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

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.

•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

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

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

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

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

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.

•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

• 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

Temporarily Changing the Amplitude Causes the Plasma Envelope to Oscillate

5 Cycles 5 Cycles

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

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

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

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

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.

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

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

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

A Smooth Change in Lattice Strength Compresses the Plasma: a First Look

A hyperbolic tangent transition from one amplitude to another at fixed frequency.

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

•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