1. A. Friedman, J. J. Barnard, R. H. Cohen, D. P. Grote, S. M. Lund, W. M. Sharp, LLNL A. Faltens, E. Henestroza, J-Y. Jung, J. W. Kwan, E. P. Lee, M. A. Leitner, B. G. Logan, J.-L. Vay, W. L. Waldron, LBNL R. C. Davidson, M. Dorf, E. P. Gilson, I. Kaganovich, PPPL ICAP 2009, San Francisco Heavy Ion Fusion Science Virtual National Laboratory Developing the Physics Design for NDCX-II, a Unique Pulse-Compressing Ion Accelerator * *This work was performed under the auspices of the USDOE by LLNL under Contract DE-AC52-07NA27344, by LBNL under Contract DE-AC02-05CH11231, and by PPPL under Contract DE-AC02-76CH03073.

2. The Heavy Ion Fusion Science Virtual National Laboratory 2 LITHIUM ION BEAM BUNCH (ultimate goals) Final beam energy:> 3 MeV Final spot diameter :~ 1 mm Final bunch length :~ 1 cm or ~ 1 ns Total charge delivered: ~ 30 nC Exiting beam available for measurement TARGET  m foil or foam 30 J/cm 2 isochoric heating  aluminum temperature ~ 1 eV NDCX-II will enable studies of warm dense matter and key physics for ion direct drive

3. The Heavy Ion Fusion Science Virtual National Laboratory 3 “Neutralized Drift Compression” produces a short pulse of ions The process is analogous to “chirped pulse amplification” in lasers A head-to-tail velocity gradient (“tilt”) is imparted to the beam by one or more induction cells This causes the beam to shorten as it moves down the beamline: Space charge would inhibit this compression, so the beam is directed through a plasma which affords neutralization Simulations and theory (Voss Scientific, PPPL) showed that the plasma density must exceed the beam density for this to work well z (beam frame) vzvz vzvz 

4. The Heavy Ion Fusion Science Virtual National Laboratory 4 NDCX-I NDCX-I at LBNL routinely achieves current amplification > 50x

5. The Heavy Ion Fusion Science Virtual National Laboratory 5 ATA induction cells with pulsed 1-3T solenoids Length ~ 15 m Avg. 0.25 MV/m Peak 0.75 MV/m Li + ion injector final focus and target chamber neutralized drift compression region with plasma sources water-filled Blumlein voltage sources oil-filled transmission lines NDCX-II

6. The Heavy Ion Fusion Science Virtual National Laboratory 6 LLNL has given the HIFS-VNL 48 induction cells from the ATA They provide short, high-voltage accelerating pulses –Ferrite core: 1.4 x 10 -3 Volt-seconds –Blumlein: 200-250 kV; 70 ns FWHM At front end, longer pulses need custom voltage sources; < 100 kV for cost Test stand at LBNL Advanced Test Accelerator (ATA)

7. The Heavy Ion Fusion Science Virtual National Laboratory 7 Outline Introduction to the project 1-D ASP code model and physics design Warp (R,Z) simulations 3-D effects: misalignments & corkscrew Status of the design

8. The Heavy Ion Fusion Science Virtual National Laboratory 8 1-D PIC code ASP (“Acceleration Schedule Program”) Follows (z,v z ) phase space using a few hundred particles (“slices”) Space-charge field via Poisson equation with finite-radius correction term  2   d 2  /dz 2 - k  2  = -  /  0 k  2 = 4 / (g 0 r beam 2 ) g 0 = 2 log (r wall / r beam ) Acceleration gaps with longitudinally-extended fringing field –Idealized waveforms –Circuit models including passive elements in “comp boxes” –Measured waveforms Centroid tracking for studying misalignment effects, steering Multiple optimization loops: –Waveforms and timings –Dipole strengths (for steering) Interactive (Python language with Fortran for intensive parts)

9. The Heavy Ion Fusion Science Virtual National Laboratory 9 Principle 1: Shorten Beam First (“non-neutral drift compression”) Equalize beam energy after injection -- then -- Compress longitudinally before main acceleration Want < 70 ns transit time through gap (with fringe field) as soon as possible ==> can then use 200-kV pulses from ATA Blumleins Compress carefully to minimize effects of space charge Seek to achieve large velocity “tilt” v z (z) ~ linear in z “right away”

10. The Heavy Ion Fusion Science Virtual National Laboratory 10 Principle 2: Let It Bounce Rapid inward motion in beam frame is required to get below 70 ns Space charge ultimately inhibits this compression However, so short a beam is not sustainable –Fields to control it can’t be “shaped” on that timescale –The beam “bounces” and starts to lengthen Fortunately, the beam still takes < 70 ns because it is now moving faster We allow it to lengthen while applying: –additional acceleration via flat pulses –confinement via ramped (“triangular”) pulses The final few gaps apply the “exit tilt” needed for neutralized drift compression

11. The Heavy Ion Fusion Science Virtual National Laboratory 11 Pulse length vs z: the “bounce” is evident pulse length (m) center of mass z position (m)

12. The Heavy Ion Fusion Science Virtual National Laboratory 12 Pulse duration vs z -time for entire beam to cross a plane at fixed z +time for a single particle at mean energy to cross finite- length gap *time for entire beam to cross finite-length gap pulse duration (ns) center of mass z position (m)

13. The Heavy Ion Fusion Science Virtual National Laboratory 13 Voltage waveforms for all gaps “ramp” (here from an ATA cell) “flat-top” (here idealized) “ear” (to confine beam ends) “shaped” (to impose velocity tilt for initial compression) gap voltage (kV) time ( µ s)

14. The Heavy Ion Fusion Science Virtual National Laboratory 14 A series of snapshots from ASP shows the evolution of the longitudinal phase space (kinetic energy vs z) and current

15. The Heavy Ion Fusion Science Virtual National Laboratory 15 Outline Introduction to the project 1-D ASP code model and physics design Warp (R,Z) simulations 3-D effects: misalignments & corkscrew Status of the design

16. The Heavy Ion Fusion Science Virtual National Laboratory 16 Design of injector for 1 mA/cm 2 Li + emission uses Warp in (r,z) extractor ~150 kV emitter ~165 kV Z (m) R (m) 0 10 cm Using Warp’s “gun” mode Using time-dependent space-charge-limited emission and simple mesh refinement

17. The Heavy Ion Fusion Science Virtual National Laboratory 17 ASP & Warp results agree (when care is taken w/ initial beam )

18. The Heavy Ion Fusion Science Virtual National Laboratory 18 Video: Warp (r,z) simulation of NDCX-II beam For video see: http://hifweb.lbl.gov/public/movies/ICAP09

19. The Heavy Ion Fusion Science Virtual National Laboratory 19 Outline Introduction to the project 1-D ASP code model and physics design Warp (R,Z) simulations 3-D effects: misalignments & corkscrew Status of the design

20. The Heavy Ion Fusion Science Virtual National Laboratory 20 Video: Warp 3-D simulation of NDCX-II beam (no misalignments) For video see: http://hifweb.lbl.gov/public/movies/ICAP09

21. The Heavy Ion Fusion Science Virtual National Laboratory 21 Video: Warp 3D simulation of NDCX-II, including random offsets of solenoid ends by up to 1 mm (0.5 mm is nominal) For video see: http://hifweb.lbl.gov/public/movies/ICAP09

22. The Heavy Ion Fusion Science Virtual National Laboratory 22 ASP employs a tuning algorithm (as in ETA-II, DARHT) † to adjust “steering” dipoles so as to minimize a penalty function Head - red Mid - green Tail – blue x - solid y - dashed Dipoles optimized; penalizing corkscrew amplitude & beam offset, and limiting dipole strength Trajectories of head, mid, tail particles, and corkscrew amplitude, for a typical ASP run. Random offsets of solenoid ends up to 1 mm were assumed; the effect is linear. Dipoles off Corkscrew amplitude - black † Y-J. Chen, Nucl. Instr. and Meth. A 398, 139 (1997).

23. The Heavy Ion Fusion Science Virtual National Laboratory 23 Outline Introduction to the project 1-D ASP code model and physics design Warp (R,Z) simulations 3-D effects: misalignments & corkscrew Status of the design

24. The Heavy Ion Fusion Science Virtual National Laboratory 24 Key technical issues are being addressed Li + ion source current density –We currently assume only 1 mA/cm 2 Solenoid misalignment effects –Steering reduces corkscrew but requires beam position measurement –If capacitive or magnetic BPM’s prove too noisy, we’ll use scintillators or apertures Require “real” acceleration waveforms –A good “ramp” has been tested and folded into ASP runs –We’re developing shaping circuits for “flatter flat-tops” Pulsed solenoid effects –Volt-seconds of ferrite cores are reduced by return flux of solenoids –Eddy currents (mainly in end plates) dissipate energy, induce noise –We’ll use flux-channeling inserts and/or windings, & thinner end plates

25. The Heavy Ion Fusion Science Virtual National Laboratory 25 We look forward to a novel and flexible research platform NDCX-II will be a unique ion-driven user facility for warm dense matter and IFE target physics studies. The machine will also allow beam dynamics experiments relevant to high-current fusion drivers. The baseline physics design makes efficient use of the ATA components through rapid beam compression and acceleration.