Erik P. GilsonPrinceton 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 BunchCompression 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

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 Dynamicsin Magnetic Alternating-Gradient Systems

Purpose:

•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

N

NS

S

x

y

z

yxqfoc

yxqfoc

q

yxz

xyzB

eexF

eexB

ˆˆ

ˆˆ

2

)()(

cm

zBZez q

q

Magnetic Alternating-Gradient Transport Systems

zBq

z

S

2 m

0.4 m ))((2

1),,( 22 yxttyxe qap

20

)(8)(

wq rm

teVt

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

f rm

eV

wq 2

max 08

sinusoidal in this work

22

1

34

23

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

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

oq

NqkTRm

42

222

12 2

2

q

ps 21

0

1 s

kT

rqrmnrn

sq

2

2exp0

22

0.1 0.950.2 0.900.3 0.840.4 0.770.5 0.710.6 0.630.7 0.550.8 0.450.9 0.320.99 0.100.999 0.03

s /0

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

0

22 0

m

qnp

Transverse Bunch Compression by Increasing q

oq

NqkTRm

42

222

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

f rm

eV

wq 2

max 08

Either1.) increasing V0 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

s = 0.2

kT ~ 0.7 eV

N ~ constant

v = 33o

v = 50o

v = 75o

oq

NqkTRm

42

222

f rm

eV

wq 2

max 08

fq

v

V0 max & f up to 1.5X

Baseline case

V0 max & f down to 0.66X

• s = p2/2q

2 = 0.20 • /0 = 0.88 • V0 max = 150 V • f = 60 kHz • v = 49o

Adiabatic Amplitude Increases Transversely Compress the Bunch

R = 0.79 cmkT = 0.16 eVs = 0.18 = 10%

Instantaneous R = 0.93 cmkT = 0.58 eVs = 0.08 = 140%

Adiabatic R = 0.63 cmkT = 0.26 eVs = 0.10 = 10%

• s = p2/2q

2 = 0.20 • /0 = 0.88 • V0 max = 150 V • f = 60 kHz • v = 49o

20% increase in V0 max 90% increase in V0 max

v = 63o v = 111o

~R√ kT

Baseline R = 0.83 cmkT = 0.12 eVs = 0.20

Less Than Four Lattice Periods Adiabatically Compress the Bunch

v = 63o

v = 111o

v = 81o

• s = p2/2q

2 = 0.20 • /0 = 0.88 • V0 max = 150 V • f = 60 kHz • v = 49o

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

f rm

eV

wq 2

max 08

.~

~

2~

2

22

constR

kTR

kTRm

q

q

.~)0( 2 constNRn

qn ~)0(

Constant emittance

Constant energy

0

21

2coshln

422

)(f

ttfft

fft iffi

2

)(tt

t

2

)(

Increasing q by Adiabatically Decreasing f

tVtV sinmax 0

f rm

eV

wq 2

max 08

1

2tanh

22

)( 21

tt

tff

tft fi

f

0

21

2coshln

422

)(f

ttfft

fft iffi

2

)(tt

t

2

)(

2

)(t

t

t

2

)(

tVtV sinmax 0

Increasing q by Adiabatically Decreasing f

tVtV sinmax 0

f rm

eV

wq 2

max 08

Adiabatically Decreasing f Compresses the Bunch

33% decrease in f

Good agreement with KV-equivalent beam envelope solutions.

f rm

eV

wq 2

max 08

• s = p2/2q

2 = 0.2.

• /0 = 0.88

• V0 max = 150 V f = 60 kHz v = 49o

Transverse Confinement is Lost When Single-Particle Orbits are Unstable

c

2

1

ffq

v

= c

1

2tanh

22

)( 21

tt

tff

tft fi

f

2

)(t t

t

2

)(

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

c f 0

f1 (kHz)

f0 = 60 kHzf0 = 60 kHz

Good Agreement Between Data and KV-Equivalent Beam Envelope Solutions

c

f0 =

f0 =

= c

f0 =

f0 = 60 kHz

•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