erik p. gilson princeton plasma physics laboratory 2005 aps-dpp denver, co october 26 th , 2005
DESCRIPTION
Experimental Simulations of Intense Beam Propagation Over Large Distances in a Compact Linear Paul Trap*. Erik P. Gilson Princeton Plasma Physics Laboratory 2005 APS-DPP Denver, CO October 26 th , 2005. - PowerPoint PPT PresentationTRANSCRIPT
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Erik P. GilsonPrinceton Plasma Physics Laboratory
2005 APS-DPPDenver, CO
October 26th, 2005
*This work is supported by the U.S. Department of Energy.
Experimental Simulationsof
Intense Beam Propagation Over Large Distancesin a
Compact Linear Paul Trap*
In collaboration with: Andy Carpe, Moses Chung, Ron Davidson, Mikhail Dorf, Phil Efthimion, Ed Startsev, Dick Majeski, and Hong Qin
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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.
• Davidson, Qin and Shvets, Phys. Plasmas 7, 1020 (2000)• Okamoto and Tanaka, Nucl. Instrum. Methods A 437, 178 (1999)• Gilson, Davidson, Efthimion and Majeski, Phys. Rev. Lett. 92, 155002 (2004)• N. Kjærgaard, K. Mølhave, M. Drewsen, Phys. Rev. E 66, 015401 (2002)• M. Walter LI2.00006.
PTSX Simulates Nonlinear Beam Dynamicsin Magnetic Alternating-Gradient Systems
Purpose:
Applications:Accelerator systems for high energy and nuclear physics applications, high energy density physics, heavy ion fusion, spallation neutron sources, and nuclear waste transmutation.
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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
•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
zBq
z
Magnetic Alternating-Gradient Transport Systems
S
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Transverse Focusing Frequency, Vacuum Phase Advance,and Normalized Intensity Parameter
Characterize the System
The smooth trajectory’s vacuum phase advance, v, is 35 degrees in this example.
Transverse focusing period, 2/q
12 2
2
q
ps
maxvq
v f
Normalized intensity parameter
To avoid instabilities,
5/f 10/f 15/f 20/f
s ~ 0.2 for Spallation Neutron Source.
to confine the space-charge.
1/f
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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 column length 2 m Maximum wall voltage ~ 400 V
Wall electrode radius 10 cm End electrode voltage < 150 V
Plasma column radius ~ 1 cm Voltage oscillation frequency
< 100 kHz
Cesium ion mass 133 amu
f rm
eV
wq 2
max 08
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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 equation
•Distributions evolve according to Vlasov equation
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1.25 in
1 cm
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 s up to 0.8.
Large dynamic range using sensitive electrometer.
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•V0 max = 235 V
•f = 75 kHz
• thold = 1 ms
• v = 49o
• q = 6.5 104 s-1
plasmaaperturelre
rQrn
2
2.02 2
2
q
ps
Radial Profiles of Trapped Plasmas are Approximately Gaussian – Consistent with Thermal Equilibrium
• n(0) = 1.4105 cm-3
• R = 1.4 cm
• s = 0.2
WARP 3D
kT
rqrmnrn
sq
2
2exp0
22
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• s = p2/2q
2 = 0.18.
• V0 max = 235 V f = 75 kHz v = 49o
• At f = 75 kHz, a lifetime of 100 ms corresponds to 7,500 lattice periods.
• If lattice period is 1 m, the PTSX simulation experiment would correspond to a 7.5 km beamline.
PTSX Simulates Equivalent PropagationDistances of 7.5 km
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Temporarily Changing the Amplitude Causes the Plasma Envelope to Oscillate
5 Cycles 5 Cycles
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0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
0 50 100 150 200 250 3000 50 100 150 200 250 300
1
0
2
r
The Mismatch When the Amplitude is Restored Depends on the Frequency of the Envelope Oscillation
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
0 500 1000 1500 2000 2500 3000 3500 4000 4500
r
ΔR
due to emittance growth
0 1000 2000 3000 4000
1
0
2
M. Dorf BP1.00100
Voltage Waveform Amplitude WARP 2D
WARP 2D
WARP 2DExp. Data: 30 % Increase
WARP 2DExp. Data: 50 % Increase
Experimental Data
oq
NqkTRm
42
222
Force Balance
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Comparison of Instantaneous Changes in Waveform Amplitude and Frequency
Baseline case:
V1 = 150 V
f = 60 kHz
q = 52,200 s-1
v = 49o
s = 0.2
kT ~ 0.7 eV
t = 1 ms
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Comparison of Instantaneous Changes in Waveform Amplitude and Frequency
f rm
eV
wq 2
max 08
fq
v
Constant voltage
Constant frequency
q q/1.5, q 1.5 q
q q/1.5, q 1.5 q
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Comparison of Instantaneous Changes in Waveform Amplitude and Frequency
f rm
eV
wq 2
max 08
fq
v
Constant transverse focusing frequency
Constant vacuum phase advance q q/1.5, q 1.5 q
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Comparison of Instantaneous Changes in Waveform Amplitude and Frequency
f rm
eV
wq 2
max 08
fq
v
q 1.5 q
q q/1.5
N ~ constant in following data.
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Changing the Voltage and Frequency Does Not Affect the Transvese Profile When the Transverse Focusing Frequency is Fixed
s = 0.2
kT ~ 0.7 eV
N ~ constant
v = 33o
v = 50o
v = 75o
oq
NqkTRm
42
222
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q q/1.5
Decreasing Transverse Focusing Frequency PreservesNormalized Intensity but Increases Emittance
s = 0.2
kT ~ 0.7 eV
N ~ constant
Emittance increases by 45%
q q/1.5
v = 22o
v = 33o
v = 50o
oq
NqkTRm
42
222
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q 1.5 q
Increasing Phase Advance Degrades Transverse Confinement
s = 0.08, kT = 1.6 eV
s = 0.14, kT = 1.4 eV
s = 0.02, kT = 4.7 eV
q 1.5 q
v = 50o 60%
v = 75o 40%
v = 112o 450%
N ~ constant Emittance increases
oq
NqkTRm
42
222
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A Smooth Change in Lattice Strength Compresses the Plasma: a First Look
A hyperbolic tangent transition from one amplitude to another at fixed frequency.
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LIF System is Being Installed
Plasma
Laser sheet
Field of View
•Nondestructive
•Image entire transverse profile at once
•Time resolution
•Velocity measurement
M. Chung BP1.00085
Barium ion source will replace Cesium ion source.
CCD camera for imaging plasma
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•PTSX is a compact and flexible laboratory experiment.
•PTSX can trap plasmas with normalized intensity s up to 0.8.
•Confinement times can correspond to up to 7,500 lattice periods.
• Instantaneous lattice changes are detrimental to transverse confinement, leading to mismatch, envelope oscillations, and subsequent emittance growth (unless transverse focusing frequency is fixed.) Large vacuum phase advance v degrades transverse confinement.
•Study of smooth lattice changes is planned.
PTSX Simulates the Transverse Dynamics of Intense Beam Propagation Over Large Distances Through Magnetic Alternating-Gradient Transport Systems