Erik P. Gilson Princeton Plasma Physics Laboratory 9 th International Workshop on Nonneutral Plasmas Columbia University June 17 th , 2008 *This work is supported by the U.S. Department of Energy. Overview of Intense Beam Simulation Experiments Performed Using the Paul Trap Simulator Experiment (PTSX)* In collaboration with: Andy Carpe, Moses Chung, Ronald C. Davidson, Mikhail Dorf, Philip Efthimion, Andrew Godbehere, Richard Majeski, Hong Qin, Edward Startsev, Hua Wang
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Erik P. GilsonPrinceton Plasma Physics Laboratory
9th International Workshop on Nonneutral Plasmas Columbia University
June 17th, 2008
*This work is supported by the U.S. Department of Energy.
Overview ofIntense Beam Simulation Experiments
Performed Using thePaul Trap Simulator Experiment (PTSX)*
In collaboration with:
Andy Carpe, Moses Chung, Ronald C. Davidson, Mikhail Dorf, Philip Efthimion, Andrew Godbehere, Richard Majeski, Hong Qin, Edward Startsev, Hua Wang
• Purpose: PTSX simulates, in a compact experiment, the transverse nonlinear dynamics of intense beam propagation over large distances through magnetic alternating-gradient transport systems.
• Applications: Accelerator systems for high energy and nuclear physics applications, heavy ion fusion, spallation neutron sources, and high energy density physics.
PTSX Simulates Nonlinear Beam Dynamicsin Magnetic Alternating-Gradient Systems
Other Intense-Beam Studies, Paul-trap-based and otherwise:
Okamoto and Tanaka
Drewsen et al.
Kishek et al.
Scientific Motivation
• Beam mismatch and envelope instabilities;
• Collective wave excitations;
• Chaotic particle dynamics and production of halo particles;
• Mechanisms for emittance growth;
• Compression techniques; and
• Effects of distribution function on stability properties.
As self-field effects become important, it is important to develop an understanding of:
( ) ( ) ( )( ) ( ) ( )yxqfoc
yxqfoc
q
yxz
xyzB
eexF
eexBˆˆ
ˆˆ
−−=
+′=
κ
2
)()(
cmzBZe
z qq βγ
κ′
≡
Magnetic Alternating-Gradient Transport Systems
SS
N
S
xz
y
Transverse Focusing Frequency andPhase Advance Characterize the Motion
In one lattice period, S, the smooth trajectory’s vacuum phase advance, σv, is 35 degrees.
2 = 0.20 • ν/ν0 = 0.88 • V0 max = 150 V • f = 60 kHz • σv = 49o
20% increase in V0 max 90% increase in V0 max
σv = 63o σv = 111o
ε ~R√ kT
BaselineR = 0.83 cmkT = 0.12 eVs = 0.20
Less Than Four Lattice Periods are Needed to Make the Transition Adiabatic
σv = 63o
σv = 111o
σv = 81o
• s = ωp2/2ωq
2 = 0.20 • ν/ν0 = 0.88 • V0 max = 150 V • f = 60 kHz • σv = 49o
WARP 2D simulations are in good agreement.
Time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
phas
e (r
ad)
0
50
100
150
200
Time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
phas
e (r
ad)
0
50
100
150
200
250
300
Time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
kHz
-150
-100
-50
0
50
100
Time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
Am
plitu
de (a
rb)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
Am
plitu
de (a
rb)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
( )⎥⎦
⎤⎢⎣
⎡+
−−−+= 1
2tanh
22)( 21
τπφ tt
tff
tft fif
( )0
21
2coshln
422)( f
ttfft
fft iffi −⎥⎦
⎤⎢⎣
⎡ −−−+
+=
ττ
πφ
πφ2
)(t
πφ2
)(t
( ) ( )tVtV φsinmax 0=
Increasing ωq by Adiabatically Decreasing f
( ) ( )tVtV φsinmax 0=ξ
πω
f rmeV
wq 2
max 08=
Adiabatically Decreasing fCompresses the Bunch
33% decrease in f
Good agreement with KV-equivalent beam envelope solutions.
ξπ
ωf rm
eV
wq 2
max 08=
• s = ωp2/2ωq
2
= 0.2.
• ν/ν0 = 0.88• V0 max = 150 V
f = 60 kHz σv = 49o
Transverse Confinement is Lost When Single-Particle Orbits are Unstable
τc
2
1qsfv f f
ωσ = ∝
τ = τc
( )⎥⎦
⎤⎢⎣
⎡+
−−−+= 1
2tanh
22)( 21
τπφ tt
tff
tft fif
πφ2
)(t
Measured τc (dots)Set σv max = 180o and solve for τc (line)
τ cf 0
f1 (kHz)
f0 = 60 kHzf0 = 60 kHz
Good Agreement Between Data and KV-Equivalent Beam Envelope Solutions
τc
τf0 = 0
τf0 = 19.9
τ = τc
τf0 = 26
f0 = 60 kHz
Spectrum of measured signal
Quadrupole mode
Breathing mode
ℓ = 2 surface-wave quadrupole mode
ℓ = 0 body-wave breathing mode
( )1 24 3q sω ω= −
( )1 24 2q sω ω= −
Measuring Beam Oscillations and Inferring Beam “Normalized Intensity” s
Segmented collective-mode capacitive pick-up diagnostic is sensitive to beam collective-mode oscillations.
Measured frequencies…
… determine unique “normalized intensity.”
Other modes?
• PTSX is a versatile research facility in which to simulate collective processes and the transverse dynamics of intense charged particle beam propagation over large distances through an alternating-gradient magnetic quadrupole focusing system using a compact laboratory Paul trap.
• PTSX explores important beam physics issues such as:
•Beam mismatch and envelope instabilities;
•Collective wave excitations;
•Chaotic particle dynamics and production of halo particles;
•Mechanisms for emittance growth;
•Compression techniques; and
•Effects of distribution function on stability properties.
PTSX is a Compact Experiment for Studying the Propagation of Beams Over Large Distances