The Heavy Ion Fusion Virtual National Laboratory

Erik P. Gilson**

PPPL

15th International Symposium on Heavy Ion Fusion

June 9th, 2004

Research supported by the U.S. Department of Energy

In collaboration with Moses Chung, Ronald C. Davidson, Philip Efthimion, Richard Majeski and Edward Startsev

*

**

Simulation of Long-Distance Beam Propagation in the Paul Trap Simulator Experiment*

The Heavy Ion Fusion Virtual National Laboratory

• Purpose: PTSX simulates, in a compact experiment, the nonlinear transverse dynamics of intense beam propagation over large distances through magnetic alternating-gradient transport systems.

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).

PTSX Simulates Nonlinear Beam Dynamicsin Magnetic Alternating-Gradient Systems

• Method: Transverse dynamics of the two systems are the same. Long PTSX plasma lifetimes correspond to large distances.

• Applications: Accelerator systems for heavy ion fusion, high energy and nuclear physics applications, spallation neutron sources, and nuclear waste transmutation.

The Heavy Ion Fusion Virtual National Laboratory

• 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 Capable of Examining a Variety ofBeam Physics Issues

The Heavy Ion Fusion Virtual National Laboratory

Evolution of distribution:

Magnetic Alternating-Gradient Transport Systems

yxqfoc

yxqfoc

q

yxz

xyzB

eexF

eexBˆˆ

ˆˆ

2

)()(

cmzBeZ

zbbb

qbq

0

bqq fyy

ysxx

xsy

yx

xs

),,(),,(),,( 22 syxAsyxcm

eZsyx selfzbselfbbb

b

bb

b fydxdN

Kyx

22

2

2

2

selfbselfzA

Applied field:

Self field:

Evolution of fields:

rb << S

Motion in beam frame is nonrelativistic

Long coasting beams

The Heavy Ion Fusion Virtual National Laboratory

2 m

0.4 m ))((21),,( 22 yxttyxe qapb

20 )(8)(

wb

bq rm

tVet

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

• The injection electrodes oscillate with the voltage ±V0(t) during cesium ion injection.

• The 40 cm long electrodes at the far end of the trap are held at a constant voltage during injection to prevent ions from leaving the trap.

• The dump electrodes oscillate with the voltage ±V0(t) during ion dumping.

The Heavy Ion Fusion Virtual National Laboratory

Ttt qq 2sinˆ

otherwise,0475.0475.0,1425.0425.0,1

ˆ

TtTt

t qq

V(t) Corresponds to Bq´(s)

Flexibility to apply any V(t) with arbitrary function generator.

The Heavy Ion Fusion Virtual National Laboratory

1.25 in

1 cm

PTSX Components – Electrodes, Ion Source,and Faraday cup

The Heavy Ion Fusion Virtual National Laboratory

12 2

2

q

ps

f rm

Ve

wb

bq 2

max 08

waveformsinusoidal a for

22

1

The average (Smooth-focusing/Ponderomotive) transverse focusing frequency is given by

where

The confining force must be strong enough to confine the space-charge.

The vacuum phase advance must be small enough to avoid instabilities.

Constraints on Vacuum Phase Advance v and Intensity Parameter s are the Same

max

fq

v

Depressed phase advance. 211 sv

The Heavy Ion Fusion Virtual National Laboratory

Stream Cs+ ions from source to collector without axial trapping of the plasma.

Confinement is Lost if Phase Advance is Too Big

The Heavy Ion Fusion Virtual National Laboratory

•Ib = 5 nA

•V0 = 235 V

•f = 75 kHz

• thold = 1 ms

•v = 49o

•q = 6.5 104 s-1

plasmaaperturelre

rQrn 2

The charge Q(r) is collected through the 1 cm aperture is averaged over 2000 plasma shots.

The density is calculated from

2.02 2

2

q

ps

Radial Profiles of Trapped Plasmas are Gaussian – Consistent with Thermal Equilibrium

n(r0) = 1.4 105 cm-3 Rb = 1.4 cm s = 0.2 (/v = 0.89)

The Heavy Ion Fusion Virtual National Laboratory

At t = 6 ms,

•s = p2/2q

2 = 0.1

•/v = 0.95

•kT = 0.5 eV

•Rb = 0.7 cm

WARP Simulations Agree Well with PTSX Data

The Heavy Ion Fusion Virtual National Laboratory

• Varying Ib over the range 0.8 nA to 35 nA gives plasmas with s up to 0.8 (/v = 0.45).

• The distribution broadens as more charge is injected into the trap.

• Here, V0 = 235 V, f = 75 kHz and v = 49o

Accessible Values of s = p2/2q

2

Range From 0 to 0.8 (/v = 0.45)

The Heavy Ion Fusion Virtual National Laboratory

o

bbq

qNkTRm

4

22

22

In thermal equilibrium,

At larger Nb, the increasing mismatch between the ion source and the trapped plasma likely leads to plasma heating. Note that kT = 0.5 eV as Nb approaches zero.

Ib < 35 nA

Data Agrees with Force-Balance Model

The Heavy Ion Fusion Virtual National Laboratory

• s = p2/2q

2 = 0.18.

•/v = 0.90

• V0 = 235 V f = 75 kHz v = 49o

• At f = 75 kHz, a lifetime of 100 ms corresponds to 7,500 lattice periods.

• If S is 1 m, the PTSX simulation experiment would correspond to a 7.5 km beamline.

PTSX Simulates Equivalent PropagationDistances of 7.5 km

The Heavy Ion Fusion Virtual National Laboratory

Linear Change One-Period Change

V1 = 235 V, f = 75 kHz, v = 49o V2 = 376 V, f = 75 kHz, v = 78o

Waveform Modifications

Instantaneous Change Smooth Change (hyperbolic tangent)

The Heavy Ion Fusion Virtual National Laboratory

V1 = 235 V

f = 75 kHz

v = 49o

Gradual Increases in Lattice Strength Give Higher Peak Density

V2 = 376 V

f = 75 kHz

v = 78o

The Heavy Ion Fusion Virtual National Laboratory

V1 = 235 V

f = 75 kHz

v = 49o

Gradual Lattice ChangeMore Important at Large V2/V1

Parabola is surface of constant s22

2

2 Vns

q

p

The Heavy Ion Fusion Virtual National Laboratory

Barium Ion Source Development

• A barium ion source is being developed in order to implement laser-induced fluorescence (LIF) to characterize the transverse distribution function.

Moses Chung and Andy Carpe load barium into the test chamber.

Moses Chung monitors barium ion current from contact ionization of barium on a rhenium plate.

Moses Chung Th.P-27

The Heavy Ion Fusion Virtual National Laboratory

• 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.

• Future plans include exploring important 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