# Presentation: 725858

## Experiments on Transverse BunchCompression on the Princeton Paul TrapSimulator Experiment*

- Erik P. Gilson
- Princeton Plasma Physics Laboratory
- 2007 Particle Accelerator Conference
- Albuquerque, NM
- June 26th, 2007

- *This work is supported by the U.S. Department of Energy.

**Experiments on Transverse Bunch****Compression on the Princeton Paul Trap****Simulator Experiment***

*In collaboration with*: Moses Chung, Ronald C. Davidson, Mikhail Dorf, Philip C. Efthimion, Richard Majeski, and Edward A. Startsev

## PTSX Simulates Nonlinear Beam Dynamicsin Magnetic Alternating-Gradient Systems

- Simulate the nonlinear transverse dynamics of intense beam propagation over large distances through magnetic alternating-gradient transport systems in *a compact experiment*.

**PTSX Simulates Nonlinear Beam Dynamics****in Magnetic Alternating-Gradient Systems**

- _Purpose_:

## Scientific Motivation

- Beam mismatch and envelope instabilities
- Collective wave excitations
- Chaotic particle dynamics and production of halo particles
- Mechanisms for emittance growth
- Effects of distribution function on stability properties
- Quiescent propagation over thousands of lattice periods
**Transverse compression techniques**

**Scientific Motivation**

## Magnetic Alternating-Gradient Transport Systems

- N

- N

- S

- S

- x

- y

- z

**Magnetic Alternating-Gradient Transport Systems**

## PTSX Configuration – A Cylindrical Paul Trap

- 0.2 m

**PTSX Configuration – A Cylindrical Paul Trap**

| Plasma length | 2 m | Maximum wall voltage | ~ 400 V |
| --- | --- | --- | --- |
| Wall radius | 10 cm | End electrode voltage | < 150 V |
| Plasma radius | ~ 1 cm | Frequency | < 100 kHz |
| Cesium ion mass | 133 amu | Pressure | 5x10-9 Torr |
| Ion source grid voltages | < 10 V |  |  |

- sinusoidal in this work

- for a sinusoidal waveform *V*(*t*).

- for a periodic step function waveform *V*(*t*) with fill factor .

- When ** = 0.572, they’re equal.

- Pure Ion Plasma

## Transverse Dynamics are the Same Including Self-Field Effects

- Long coasting beams
- Beam radius << lattice period
- Motion in beam frame is nonrelativistic

- Ions in PTSX have the same transverse equations of motion as ions in an alternating-gradient system ***in the beam frame***.

- If...

- Then, when in the beam frame, both systems have...

- Quadrupolar external forces
- Self-forces governed by a Poisson-like equation
- Distributions evolve according to nonlinear Vlasov-Maxwell equation

## Electrodes, Ion Source, and Collector

- 1.25 in

**Electrodes, Ion Source, and Collector**

- 5 mm

- Broad flexibility in applying V(t) to electrodes with arbitrary function generator.

- Increasing source current creates plasmas with intense space-charge.

- Large dynamic range using sensitive electrometer.

- Measures average Q(r).

## Force Balance and Normalized Intensity s

**Force Balance and Normalized Intensity *****s***

- If *p* = *n** **kT*, then the statement of local force balance on a fluid element can be integrated over a radial density distribution such as,

- to give the global force balance equation,

- for a flat-top radial density distribution

- PTSX- accessible

## Transverse Bunch Compression by Increasing q

**Transverse Bunch Compression by Increasing ********q**

- If line density *N* is constant and *kT* doesn’t change too much, then increasing q decreases *R,* and the bunch is compressed.

- Either
- 1.)  increasing *V*0 max (increasing magnetic field strength) or 2.)  decreasing *f*       (increasing the magnet spacing)
- increases q

## Instantaneous Changes in the Voltage and Frequency Do Not Compress the Bunch When q is Fixed

**Instantaneous Changes in the Voltage and Frequency Do Not Compress the Bunch When ********q**** is Fixed**

*s* = 0.2
*kT* ~ 0.7 eV
*N* ~ constant

- v = 33o
- v = 50o
- v = 75o

*V*0 max & *f* up to 1.5X
- Baseline case
*V*0 max & *f* down to 0.66X

*• **s = ****p*2/2***q*2 = 0.20          *•* **/**0 *= *0.88      *• **V*0 max = 150 V          *•* *f* = 60 kHz            *•* v = 49o

## Adiabatic Amplitude Increases Transversely Compress the Bunch

**Adiabatic Amplitude Increases Transversely Compress the Bunch**

*R** *= 0.79 cm
*kT** * = 0.16 eV
*s** *= 0.18
-  = 10%

- _Instantaneous_* **R** *= 0.93 cm
*kT** * = 0.58 eV
*s** *= 0.08
-  = 140%

- _Adiabatic__* *_*     **R** *= 0.63 cm
*kT** * = 0.26 eV
*s** *= 0.10
-  = 10%

*• **s = ****p*2/2***q*2 = 0.20          *•* **/**0 *= *0.88      *• **V*0 max = 150 V          *•* *f* = 60 kHz            *•* v = 49o

- 20% increase in *V*0 max

- 90% increase in *V*0 max

***v** *= 63o

***v** *= 111o

-  ~*R**√** **kT*

- _Baseline_
*R** *= 0.83 cm
*kT** * = 0.12 eV
*s** *= 0.20

## Less Than Four Lattice Periods Adiabatically Compress the Bunch

**Less Than Four Lattice Periods Adiabatically Compress the Bunch**

***v** *= 63o

***v** *= 111o

***v** *= 81o

*• **s = ****p*2/2***q*2 = 0.20          *•* **/**0 *= *0.88      *• **V*0 max = 150 V          *•* *f* = 60 kHz            *•* v = 49o

## 2D WARP PIC Simulations Corroborate Adiabatic Transitions in Only Four Lattice Periods

**2D WARP PIC Simulations Corroborate Adiabatic Transitions in Only Four Lattice Periods**

- Instantaneous Change.

- Change Over Four Lattice Periods.

## Peak Density Scales Linearly With q

**Peak Density Scales Linearly With ********q**

- Constant emittance

- Constant energy

## Increasing q by Adiabatically Decreasing f

**Increasing **********q**** by Adiabatically Decreasing *****f***

## Increasing q by Adiabatically Decreasing f

**Increasing **********q**** by Adiabatically Decreasing *****f***

## Adiabatically Decreasing f Compresses the Bunch

**Adiabatically Decreasing *****f***** Compresses the Bunch**

- 33% decrease in *f*

- Good agreement with KV-equivalent beam envelope solutions.

*s = ****p*2/2***q*2         = 0.2.
* ***/**0 *= *0.88
*V*0 max = 150 V       *f* = 60 kHz          v = 49o

## Transverse Confinement is Lost When Single-Particle Orbits are Unstable

**Transverse Confinement is Lost When Single-Particle Orbits are Unstable**

-  = c

- Measured c (dots)
- Set v max = 180o and solve for c (line)

- c *f*0

*f*1 (kHz)

*f*0 = 60 kHz

*f*0 = 60 kHz

## Good Agreement Between Data and KV-Equivalent Beam Envelope Solutions

**Good Agreement Between Data and KV-Equivalent Beam Envelope Solutions**

*f*0 = 60 kHz

## Summary 

- PTSX is a compact and flexible laboratory experiment.
- PTSX has performed experiments on plasmas with normalized intensity *s* up to 0.2.
- Instantaneous changes can cause significant emittance growth and lead to halo particle production.
- Adiabatic increases in q approximately 100% can be applied over only four lattice periods.
- The charge bunch will “follow” even non-monotonic changes in q.

**Summary **