-49BB_CATHODE

J16-24

J16-48J16-23

J16-46

J16-21
J16-47

J16-45

BB_CURRENT
BB_-V

J16-20J16-22

J16-44

BB_+V

J16-19J16-43

J16-42

TB_ANODE

J16-16

J16-18J16-41

TB_CATHODE

J16-40J16-13

J16-15

J16-38

TB_CURRENT

J16-12

J16-39J16-37

TB_+V

J16-11

J16-14

J16-36

TB_-V

J16-35

J16-33

HV_MONITOR

J16-8

J16-10J16-32+V1

J16-7

J16-31

J16-27

FAN_GND

J16-2

J16-6

J16-26

FAN_PWR

J16-1

H5
4-40

H6
4-40

FAN_GND

FAN_PWR

50 pin cable breakout into shielded ethernet connectors

7

FAN1_TACH

5

TB_CATHODE

TB_ANODE

TB_-V

TB_+V

R20
10k

2

BB_ANODE

BB_-V

BB_+V

8

7

6

5

J4

J30

J17

D8
P6SMB33CA
20V

BB_CATHODE

D6
P6SMB33CA
20V

D4P6SMB33CA
20V

D2
P6SMB33CA
20V

BB_-V

BOT_CURRENT

4

3

2

BB_+V

1

BB_ANODE8

BB_CATHODE

TB_-V

6

TOP_CURRENT
7

5

TB_+V

4

3

1

8

7

6

5

4

3

2

1

TB_ANODE

R21
10k

+5V

TB_CATHODE

FAN_PWR

FAN_GND

FAN2_TACH

54

D9P6SMB33CA
20V

D7
P6SMB33CA
20V

D5P6SMB33CA
20V

D3
P6SMB33CA
20V

To Bottom Bank

To Top BankTo Fans

4

3

DN: LEW0099

2

1

BUILT FOR:

Lewandowski
H DRAWN BY: N. Fitch

1

5/3/2013 SHEET 1 OF 2

VERSION:INPUT_AND_OUTPUTS

Amplifier Breakout

JILA ELECTRONICS LAB

HV_PROBE

DATE:

N. Fitch

J10

2

UPDATE: 2/26/2018

DESIGN BY:

electronics

To scope probe divider (100Mohm)

3

H

A

B

C

D

236

8 pin connectors are shielded ethernet RJ45

A

B

C

8

7

so only one adjustment for zeroing current measurement

both current sensors should have similar DC offsets

7

D35
10.0V
0.1uF LM4040
C117

BB_-V

R39
1k

TOP_CURRENT

6

BOT_CURRENT

10k
R134

current sensor offset adjust

Signal in with ~1V of DC offset + Iout @ 1V/A

6

CW

D

8

D1
P6SMB33CA
20V

10k

R120

R121
51k

R130
51k

D22
P6SMB33CA
20V

R129
10k

5

5

R114
10k

R107
10k

7

1

U38

R135
10k

CW

LF356M

6

C115
0.1uF

5

R128
5.1k

TB_-V

4

-

+

7

5

C109
0.1uF

1

U40

R116
5.1k

BB_-V

4

-

+
6

R125
10k

CW

LF356M

current sensor gain adjust

2

3

C108
0.1uF

BB_+V

current sensor gain adjust

2

3

C114
0.1uF

TB_+V

R127
100

R137
100

4

4

BB_CURRENTTB_CURRENT

HV_PROBE

3

C8
180pF

C6
100pF

C4
470pF

C9
10-120pF

C7
10-120pF

10-120pF
C5

Jump for adjusting compensation here

3

1

2

CW

C33

-V1

7
AD825AR+6
U20
C29 0.1uF

0.1uF

R63
100

DN: LEW0099

2

Amplifier Breakout
BUILT FOR:

Lewandowski
H DRAWN BY: N. Fitch

1

5/3/2013 SHEET 2 OF 2

VERSION:

CURRENT_AND_VOLTAGE_MONITORSDATE:

N. Fitch

HV_MONITOR

1JILA ELECTRONICS LAB

Trimcap: Round edge connected to screw
connect round/arrow side to low impedance for best results

Adjusting Compensation
R22 adjusts DC gain (division)
C5 adjusts front corner and overall levelC7 adjusts response over 0.5us - 100us
C9 adjusts response over 2us - 120us
Probe rotation may be necessary for decent compensation

4

2

3

UPDATE: 2/26/2018

DESIGN BY:

electronics

R22
20k

R1
5k

R25
24k

R26
27k

J5

1500:1

+V1

2

H

A

B

C

D

237

A

B

C

D

J17-10J17-49J17-50-HV_OFF-HV_EXTERNAL_INTERLOCK

J17-24

J17-25

7

J17-48J17-238

J17-47-HV_INHIBIT

J17-22

J17-46

J17-21-HV_OFF_BUTTON

J17-45

J17-44

J17-20J17-43

J17-42

J17-19J17-51

J17-41

J17-18J17-17

J17-16

J17-40J17-15

J17-52

J17-39J17-14

J17-38J17-35+HV_CURRENT_KNOB

J17-9

J17-37

J17-34+HV_CURRENT_PROGRAM

J17-8+HV_VOLTAGE_KNOB

J17-33+HV_VOLTAGE_MONITOR

J17-13

J17-32+HV_CURRENT_MONITOR

J17-7

J17-12

J17-31+HV_EXTERNAL_INTERLOCK_RTN

J17-6+HV_15V

J17-30+HV_EXTERNAL_INTERLOCK

J17-5

J17-36

J17-29

+HV_OFF

J17-4+HV_VOLTAGE_PROGRAM

J17-28+HV_INHIBIT

J17-3

J17-11

J17-27

J17-2

J17-26

J17-1+HV_OFF_BUTTON

1/2 of 50 pin ribbon cable

1/2 of 50 pin ribbon cable

6-HV_RAIL+HV_RAIL

TRAP_ENABLE

4

NO water flow switch
closes at ~0.5gpm

J2

J6

5

R72
51

R69
51

R66
51

R63
51

R60
51

R57
51

R54
51

+5V

R5
1k

+5V

R3
1k

J55

J53

J51

J49

J47

J45

J43

R32
51

WATER_FLOW_ERROR

4

AMP7_OUT

AMP6_OUT

AMP5_OUT

AMP4_OUT

AMP3_OUT

AMP2_OUT

AMP1_OUT

AMP0_OUT

WATER_PRESSURE_ERROR

AMP7_IN

AMP6_IN

AMP5_IN

AMP4_IN

AMP3_IN

AMP2_IN

AMP1_IN

AMP0_IN

To Amp7

To Amp6

To Amp5

To Amp4

To Amp3

To Amp2

To Amp1

To Amp0

J5

J21

J24

R2
51

R35
51

R36
51

3

HOLD/SAMPLE

3

R51
51

R48
51

R45
51

R41
51

R37
51

R21
51

R12
51

R19
51

AMP15_IN

AMP14_IN

AMP13_IN

AMP12_IN

AMP11_IN

AMP10_IN

AMP9_IN

AMP8_IN

N. Fitch

DN: LEW0099

2

J42

J40

J38

J36

J34

J32

J30

J18

To Amp15

To Amp14

To Amp13

To Amp12

To Amp11

To Amp10

To Amp9

To Amp8

H

DATE:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 1 OF 6

H DRAWN BY:

BUILT FOR:INPUT/OUTPUT_CONNECTIONS

Master Interlock

JILA ELECTRONICS LAB

To Compugen/Gage 8152 AWG (Trap) Trigger

To Compugen/Gage 8152 AWG (Decelerator) Trigger

Far right viewed from front of box

AMP15_OUTAMP14_OUTAMP13_OUTAMP12_OUTAMP11_OUTAMP10_OUT

AMP9_OUT

AMP8_OUT

VERSION:J19

J10

UPDATE: 2/26/2018

DESIGN BY:

electronics

TRAP_AWG_TRIGGER

1

Trap Control Input/Output Signals

2

Far left viewed from rear of box

J41

J39

J37

J35

J33

J31

J29

J1

DECELERATOR_AWG_TRIGGER

DECELERATOR_ENABLE_DIO64

TRAP_ENABLE_DIO64

Front panel BNC connectors

J56

J54

J52

J50

J48

J46

J44

J16

Decelerator Control Input/Output Signals

5

Rear SMA connectors from arbitrary waveform generator
Front SMA connectors to amplifier control circuits
Far right viewed from rear of box
Far left viewed from front of box
J4

NO water pressure switch
closes at ~35psi

DECELERATOR_ENABLE

AMP_ERROR_BUS

A3

A2

A1

A0

-HV_VOLTAGE_KNOB-HV_15V-HV_VOLTAGE_PROGRAM-HV_CURRENT_KNOB-HV_CURRENT_PROGRAM-HV_VOLTAGE_MONITOR-HV_CURRENT_MONITOR-HV_EXTERNAL_INTERLOCK_RTN

1

50 pin ribbon cable (RB50) from Master_Interlock_Breakout

6

2
1

7

2

8

A

B

C

D

238

A

B

C

D

2

1

WATER_FLOW_ERRORAMP_ERROR_BUS

R10
10k

4

3

WATER_PRESSURE_ERROR

8

7

74LVC1G11

U59

6

3

ALL_IS_WELL+5V

1

TRAP_ENABLE_DIO64

74LVC1G11

U61

6

3

ALL_IS_WELL

U27
74LVC1G332
1
A
4
3
Y
B
6
C

1

+5V

4

4

All 4 red

U4
74LVC1G332
1
A
4
3
Y
B
6
C

DECELERATOR_ENABLE_DIO64

AMP_ERROR_BUS

WATER_ERRORWATER_FLOW_ERRORWATER_PRESSURE_ERROR

6

5

2

1

LED1
LED_STACK_4HIGH

8

7

R8 1k
R9 1k
R15 1k
R44 1k

7

ERROR

8

4

DECELERATOR_ENABLE

TRAP_ENABLE

R4
100k

6

ALL_IS_WELL

DECELERATOR_ENABLE

74HC1G00

U7

ERROR

WATER_ERROR

6

3

1

SET

DIV

TRIG OUT

U2
LTC6993

4

6

R16
1k

R7
560

+5V

2

4

C

74HC1G00

U50

A3

A2

A1

A0

C31
0.01uF

1

Ra

R29
Rb
30k

R28
100k

+5V

TR OUTCV GND
1

2

5

AMP_OK

4

TRAP_ENABLE

5

4

9

R40
100k

6

U28-B
74HCT125

3

1

10

12

DIV

TRIG OUT

SET

74HC161

A0
A1
A2
A3

4

6

13

3

R106
1k

2

4

6

8

All 4 red2

N. Fitch

DN: LEW0099

2

UPDATE: 2/26/2018

DESIGN BY:

electronics

H DRAWN BY:

BUILT FOR:LOGIC
N. Fitch

Lewandowski

Master Interlock

1

5/2/2013 SHEET 2 OF 6

VERSION:DATE:

1

JILA ELECTRONICS LAB

Indicates which amplifier encountered an error (rail or fan)

LED2
LED_STACK_4HIGH

1

3

5

7

TRAP_AWG_TRIGGER

AMP_OK

R76
560

+5V

11

U28-D
74HCT125

R26 1k
R27 1kR30 1kR31 1kstops incrementing amplifier address if an amplifier error is detected
continues once error is cleared

U6
LTC6993

8

15

3

14
Q0
13
Q1
12
Q2
11
Q3

RCO

U24
CLR
LD
ENT
ENP
CLK

3
D0
4
D1
5
D2
6
D3

1
9
7
10
2

+5V

U28-C
74HCT125

fout = 1.44/( C*(Ra + 2Rb))
duty cycle = Rb/( Ra + 2Rb)

3

4

8

+5V

4

One-shots configured for a ~66ms duration low output pulse(single output pulse occurs on a rising edge of the clock input)

1

3

U28-A
74HCT125

C30
0.1uF

5

2

RS

THR

6

V+

DIS

U25
ICM7555
7

DECELERATOR_AWG_TRIGGER

AMP_ERROR_BUS

5

H

A

B

C

D

239

A

B

C

8

AMP3_IN

AMP2_IN

AMP1_IN

AMP0_IN

U23-D
ADG613

3

6

7

DECELERATOR_ENABLE

R62
0

3

U26-A
ADG613

DECELERATOR_ENABLE

R59
0

2

7

U26-D
ADG613

DECELERATOR_ENABLE

R56
0

U23-A
ADG613

DECELERATOR_ENABLE

R34
0

6

2

7

D
S

7

9
16

8
1
8
1

R109
1M

R108
1M

R107
1M

ADG613
U23-B

10
11
15
9
16

ADG613
U23-C

D
S
D
S

14
10
11
15
14

D
S

R110
1M

ADG613
U26-C
ADG613
U26-B

7

2

3

2

3

2

3

-5V

6

+
6
U67
AD825AR
4

7

+5V

-5V

+
6
U64
AD825AR
4

7

+5V

-5V

+
6
U60
AD825AR
4

7

+5V

-5V

+
6
U22
2
AD825AR
4

3

+5V

6

R61
51

R58
51

R55
51

R33
51

AMP3_OUT

AMP2_OUT

AMP1_OUT

AMP0_OUT

5

5

4

AMP7_IN

AMP6_IN

AMP5_IN

AMP4_IN

4

U34-D
ADG613

3

6

3

DECELERATOR_ENABLE

R74
0

U35-A
ADG613

DECELERATOR_ENABLE

R71
0

2

7

2

7

U35-D
ADG613

DECELERATOR_ENABLE

R68
0

U34-A
ADG613

DECELERATOR_ENABLE

R65
0

6

3

3

R111
1M

R112
1M

R113
1M

R114
1M

ADG613
U34-C

D

8
1

10
16
15
14

8
1

9
16

D
D
S

9

S

10
11

S

11
15
14
D
S

ADG613
U34-B
ADG613
U35-C

ADG613
U35-B

D

8

7

7

+5V

-5V

+
6
U76
AD825AR
4

7

+5V

-5V

+
6
U73
AD825AR
4

7

+5V

-5V

+
6
U70
AD825AR4electronics

DN: LEW0099

2

Master Interlock

JILA ELECTRONICS LAB

AMP7_OUT

AMP6_OUT

AMP5_OUT

AMP4_OUT

1

H

DATE:

BUILT FOR:H DRAWN BY:

N. Fitch

Lewandowski

1

5/2/2013 SHEET 3 OF 6

VERSION:

DECELERATOR_CONTROL_SIGNALS

R73
51

R70
51

R67
51

R64
51

N. Fitch
UPDATE: 2/26/2018

DESIGN BY:

-5V

+
6
U79
2
AD825AR
4

3

2

3

2

3

2

3

+5V

2

A

B

C

D

240

A

B

C

D

8

HOLD/SAMPLE

AMP11_IN

3

11

5

12

HOLD/SAMPLE

AMP10_IN

HOLD/SAMPLE

AMP9_IN

HOLD/SAMPLE

AMP8_IN

10

U1-D

9

2

14

SMP-0415

SMP-041

SMP-04

SMP-04

U1-C

7

U1-B

6

U1-A

3

U12-D
ADG613

7

7

2

2

7

U17-A
ADG613

U17-D
ADG613

TRAP_ENABLE

R39
0

6

TRAP_ENABLE

R25
0

3

TRAP_ENABLE

R20
0

6

TRAP_ENABLE

R6
0
D
S

U12-A
ADG613

1
8
1
8

R118
1M

R117
1M

R116
1M

R115
1M

7

+5V

6

-5V

6

+
6
U33
2
AD825AR
4

7

+5V

-5V

+
6
U29
2
AD825AR
4

3

U8

-5V

4

-

2

7
+
AD825AR

-5V

+5V

3

3

7
+
6
U45
2
AD825AR
4

3

+5V

6

51

R38

51

R22

51

R13

51

R1

AMP11_OUTAMP10_OUT

AMP9_OUT

AMP8_OUT

55

HOLD/SAMPLE

AMP15_IN

11

5

4

12

HOLD/SAMPLE

AMP14_IN

HOLD/SAMPLE

AMP13_IN

HOLD/SAMPLE

AMP12_IN

9101

SMP-042

SMP-0414

SMP-0415

SMP-04

U40-C

7

U40-B

6

U40-A

U40-D

3

4

6

3

6

TRAP_ENABLE

R53
0

7

2

2

7

U42-A
ADG613

U42-D
ADG613

TRAP_ENABLE

R500

TRAP_ENABLE

R47
0

U88-D
ADG613

TRAP_ENABLE

R43
0

3

U88-A
ADG613

3

3

D
S

7

9

16
11
15

15
D

9
16

10
S

ADG613
U12-B

S
S

14
10
11

14
D

ADG613
U12-C
ADG613
U17-B
ADG613
U17-C

D

16
10
11
15

1
8
1
8

15
D
D

9
16

R119
1M

R120
1M

R121
1M

R122
1M

ADG613
U88-B

S
S
S

14
10
9
11

14
D

ADG613
U88-C
ADG613
U42-B
ADG613U42-C

8electronics

-5V

+
6
U54
AD825AR
4

7

+5V

-5V

+
6
U48
AD825AR
4

7

+5V

-5V

+
6
U41
AD825AR
4

7

+5V

-5V

N. Fitch

51

R52

51

DN: LEW0099

2

AMP12_OUT

1

N. Fitch

Lewandowski

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H DRAWN BY:

BUILT FOR:

TRAP_CONTROL_SIGNALS

Master Interlock

JILA ELECTRONICS LAB

AMP15_OUTAMP14_OUTAMP13_OUT

VERSION:
DATE:

R49

51

R46

51

R42

UPDATE: 2/26/2018

DESIGN BY:

2

3

2

3

2

3

7
+
6
U32
2
AD825AR
4

3

+5V

2

H

A

B

C

D

241

A

B

C

D

8

-HV_VOLTAGE_MONITOR-HV_CURRENT_MONITOR

8

R83
5.1k

R80
100

R77
5.1k

R11
100

U13
+
1
4

7
-

3

2
U82
+
1
4

7
-

-HV_15V

3

2-HV_15V

6

6

7

R84
2.7k

5 INA105

8

R78
2.7k

5 INA105

8+HV_VOLTAGE_MONITOR+HV_CURRENT_MONITOR

Zout for Spellman monitor is 4.99kohm

7

R85
10k

U16
+
1
4

3

2
U86

16

D2

16
-V1

0V1

15 VIN

2

+V1

1

6

R89
2.7k

+V1

-V1

9

6

-V1

10

-V2

+V2

9

10

-V2

+V2

+V1

R96
2.7k

5 INA1058-HV_15V

-V1

0V1

2

+V1

1

6

5 INA1058-HV_15V

+
1
4

7
-

+HV_15V3

15 VIND1-HV_15V

R79
10k-HV_15V

R95
5.1k

R92
100

R88
5.1k

R18
100

7
2
-

+HV_15V

6

0V2

0V2

R97
10k

8

8

16
-V1

0V1

1

7

R14
10k

VOUT

7

R81
10k

U20
ISO124P

VOUT

U19
ISO124PD6
1N4689

-V1

0V1

2

+V1
15 VIN162+HV_15VD5
1N4689

+HV_15V

R90
10k+HV_15V+V1
15 VIN1+HV_15V

2

3

2

3

+V1

-V1

7

1

1

U83

-V1

4

-

+

7

+V1

-V1

4

-

U14

+V1

-V1

+

9

10

-V2

+V2

9

10

-V2

+V2

+V1

R86
10k

7

R23
100

R93
10k

R24
100

-HV_INHIBIT

VOUT

5

7

U85
ISO124P

6
LF356M

R82
10k

5

R75
10k

5

8

8

VOUT

U15
ISO124P

6
LF356M

0V2

0V2

5

7

1

U84

1

J22

Q2
3904

R94
10k

5

6
LF356M

R87
10k

5

6
LF356M

R91
100

R17
100

7

-HV_RAIL

4

J14

J8

5

3

U18
8 SFH6720
2-HV Spellman Voltage Monitor

R104
10k

-HV_15V-HV Spellman Current Monitor

U87

-V1

4

-

+

7

+V1

-V1

4

-

+

J15

2

3

2

3

+V1

4

Q1
3904

R105
2k

+HV_RAIL

3

WATER_ERROR+HV Spellman Voltage Monitor+HV_INHIBIT+HV Spellman Current Monitor

3

7
5

3

U5
8 SFH6720
2

DN: LEW0099

2

J7

J23

J26

J25

J13

J12

J11

J3

WATER_ERROR

1

DATE:

N. Fitch

Lewandowski

1

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H DRAWN BY:

BUILT FOR:

HV_SUPPLY_INTERFACE

Master Interlock

JILA ELECTRONICS LAB

Jump 2:3 to enable front panel (FP) voltage control knob
Jump 1:2 to enable bipolar/slave operation
Pin 1 is most inboard (towards the voltage regulators)

Jump to enable front panel (FP) current control knob
(default is jumped)

Jump to enable front panel (FP) off button(default is jumped)

Jump to enable front panel (FP) voltage control knob

Jump to enable front panel (FP) current control knob
(default is jumped)

Jump to enable front panel (FP) off button(default is jumped)

VERSION:

2

1

N. Fitch
UPDATE: 2/26/2018

DESIGN BY:

electronics-HV_EXTERNAL_INTERLOCK_RTN-HV_EXTERNAL_INTERLOCK

2
3-HV_VOLTAGE_KNOB

1

2

1

2

1

2

-HV_VOLTAGE_PROGRAM+HV_VOLTAGE_MONITOR-HV_CURRENT_PROGRAM-HV_CURRENT_KNOB-HV_OFF-HV_OFF_BUTTON+HV_VOLTAGE_PROGRAM

1

2+HV_VOLTAGE_KNOB

1

2

1

2

1

+HV_CURRENT_KNOB

R103
2k

+HV_CURRENT_PROGRAM+HV_OFF+HV_OFF_BUTTON+HV_EXTERNAL_INTERLOCK_RTN+HV_EXTERNAL_INTERLOCK

R102
10k

+HV_15V

2

H

A

B

C

D

242

A

B

C

8

1

-V1

+V1

3

+-RTN

-15V/-12V IN

S9

2

S6

1

+15V/+12V IN

J9POWER IN

1

1

D

8

2

IN

GND

1

GND

C16
10uF

C8
10uF

-V1

+

+

+V1

IN

3

3

-5V

+5V

7

U23-E
ADG613D4P6SMB33CA
20V

D3
P6SMB33CA
20V

OUT

LM7905CT
U3

2

OUT

LM7805CT
U47

7

C7

C32

C90

C92

-5V

G V5 4

U26-E
ADG613-5V

G V5 4

+5V
12 13
V+

+5V
12 13
V+

-5V

C27

C29

6

U34-E
ADG613

C1
0.1uF

C28
0.1uF

-5V

G V5 4

12 13
V+

+5V

C26
0.1uF

C34

C87

C89

C108
0.1uF

C91

C21
0.1uF

C93

C22
0.1uF

-HV_15V

C107
0.1uF

+HV_15V

5

C95

C97

C23
0.1uF

C109
0.1uF

C99

C24
0.1uF

C110
0.1uF

C44

C54
0.1uF

C51
0.1uF

C52

4

C4

C3

-V1

C41

C17
0.1uF

C45

C18
0.1uF

C13
0.1uF

+V1

C12
0.1uF

C85

C105
0.1uF

C14
0.1uF

C63

C75

C106
0.1uF

C15
0.1uF

3

C67

C101
0.1uF

C19
0.1uF

C79

C102
0.1uF

C9
0.1uF

C48

C154

C104
0.1uF

C20
0.1uF

C60

C103
0.1uF

C10
0.1uF

C11

C39

2

C47

C94
C96

C98
C100

C53
C5

C25

C42

C46

C37

C38

C40

C43

C86

C64

C68

C76

C80

U35-E
ADG613-5V

G V5 4

12 13
V+

+5V

5

U12-E
ADG613-5V

G V5 4-5V

G V5 4

+5V
12 13
V+

+5V
12 13
V+

U17-E
ADG613

4

U88-E
ADG613-5V

G V5 4-5V

G V5 4

+5V
12 13
V+

+5V
12 13
V+

U42-E
ADG6133

0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C36

N. Fitch

DN: LEW0099

2

UPDATE: 2/26/2018

DESIGN BY:

electronics

Master Interlock

N. Fitch

Lewandowski

1

5/2/2013 SHEET 6 OF 6

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BUILT FOR:

POWER_CONNECTIONSVERSION:DATE:

1

JILA ELECTRONICS LAB

RED
D11

RED
D10

-5V

5.11k

R100
5.11k

+5V

0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF 0.1uF

C33

RED
D9

R99
10k

-HV_15V

RED
D15

R98
10k

+HV_15V

0.1uF 0.1uF 0.1uF 0.1uF

0.1uF 0.1uF 0.1uF 0.1uF

C88

0.1uF

C35

C6
0.1uF

C59

+5V

+
D7
C2
P6SMB33CA 10uF
20V

+
D8
C58
P6SMB33CA 10uF
20V

6

H

A

B

C

D

243

A

B

C

D

8

J4-26

+HV_15V+HV_VOLTAGE_KNOB

J2-12

J2-13

-HV_INHIBIT-HV_OFF-HV_EXTERNAL_INTERLOCK

J2-23

J2-24

J2-25

7

-HV_OFF_BUTTON

J2-22

J4-27

-HV_GND

J2-21

J2-20

J2-19

J2-18

J2-17

J2-16

J2-15

J2-14

+HV_VOLTAGE_PROGRAM

J2-11+HV_CURRENT_MONITOR

J2-7+HV_CURRENT_KNOB+HV_EXTERNAL_INTERLOCK_RTN

J2-6

J2-10

+HV_EXTERNAL_INTERLOCK

J2-5+HV_CURRENT_PROGRAM+HV_OFF

J2-4

J2-9

+HV_INHIBIT

J2-3+HV_VOLTAGE_MONITOR+HV_OFF_BUTTON

J2-2

J2-8

+HV_GND

J2-1

6

J1-27

J1-26

J2-50

J2-49

J2-48

J2-47

J2-46

J2-45

J2-44

J2-43

J2-42

J2-41

J2-40

J2-39

J2-38

J2-37

J2-36

J2-35

J2-34

J2-33

J2-32

J2-31

J2-30

J2-29

J2-28

J2-27

J2-26

50 pin ribbon cable to/from "Master Interlock" board

6

5+HV_EXTERNAL_INTERLOCK

J4-8

H2

H1

-HV_RAIL+HV_RAIL

TRAP_ENABLE

5DECELERATOR_ENABLE

AMP_ERROR_BUS

A3

A2

A1

A0

-HV_VOLTAGE_KNOB-HV_15V-HV_VOLTAGE_PROGRAM-HV_CURRENT_KNOB

4

1
2
3
4

-HV_RAIL

A0
A1
A2
A3

-HV_RAIL+HV_RAIL

J7

4

8

7

6

5

8

+HV_RAILAMP_ERROR_BUS
TRAP_ENABLE

7

6

5

3

-HV_SHIELD
J4-25+HV_SHIELD

A3

J1-25

-HV_GND2

J4-24+HV_GND2

2

J1-23
J1-24

-HV_15V
J4-23+HV_15V

A2

J1-22-HV_SUPPLY_FAULT

J4-22+HV_SUPPLY_FAULT

A1

J1-21

-HV_POWER_MODE_INDICATOR
J4-21+HV_POWER_MODE_INDICATOR

J5

J1-20

-HV_CURRENT_MODE_INDICATOR

J4-20+HV_CURRENT_MODE_INDICATOR

1

J1-18

-HV_VOLTAGE_MODE_INDICATOR

J4-19+HV_VOLTAGE_MODE_INDICATOR

Shielded ethernet bus for trap control boards

3

Shielded ethernet bus for decelerator control boards

DATE:

DN: LEW0099

2

VERSION:

N. Fitch

Master Interlock Breakout

5/2/2013 SHEET 1 OF

H DRAWN BY:

BUILT FOR:

1

1

N. Fitch

Lewandowski{2X_DB25,2X_RJ45}_TO_{RB50}
UPDATE: 8/30/2013

DESIGN BY:

elect ronics

JILA ELECTRONICS LAB

Note: JILA DB25 and Industrial Standard DB25 connector have opposite pin numbers
These pin numbers are assigned according to the industry standard

J1-19

J1-17

-HV_ON_INDICATOR
J4-18+HV_ON_INDICATOR

J1-16-HV_ON

J4-16-HV_OFF_INDICATOR

J1-15

J1-13
J1-14

-HV_OFF_BUTTON-HV_OFF

J1-12-HV_EXTERNAL_FAULT_RELAY

J1-11

J4-17

A0

AMP_ERROR_BUS
DECELERATOR_ENABLE

J1-9
J1-10

-HV_EXTERNAL_FAULT_RELAY_GND-HV_VOLTAGE_KNOB-HV_VOLTAGE_PROGRAM-HV_CURRENT_KNOB

J1-8

J1-7

-HV_10V_REF-HV_CURRENT_PROGRAM

J1-5
J1-6

-HV_VOLTAGE_MONITOR

J1-4-HV_CURRENT_MONITOR

J1-3-HV_EXTERNAL_INTERLOCK-HV_EXTERNAL_INTERLOCK_RTN

J1-1
J1-2

-HV_GND+HV_OFF_INDICATOR+HV_ON

1
DB25 from -HV Spellman
Factory default jumpers shown-HV_INHIBIT

2

J4-15

J4-14

+HV_OFF_BUTTON+HV_OFF

J4-13+HV_EXTERNAL_FAULT_RELAY

J4-11
J4-12

+HV_VOLTAGE_KNOB

J4-10+HV_EXTERNAL_FAULT_RELAY_GND+HV_VOLTAGE_PROGRAM

J4-9

J4-7

+HV_10V_REF+HV_CURRENT_PROGRAM-HV_VOLTAGE_MONITOR+HV_CURRENT_KNOB

J4-5
J4-6

+HV_VOLTAGE_MONITOR

J4-4

J4-3

J4-1
J4-2

+HV_GND+HV_INHIBIT+HV_CURRENT_MONITOR-HV_CURRENT_PROGRAM

3
DB25 from +HV Spellman
Factory default jumpers shown+HV_EXTERNAL_INTERLOCK_RTN

4-HV_CURRENT_MONITOR-HV_EXTERNAL_INTERLOCK_RTN

1

7

1

8

H

A

B

C

D

244

Appendix B

Modifications summary

This appendix contains a concise summary of all the changes discussed in Chapter 5 sorted byboard. The original values referenced here refer to the amplifier circuits presented in Noah Fitch’s
dissertation [95] and the update values are the ones given in Appendix A.

B.1

Amplifier bank
• The change to R21 is optional if Q8 or Q7 are not installed, see Chapter 5 for an explanation.
• The following list of parts do not have a part number listed, they are all MMSZ4701 15V
zener diodes: D1, D12, D22, D23, D40, D52, D55, D67, D70, D82, D85, D97, D100, D112,
D115, D127, D130, D142, D145.
• The brass shield on leader control circuit is no longer used.
• The voltage limiters remain on the circuit diagram but they are not installed. They arecomponents: Q3-8, Q17-18, Q20, Q21, Q24.
• The bottom bank current monitors was shorted by connecting TP4 to TP7. This removes
it from the circuit but it is left in for structural rigidity of the elevated ethernet board.

Component number
R21
R159

Original value
470 Ω
300 Ω

Updated value
430 Ω
100 Ω

246

B.2

Amplifier breakout boards
Component number
C4
C6

B.3

Original value
330 pF Ω
180 pF Ω

Updated value
470 pF Ω
100 pF Ω

Original value
51 Ω
200 kΩ
200 kΩ
100k Ω
10k Ω
5.11k Ω
10k Ω
100k Ω
5.11k Ω

Updated value
1M Ω
390 kΩ
390 kΩ
10k Ω
7.5k Ω
7.5k Ω
7.5k Ω
10k Ω
7.5k Ω

Control boards
Component number
R13
R35
R38
R166
R167
R168
R170
R171
R173

B.4

Master interlock
Pin 3 of the following components must be tied to ground using a 1 MΩ resistor: U8, U22,

U29, U32, U33, U41, U45, U48, U54 U60, U64, U67, U70, U73, U76, U79

B.5

Insulation
In order to present current oscillations at output voltages greater than ±8 kV, the amplifierbanks and cables are potted with RTVS 3-95-1 and the high-voltage probes are potted with Hysol
ES1001.