1. The Heavy Ion Fusion Virtual National Laboratory Erik P. Gilson** PPPL 15 th International Symposium on Heavy Ion Fusion June 9 th, 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*

2. 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 Dynamics in 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.

3. 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 of Beam Physics Issues

4. The Heavy Ion Fusion Virtual National Laboratory Evolution of distribution: Magnetic Alternating-Gradient Transport Systems Applied field: Self field: Evolution of fields: r b << S Motion in beam frame is nonrelativistic Long coasting beams

5. The Heavy Ion Fusion Virtual National Laboratory 2 m 0.4 m 0.2 m PTSX Configuration – A Cylindrical Paul Trap Plasma column length2 mMaximum wall voltage400 V Wall electrode radius10 cmEnd electrode voltage150 V Plasma column radius1 cmVoltage oscillation frequency 100 kHz The injection electrodes oscillate with the voltage ±V 0 (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 ±V 0 (t) during ion dumping.

6. The Heavy Ion Fusion Virtual National Laboratory V(t) Corresponds to B q ´(s) Flexibility to apply any V(t) with arbitrary function generator.

7. The Heavy Ion Fusion Virtual National Laboratory 1.25 in 1 cm PTSX Components – Electrodes, Ion Source, and Faraday cup

8. The Heavy Ion Fusion Virtual National Laboratory 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 Depressed phase advance.

9. 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

10. The Heavy Ion Fusion Virtual National Laboratory I b = 5 nA V 0 = 235 V f = 75 kHz t hold = 1 ms  v = 49 o  q = 6.5  10 4 s -1 The charge Q(r) is collected through the 1 cm aperture is averaged over 2000 plasma shots. The density is calculated from Radial Profiles of Trapped Plasmas are Gaussian – Consistent with Thermal Equilibrium n(r 0 ) = 1.4  10 5 cm -3 R b = 1.4 cm s = 0.2 (  /  v = 0.89)

11. The Heavy Ion Fusion Virtual National Laboratory At t = 6 ms, s =  p 2 /2  q 2 = 0.1  /  v = 0.95 kT = 0.5 eV R b = 0.7 cm WARP Simulations Agree Well with PTSX Data

12. The Heavy Ion Fusion Virtual National Laboratory Varying I b 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, V 0 = 235 V, f = 75 kHz and  v = 49 o Accessible Values of s =  p 2 /2  q 2 Range From 0 to 0.8 (  /  v = 0.45)

13. The Heavy Ion Fusion Virtual National Laboratory In thermal equilibrium, At larger N b, the increasing mismatch between the ion source and the trapped plasma likely leads to plasma heating. Note that kT = 0.5 eV as N b approaches zero. I b < 35 nA Data Agrees with Force-Balance Model

14. The Heavy Ion Fusion Virtual National Laboratory s =  p 2 /2  q 2 = 0.18.  /  v = 0.90 V 0 = 235 V f = 75 kHz  v = 49 o 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 Propagation Distances of 7.5 km

15. The Heavy Ion Fusion Virtual National Laboratory Linear ChangeOne-Period Change V 1 = 235 V, f = 75 kHz,  v = 49 o V 2 = 376 V, f = 75 kHz,  v = 78 o Waveform Modifications Instantaneous ChangeSmooth Change (hyperbolic tangent)

16. The Heavy Ion Fusion Virtual National Laboratory V 1 = 235 V f = 75 kHz  v = 49 o Gradual Increases in Lattice Strength Give Higher Peak Density V 2 = 376 V f = 75 kHz  v = 78 o

17. The Heavy Ion Fusion Virtual National Laboratory V 1 = 235 V f = 75 kHz  v = 49 o Gradual Lattice Change More Important at Large V 2 /V 1 Parabola is surface of constant s

18. 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

19. 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