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

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

2. PTSX Simulates Nonlinear Beam Dynamicsin Magnetic Alternating-Gradient Systems • Purpose: PTSX simulates, in a compact experiment, the nonlinear transverse dynamics of intense beam propagation over large distances through magnetic alternating-gradient transport 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. 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).

3. PTSX is Capable of Examining a Variety ofBeam Physics Issues • 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.

4. Magnetic Alternating-Gradient Transport Systems rb << S Motion in beam frame is nonrelativistic Long coasting beams Applied field: Self field: Evolution of fields: Evolution of distribution:

5. PTSX Configuration – A Cylindrical Paul Trap 2 m 0.4 m 0.2 m • 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.

6. V(t) Corresponds to Bq´(s) Flexibility to apply any V(t) with arbitrary function generator.

7. PTSX Components – Electrodes, Ion Source,and Faraday cup 1 cm 1.25 in

8. Constraints on Vacuum Phase Advance sv and Intensity Parameter s are the Same The average (Smooth-focusing/Ponderomotive) transverse focusing frequency is given by where The vacuum phase advance must be small enough to avoid instabilities. The confining force must be strong enough to confine the space-charge. Depressed phase advance.

9. Confinement is Lost if Phase Advance is Too Big Stream Cs+ ions from source to collector without axial trapping of the plasma.

10. Radial Profiles of Trapped Plasmas are Gaussian – Consistent with Thermal Equilibrium The charge Q(r)is collected through the 1 cm aperture is averaged over 2000 plasma shots. The density is calculated from • Ib = 5 nA • V0 = 235 V • f = 75 kHz • thold = 1 ms • sv = 49o • wq = 6.5  104 s-1 n(r0) = 1.4  105 cm-3 Rb = 1.4 cm s = 0.2 (s/sv = 0.89)

11. WARP Simulations Agree Well with PTSX Data At t = 6 ms, • s = wp2/2wq2 = 0.1 • s/sv = 0.95 • kT = 0.5 eV • Rb = 0.7 cm

12. Accessible Values of s = wp2/2wq2Range From 0 to 0.8 (s/sv = 0.45) • Varying Ib over the range 0.8 nA to 35 nA gives plasmas with s up to 0.8 (s/sv = 0.45). • The distribution broadens as more charge is injected into the trap. • Here, V0 = 235 V, f = 75 kHz and sv = 49o

13. Data Agrees with Force-Balance Model Ib < 35 nA 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.

14. PTSX Simulates Equivalent PropagationDistances of 7.5 km • 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. • s = wp2/2wq2 = 0.18. • s/sv = 0.90 • V0 = 235 V f = 75 kHz sv = 49o

15. Waveform Modifications V1 = 235 V, f = 75 kHz, sv = 49o V2 = 376 V, f = 75 kHz, sv = 78o Linear Change One-Period Change Instantaneous Change Smooth Change (hyperbolic tangent)

16. Gradual Increases in Lattice Strength Give Higher Peak Density V1 = 235 V f = 75 kHz sv = 49o V2 = 376 V f = 75 kHz sv = 78o

17. Gradual Lattice ChangeMore Important at Large V2/V1 V1 = 235 V f = 75 kHz sv = 49o Parabola is surface of constant s

18. 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

19. PTSX is a Compact Experiment for Studying the Propagation of Beams Over Large Distances • 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.