LASER PROBING of
TRANSPORT PROPERTIES andROTATIONAL ALIGNMENT of
N2+ DRIFTED in Heby
Eric Baxley Anthony
B. A., Middlebury College, 1987

A thesis submitted to theFaculty of the Graduate School of theUniversity of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
1998

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This thesis for the Doctor of Philosophy Degree by
Eric Baxley Anthonyhas been approved for theDepartment of Physics
byStephen R. Leone

Veronica M. Bierbaum

Date _______________________

iiiAnthony, Eric Baxley (Ph. D., Physics)
Laser Probing of Transport Properties and Rotational Alignment of N 2+ Drifted in He
Thesis directed by Professor Adjoint Stephen R. Leoneand Research Professor Veronica M. Bierbaum
Results of transport property and rotational alignment experiments of theatmospherically important molecule N 2+ are presented, as measured in a flow-drift
apparatus using the technique of single-frequency laser-induced fluorescence (LIF). A
trace amount of N 2+ is drifted in helium as a buffer gas; the external axial electricfield of the drift tube varies the center-of-mass collision energy of the ion-neutral pair.
The net effect over hundreds of buffer gas collisions is to establish a steady-stateanisotropic ion velocity distribution, the precise character of which is determined by
the ion-neutral interaction potential, mass ratio, and field strength. A single-frequency
ring dye laser is used to probe Doppler profiles of various rotational lines of the(v ′, v ′′ ) = (0, 0) band in the B 2 Σ u+ − X 2 Σ +g system at 390 nm. The single-frequency
cw laser technique allows one to measure the velocity component distributionfunction (VCDF) along the laser propagation direction k; the VCDF is a projection of
the complete ion velocity distribution function. Additionally, the rotational alignmentof the ions as a function of one component of sub-Doppler laboratory velocity isprobed by polarized LIF.
Drift velocities and ion mobilities are determined from the shift of the first
moments of the coaxial LIF Doppler profiles, while perpendicular and paralleltranslational temperatures are determined from the widths or second central momentsof the profiles in the direction probed. Drift velocities measured up to a field strength

ivof 16 Td appear to be in good agreement with data derived from earlier arrival-timemeasurements. A small but definite increase in mobility with increasing rotational
state from J=13.5 to J=22.5 is observed. A significant difference of over 100 K
between the parallel and perpendicular temperatures is measured at the highest fieldstrength employed (16 Td). A small degree of positive skewness or third central
moment is observed as well in the parallel VCDF’s, which is of particular interest
since a high-velocity tail has not been previously reported for any molecular ionsystem. Additionally, by probing with linearly polarized light and measuring thedegree of polarization of the resultant LIF, the collision-induced quadrupole rotationalalignment parameter A0( 2 ) is determined as a function of field strength and velocitysubgroup. A strong correlation is found between the degree of rotational alignment
and the velocity subgroup when probed parallel to the field direction, with thealignment parameters generally increasing monotonically across the distribution. A
dramatic difference in velocity-selected alignment as a function of rotational state isobserved as well, for experiments conducted on various rotational lines at a fixed
field strength of 12 Td. For sufficiently low rotational state (J about 9), it appears thatA0( 2 ) changes sign across the Doppler profile.

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Acknowledgments
As I reach the end of the valley of sweat, blood, and tears (in approximatelythat order) that has been the graduate school experience for me, I become very muchaware that, although it has been largely a solitary enterprise, I didn’t get through italone. There is a long list of “invisible contributors” that I need to thank somehow.
Coupled with the frustration, at the end, of realizing that I seemed to have had to learn
absolutely everything the hard way, is the realization that it would have been infinitely
worse without the many people I’ve interacted with along the way.
Firstly, I need to thank my co-advisors Steve Leone and Veronica Bierbaum.
Although I have certainly not been one of Steve and Ronnie’s most successful (farfrom!) or their easiest graduate student, they have been extraordinarily patient
throughout the whole process. They never completely gave up on me, even though, attimes, they certainly had every right to. Particularly in this last year, I have reallygrown to appreciate Steve’s truly encyclopedic knowledge of chemical physics andhis wisdom about the “big picture” of the field. Ronnie’s ever-cheerful demeanor,scientific precision, and willingness to drop everything in the middle of an otherwise
hectic day to sit down and talk about a scientific or personal problem has always been
appreciated.
Secondly, I would like to thank my committee members: Chris Greene, David
Nesbitt, and Robert Parson. Chris is one of the best teachers I’ve had at CU and eventhough always busy, has somehow found the time and patience to talk to a dumb
experimentalist such as myself. I’ve always respected David for his extraordinary
insights, the enthusiasm he always brings to science, and for always encouraging

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people to do their absolute best. Robert has been an absolutely great person to talk toand bounce ideas off through the years; I’ve always been astonished by his ability toboth ask and field good questions on almost any topic.
It has been a privilege to have served as a graduate student at JILA. It would
not be possible to thank each individual that has contributed to my education at JILA
by name—but that won’t stop me from trying. JILA is well-renowned for having thebest support staff on this planet. Without the help of the instrument shop staff of John
Andru, Dave Alchenberger, Jim Csotty, Hans Green, Blaine Horner, and SethWieman, and electronics shop staff of James Fung-a-Fat, Paul Beckingham, TerryBrown, and Mike Whitmore, I wouldn’t have graduated. The computing staff ofRalph Mitchell, Alan Dunwell, Joel Frahm, Anne Hammond, Patti Krog, and ChelaKunasz have been consistently fantastic. I always enjoyed visiting SRO, mostly
because of the great staff of Marilee DeGoede, Judy McCorkel, Laurie Kovalenko,and Lorraine Volsky.
Thanks as always to the invisible hand of the administrative staff for keeping
everything going. Marilyn Greves and Leslie Haas somehow insured I always got
paid. I would particularly like to thank Jim Faller and Pat McInerny, who came upwith capital funds for my project when they were most desperately needed, and Pat
for providing me with an office in the tower for thesis-writing.
A couple of additional scientific thanks are in order. I am indebted to theintellectual godfathers of this experiment, Dr. Rainer Dressler of Philips Lab,Hanscom AFB, and Professor Henning Meyer of the University of Georgia. Henningin particular has been of extraordinary help through the years and always anvii
inspiration; anything in this thesis that sounds right or “profound” is almost certainly
due to my interactions with him. I would especially like to thank Professor S. David
Rosner of the University of Western Ontario for his invaluable help on N 2+ hyperfine
spectroscopy issues. Professor Millard Alexander of the University of Maryland
encouraged me throughout much of this work, most especially when I was prepared togive up. Dr. John Bohn was invaluable in the very late stages of this work as a good
person to bounce ideas off.
The Leone group is too large, and too many people have moved in and out
over the years I’ve been here other than to thank the group en-masse. I would like tothank all of my personal friends both in and out of JILA. The JILA friends start withthe basement: Kurt, Jun, Tom, Scott Diddams, Nada—and move up: Scott Davis,Nikki, Brad, Brana. Outside of JILA: Maela, Kristen, Linda, Jeanette, Will, Sue,Chris, Matt, Leif, Dave, Mark. My housemates through the years: Elizabeth, Charlie,James, Jos, Gina, Peter, and Sarah have kept me sane and going—I couldn’t havedone it without them. I would particularly like to thank my long-time housemate andfriend Jetty, for having the knack of always being there when I needed her.
Lastly, and most importantly I need to thank both of my parents and my twin
brother for the love and support they have always given me throughout my life, andfor continually standing by me beyond all reason in my probably ill-advised decision
to go to graduate school. Particularly in the last year, their unwavering support has
been phenomenal—countless times I wanted to give up but they would not let me.
This thesis is dedicated to the memory of my late grandfather C. Herbert Baxley, whoalways encouraged me to pursue my highest educational goals regardless of their cost.

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TABLE OF CONTENTSChapterPage

I. INTRODUCTION...................................................................................................... 1
A. General motivation ....................................................................................... 1
B. Interaction potential ...................................................................................... 6
C. Ion transport properties................................................................................. 9
D. Collision-induced rotational alignment ...................................................... 10
References for Chapter I.................................................................................. 12
II. GENERAL EXPERIMENTAL TECHNIQUES .................................................... 14
A. Introduction ................................................................................................ 14
B. Ion source & flow-drift region.................................................................... 14
1. Ion source & production conditions ................................................ 16
2. Flow tube considerations................................................................. 23
3. Drift & charge separation regions ................................................... 25
C. Ring dye laser system & diagnostic tools ................................................... 29
1. General description ......................................................................... 30
2. Diagnostic tools............................................................................... 34
3. Beam transport & polarization control............................................ 43
D. Laser-induced fluorescence detection techniques ...................................... 46
1. Unpolarized detection ..................................................................... 46
2. Polarized detection .......................................................................... 50
E. Electronics and data acquisition programming........................................... 55
F. General data analysis considerations........................................................... 59

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G. Spectroscopy of the N 2+ B 2 Σ u+ − X 2 Σ +g system ....................................... 61
1. General spectroscopic structure....................................................... 61
2. Hyperfine spectroscopy ................................................................... 67
References for Chapter II ................................................................................ 69
III. ROTATIONALLY-RESOLVED TRANSPORT PROPERTIES OF N 2+ IN He .. 71
A. Introduction ................................................................................................ 71
B. Descriptive theory....................................................................................... 71
C. Measurement & analysis techniques........................................................... 77
1. Measurement details........................................................................ 77
2. Velocity component distribution functional forms ......................... 84
3. Line shape analysis.......................................................................... 90
D. Results ........................................................................................................ 95
1. First moments: drift velocities & mobilities ................................... 96
2. Second central moments: translational temperatures .................... 104
3. Third central moments: direct measure of skewness..................... 109
E. Possible systematics.................................................................................. 111
1. Axial ion flow-velocity experiments............................................. 113
2. LIF intensity vs. tube voltage experiments.................................... 122
F. Discussion & theory.................................................................................. 125
1. First moments................................................................................ 127
2. Second central moments................................................................ 135
G. Conclusions .............................................................................................. 136
References for Chapter III ............................................................................. 138

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IV. COLLISION-INDUCED ROTATIONAL ALIGNMENT OF N 2+ IN He .......... 141
A. Introduction .............................................................................................. 141
B. Descriptive theory..................................................................................... 144
1. Qualitative & heuristic arguments................................................. 144
2. Simple classical theory.................................................................. 150
3. Quantum theory............................................................................. 157
4. Extensions to quantum theory....................................................... 160
C. Experimental & analysis techniques......................................................... 165
D. Results ...................................................................................................... 175
1. Field dependence of alignment for single rotational line .............. 176
2. Rotational quantum state dependence of alignment...................... 182
E. Possible systematics.................................................................................. 188
F. Discussion & dynamics theory.................................................................. 192
1. Steady-state fully-velocity averaged theory................................... 195
2. Partial velocity selection ............................................................... 200
G. Conclusions .............................................................................................. 205
References for Chapter IV............................................................................. 206
BIBLIOGRAPHY ..................................................................................................... 208
APPENDIXES .......................................................................................................... 218
A. Relevant circuit diagrams ......................................................................... 218
B. Eta-Spex program listing ............................................................ (on diskette)
C. AMCalc angular momentum calculator program ....................... (on diskette)

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LIST OF TABLES
TablePage

2.1 Relevant transition frequencies for (0,0) band of N 2+ B 2 Σ u+ − X 2 Σ +g system .. 66

3.1 Tabulated results of first moment experiments .................................................... 99
3.2 Tabulated results of second central moment experiments.................................. 108

4.1 Example of data collection sequence for sub-Doppler alignment experiment... 169
4.2 Example of program data output ........................................................................ 172
4.3 Example of program data analysis output .......................................................... 174
4.4 Tabulated results of rotational state alignment experiment................................ 190

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LIST OF FIGURES
FigurePage

1.1 N 2+ -He interaction potential in Jacobi coordinates ................................................ 8

2.1 Overall schematic of experimental apparatus ...................................................... 15
2.2 To-scale diagram of ion source region ................................................................. 17
2.3 Representative mass spectra for Fall ’95 experiments ......................................... 20
2.4 Representative mass spectra for Fall ’97 & Spring ‘98 experiments ................... 21
2.5 Schematic of drift tube electrical connections ..................................................... 26
2.6 Ring dye laser optical and electronic schematic................................................... 31
2.7 Optics table components schematic ..................................................................... 35
2.8 Construction diagram of 20 cm long ULE Fabry-Perot cavity............................. 38
2.9 Scope trace of Fabry-Perot transmission peaks.................................................... 39
2.10 Perspective view of apparatus and PMT stack................................................... 47
2.11 To-scale plan view of stepper-motor driven PMT stack .................................... 53
2.12 Block schematic of counter portion of acquisition system................................. 58
2.13 Typical LIF spectra of single spin-rotation line ................................................. 62
2.14 Pump-fluoresce diagram for R1(15) transition ................................................... 64
2.15 LIF survey spectra of five rotational lines.......................................................... 65

3.1 Representative first-moment LIF data.................................................................. 78
3.2 Representative second central moment LIF data.................................................. 83
3.3 Whealton-Woo functional form for various skewness parameters ...................... 88

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3.4 Simulated spectra of underlying hyperfine structure............................................ 91
3.5 R1(15) drift velocities .......................................................................................... 97
3.6 R1(15) mobilities ................................................................................................. 98
3.7 Drift velocities and mobilities for various rotational lines at 12 Td .................. 102
3.8 J-dependent mobilities at 12 Td, broken down by day of observation............... 103
3.9 Second and third central moment data on R1(15), Fall ‘95 ............................... 105
3.10 Translational temperatures for R1(15) ............................................................. 107
3.11 Evidence of positive skewness in coaxial probe data....................................... 110
3.12 Field off/field on line centers as function of charge separation voltage........... 115
3.13 Diagnostic data on axial ion flow velocity systematic ..................................... 118
3.14 Axial ion flow velocity experiments with different source aperture sizes ....... 120
3.15 Results of charge-separation voltage scanning experiments ............................ 123
3.16 Results of drift voltage scanning experiments ................................................. 124
3.17 Summary plot of CO+-He LIF and arrival time mobilities .............................. 126
3.18 Literature values of N 2+ and CO+ mobilities ................................................... 129

4.1 Cartoon diagram of LIF probe-detection scheme............................................... 145
4.2 Cartoon mJ distribution picture .......................................................................... 148
4.3 Schematic of “two-angle” LIF geometry for alignment experiment .................. 152
4.4 Isotropic and aligned fluorescence intensities for the two probe directions....... 156
4.5a) Perpendicular probe polarization results for R1(15) ....................................... 177
4.5b) Coaxial probe polarization results for R1(15) ................................................ 178

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4.6 Corresponding mJ distributions for R1(15) at 16 Td ......................................... 183
4.7 Raw polarization data from rotational state alignment experiment ................... 185
4.8 Systematic plasma polarization checks .............................................................. 187
4.9 Polarization data of Fig. 4.7 with simple subtractive correction........................ 189

A.1 Simple analog divider circuit ............................................................................ 219
A.2 Simple window detector circuit......................................................................... 220
A.3 Stepper motor driver circuit for rotation stage .................................................. 221