Experiments on Transverse Bunch Compression on the Princeton Paul Trap Simulator Experiment*
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Transcript of Experiments on Transverse Bunch Compression on the Princeton Paul Trap Simulator Experiment*
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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
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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:
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•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
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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
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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
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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
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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).
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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
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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
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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
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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
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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
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2D WARP PIC Simulations Corroborate Adiabatic Transitions in Only Four Lattice Periods
Instantaneous Change.
Change Over Four Lattice Periods.
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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
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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
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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
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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
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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
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Good Agreement Between Data and KV-Equivalent Beam Envelope Solutions
c
f0 =
f0 =
= c
f0 =
f0 = 60 kHz
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•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