Overview of NDCX-II Physics Design and Comments on final beam-lines for a driver *

1. Overview of NDCX-II Physics Design andComments on final beam-lines for a driver* Alex Friedman Fusion Energy Program, LLNL and Heavy Ion Fusion Science Virtual National Laboratory Workshop on Accelerators for Heavy Ion Inertial Fusion LBNL, May 23-26, 2011 The Heavy Ion Fusion Science Virtual National Laboratory * This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, by LBNL under Contract DE-AC02-05CH11231, and by PPPL under Contract DE-AC02-76CH03073.

2. Overview of NDCX-II Physics Design Beam traversing an acceleration gap

3. The drift compression process is used to shorten an ion bunch Induction cells impart a head-to-tail velocity gradient (“tilt”) to the beam The beam shortens as it “drifts” down the beam line In non-neutral drift compression, the space charge force opposes (“stagnates”) the inward flow, leading to a nearly mono-energetic compressed pulse: vz vz  (in beam frame) z z  • In neutralized drift compression, the space charge force is eliminated, resulting in a shorter pulse but a larger velocity spread: vz vz   z z  

4. Drift compression is used twice in NDCX-II Initial non-neutral pre-bunching for: • better use of induction-core Volt-seconds • early use of 70-ns 250-kV Blumlein power supplies from ATA inject apply tilt drift accelerate apply tilt neutral-ized drift target • Final neutralized drift compression onto the target • Electrons in plasma move so as to cancel the beam’s electric field • Require nplasma > nbeam for this to work well

5. The baseline hardware configuration is as presented during the April 2010 DOE Project Review • 27 lattice periods after the injector • 12 active induction cells • Beam charge ~50 nano-Coulombs • FWHM < 1 ns • Kinetic energy ~ 1.2 MeV

6. 12-cell NDCX-II baseline layout long-pulse voltage sources Li+ ion injector ATA Blumlein voltage sources ATA induction cells with pulsed 2.5 T solenoids NDCX-II final-focus solenoid and target chamber neutralized drift-compression line with plasma sources oil-filled ATA transmission lines

7. 12-cell NDCX-II baseline layout long-pulse voltage sources Li+ ion injector ATA Blumlein voltage sources 12 active cells ATA induction cells with pulsed 2.5 T solenoids NDCX-II final-focus solenoid and target chamber neutralized drift-compression line with plasma sources oil-filled ATA transmission lines

8. 12-cell NDCX-II baseline layout long-pulse voltage sources Li+ ion injector ATA Blumlein voltage sources 9 inactive cells ATA induction cells with pulsed 2.5 T solenoids NDCX-II final-focus solenoid and target chamber neutralized drift-compression line with plasma sources oil-filled ATA transmission lines

9. 12-cell NDCX-II baseline layout long-pulse voltage sources Li+ ion injector ATA Blumlein voltage sources 6 diagnostic cells ATA induction cells with pulsed 2.5 T solenoids NDCX-II final-focus solenoid and target chamber neutralized drift-compression line with plasma sources oil-filled ATA transmission lines

10. Simulations enabled development of the NDCX-II physics design • ASP is a purpose-built, fast 1-D (z) particle-in-cellcode to develop acceleration schedules • 1-D Poisson solver, with radial-geometry correction • realistic variation of acceleration-gap fields with z • several optimization options • Warp is our full-physics beam simulation code • 1, 2, and 3-D ES and EM field solvers • first-principles & approximate models of lattice elements • space-charge-limited and current-limited injection • cut-cell boundaries for internal conductors in ES solver • Adaptive Mesh Refinement (AMR) • large Δt algorithms (implicit electrostatic, large ωcΔt) • emission, ionization, secondaries, Coulomb collisions... • parallel processing A. Friedman, et al., Phys. Plasmas17, 056704 (2010).

11. V (kV) Steps in development of the NDCX-II physics design … 10 100 r (m) 50 0 0 0 1 z (m) first, use Warp steady-flow “gun” mode to design the injector for a nearly laminar flow second, carry out a time-dependent r-z simulation from the source with Warp accel 20 kV extractor 117 kV emitter 130 kV 10 cm 0 1 mA/cm2 Li+ ion source 40g-12

12. perveance neutral Steps in development of the NDCX-II physics design … - maximum - average third, iterate with ASP to find an acceleration schedule that delivers a beam with an acceptable final phase-space distribution beam length beam length (m) center of mass z position (m) center of mass z position (m)

13. 250 kV “flat-top” measured waveform from test stand Steps in development of the NDCX-II physics design … 200 kV “ramp” measured waveform from test stand “shaped” for initial bunch compression (scaled from measured waveforms) “shaped” to equalize beam energy after injection fourth, pass the waveforms back to Warp and verify with time-dependent r-z simulation 40g.002-12

14. Pulse duration vs. z: the finite length of the gap field folds in - time for entire beam to cross a plane at fixed z * time for a single particle at meanenergy to cross finite-length gap + time for entire beam to crossfinite-length gap center of mass z position (m) 40g.002-12

15. Steps in development of the NDCX-II physics design … fifth, adjust transverse focusing to maintain nearly constant radius 3 edge radius (cm) 2 1 0 2 4 6 8 0 center of mass z position (m) 40g.002-12

16. Snapshots from a Warp (r,z) simulation compressing approaching maximum compression Beam appears long because we plot many particles … … but current profile shows that it is short exiting at focus 40g-12

17. 3-D Warp simulation with perfectly aligned solenoids 40ga24-12 simulation and movie from D P Grote

18. Steps in development of the NDCX-II physics design … sixth, test sensitivity to random timing error in acceleration waveforms voltage jitter 2-ns nominal jitter 40g-12 with random timing shifts in acceleration voltage pulses

19. solenoid alignment Steps in development of the NDCX-II physics design … seventh, test sensitivity to random solenoid misalignments 0.5-mm nominal misalignment Beam “steering” via dipole magnets will center beam and minimize “corkscrew” distortion. 40g-12 with random offsets to both ends of each solenoid

20. J/cm2 J/cm2 Warp runs illustrate effects of solenoid alignment errors ASP and Warp runs show that steering can improve intensity and stabilize spot location seeY-J Chen, et al., Nucl. Inst. Meth. in Phys. Res. A 292, 455 (1990) y (mm) y (mm) x (mm) x (mm) plots show beam deposition for three ensembles of solenoid offsets • maximum offset for each case is 0.5 mm • red circles include half of deposited energy • smaller circles indicate hot spots J/cm2 y (mm) x (mm)

21. A “zero-dimensional” Python code (essentially, a spreadsheet)captures the essence of the NDCX-II acceleration schedule • Computes energy jumps of nominal head and tail particles at gaps • Space-charge-induced energy increments between gaps via a “g-factor” model ASP 0-D • The final head and tail energies (keV) are off; the g-factor model does not accurately push the head and tail outward: • But – not bad, for a main loop of 16 lines.        0-D          ASP head      923         1100 tail     1082         1300

22. Things we need to measure, and the diagnostics we’ll use Non-intercepting (in multiple locations): • Accelerating voltages: voltage dividers on cells • Beam transverse position: four-quadrant electrostatic capacitive probes • Beam line charge density: capacitive probes • Beam mean kinetic energy: time-of-flight to capacitive probes Intercepting (in two special “inter-cell” sections): • Beam current: Faraday cup • Beam emittance: two-slit or slit-scintillator scanner • Beam profile: scintillator-based optical imaging • Beam kinetic energy profile: time-of-flight to Faraday cup • Beam energy distribution:electrostatic energy analyzer (Underlined items will be available at commissioning)

23. “Physics risks” concern beam intensity on target, not project completion or risk to the machine due to beam impact • Alignment errors exceeding nominal 0.5 mm • Machine usable with larger errors with intensity degradation • Beam “steering,” using dipoles in diagnostic cells, can mitigate “corkscrew” deformation of beam • Off-center beam, if reproducible, is not a significant issue • Jitter of spark-gap firing times exceeding nominal 2 ns • Slow degradation of performance with jitter expected, per simulations • Similar slow degradation as waveform fidelity decreases • Source emission non-uniform, or with density less than nominal 1 mA/cm2 • Simulations show a usable beam at 0.5 mA/cm2 • Will run in this mode initially, to maximize source lifetime • Space-charge-limited emission mode offers best uniformity • Imperfect neutralization because final-focus solenoid not filled with plasma • Build and use a larger-radius solenoid at modest cost to program

24. NDCX-II, when mature, should be far more capable than NDCX-I * NDCX-II estimates of ideal performance are from (r,z) Warp runs (no misalignments), and assume uniform 1 mA/cm2 ion emission, no timing or voltage jitter in acceleration pulses, no jitter in solenoid excitation, and perfect beam neutralization; they also assume no fine energy correction (e.g., tuning the final tilt waveforms)

25. NDCX-II will be a unique user facility for HIF-relevant physics. Heavy Ion Fusion Science Virtual National Laboratory

26. Comments on final beam-lines for a driver

27. Schematic of final beamlines for ion indirect drive (only representative beamlines are shown) from accelerator axis final focus

28. Schematic of final beamlines for ion direct drive (only representative beamlines are shown) from accelerator axis final focus

29. With a single linac, arcs transport the beams to the two sides of the target (for most target concepts) • In the final section of the driver, the beams are separated so that they may converge onto the target in an appropriate pattern. • They also undergo non-neutral drift-compression, and ultimately “stagnate” to nearly-uniform energy, and pass through the final focusing optic. • In the scenario examined by Dave Judd (1998), the arcs are ~ 600 m long, while the drift distance should be < 240 m. • Thus, the velocity “tilt” must be imposed in the arcs, or upon exit from the arcs. • To maintain a quiescent beam, “ear fields” are needed in the arcs. • For pulse-shaping, the arcs may represent an opportunity to pre-configure the beams before final compression. direct drive or indirect drive

30. If a foot pulse of lower K.E. is needed, those beams are “traditionally” extracted from the linac early and routed via shorter arcs David L. Judd, “A Conceptual Design of Transport Lines for a Heavy-Ion Inertial-Fusion Power Plant” (1998)

31. Delay between foot and main pulses can be inserted in a nearly linear system This concept may be useful … • if two linacs are used, one from each side • with a single linac, for a single-sided target • with a single linac, for a two-sided target (see next slide) main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first z = 0 z1 z2 z3 z4

32. A single linac with common arcs could drive a 2-sided target acceleration drift (with ears, corrections z2 z3 apply tilt rearrange drift-compress main foot z4 z1 z = 0

33. Example: for an indirect-drive target requiring two beam energies Aion = 208.980 amu Accelgradient = 3.0 MV/m Int. Vz = 48.046 m/us, beta = 0.1603 Foot Vz = 52.632 m/us, beta = 0.1756 Main Vz = 60.774 m/us, beta = 0.2027 Int. Ek = 2.5 GeV Foot Ek = 3.0 GeV Main Ek = 4.0 GeV t1foot = 3310.884 ns t1main = 3468.888 ns t2foot = 10435.840 ns t2main = 11273.886 ns t3foot = 19935.780 ns t3main = 20463.353 ns t4foot = 23735.757 ns t4main = 23754.229 ns delay = 18.473 ns main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first z1 = 0.167 km z2 = 0.542 km z3 = 1.042 km z4 = 1.242 km z = 0 z1 z2 z3 z4

34. Example: for an X-target requiring a single beam energy Aion = 84.910 amu Accelgradient = 3.0 MV/m Int. Vz = 165.140 m/us, beta = 0.5509 Foot Vz = 171.883 m/us, beta = 0.5733 Main Vz = 171.883 m/us, beta = 0.5733 Int. Ek = 12.0 GeV Foot Ek = 13.0 GeV Main Ek = 13.0 GeV t1foot = 1978.104 ns t1main = 2018.490 ns t2foot = 2559.895 ns t2main = 2624.038 ns t3foot = 4499.198 ns t3main = 4602.142 ns t4foot = 6244.571 ns t4main = 6347.515 ns delay = 102.944 ns main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first z1 = 0.333 km z2 = 0.433 km z3 = 0.767 km z4 = 1.067 km z = 0 z1 z2 z3 z4

35. The drift compression process is used to shorten an ion bunch • Induction cells impart a head-to-tail velocity gradient (“tilt”) to the beam • The beam shortens as it “drifts” down the beam line • In non-neutral drift compression, the space charge force opposes (“stagnates”) the inward flow, leading to a nearly mono-energetic compressed pulse: vz vz  (in beam frame) z z  • In neutralized drift compression, the space charge force is eliminated, resulting in a shorter pulse but a larger velocity spread: vz vz   z z  

36. Experiments on NDCX-II can explore non-neutral compression, bending, and focusing of beams in driver-like geometry non-neutral drift compression line (magnetic quads & dipoles) In a driver … from accelerator final focus target On NDCX-II, two configurations to test … NDCX-II w/ optional new non-neutral drift new final target programmable match line w/ quadrupoles focus induction cell (and dipoles for bend)

37. HIF-motivated beam experiments on NDCX-II can study … • How well can space charge “stagnate” the compression to produce a “mono-energetic”beam at the final focus? • How well can we pulse-shape a beam during drift compression (vs. the Robust Point Design’s “building blocks”)? • How well can we compress a beam while bending it?: • “achromatic” design, so that particles with all energies exit bend similarly • or, leave some chromatic effect in for radial zooming • emittance growth due to dispersion in the bend • Are there any issues with final focus using a set of quadrupole magnets? Final line-charge profile Initial vz profile J. W-K. Mark, et al., AIP Conf. Proc 152, 227 (1986) Most dimensionless parameters (perveance, “tune depression,” compression ratio, etc.) will be similar to, or more aggressive than, those in a driver.

38. EXTRAS – NDCX-II misc

39. NDCX-II performance for typical cases in 12-21 cell configurations NDCX-II estimates are from (r,z) Warp runs (no misalignments), and assume uniform 1 mA/cm2 emission, high-fidelity acceleration pulses and solenoid excitation, perfect neutralization in the drift line, and an 8-T final-focus solenoid; they also employ no fine energy correction (e.g., tuning the final tilt waveforms)

40. EXTRAS – ASP code

41. 1-D PIC code ASP (“Acceleration Schedule Program”) Follows (z,vz) phase space using a few hundred particles (“slices”) Accumulates line charge density l(z) on a grid via particle-in-cell Space-charge field via Poisson equation with finite-radius correction term Here, α is between 0 (incompressible beam) and ½ (constant radius 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 Optimization loops for waveforms & timings, dipole strengths (steering) Interactive (Python language with Fortran for intensive parts)

42. The field model in ASP yields the correct long-wavelength limit For hard-edged beam of radius rb in pipe of radius rw , 1-D (radial) Poisson eqn gives: The axial electric field within the beam is: For a space-charge-dominated beam in a uniform transport line, l/rb2 ≈ const.; find: For an emittance-dominated beam rb ≈ const.; average over beam cross-section, find: The ASP field equation limits to such a “g-factor” model when the k⊥2 term dominates In NDCX-II we have a space-charge-dominated beam, but we adjust the solenoid strengths to keep rb more nearly constant; In practice we tune α to obtain agreement with Warp results

43. EXTRAS – Warp code

44. The HIF program has developed advanced methods to enable efficient simulation of beam and plasma systems quad beam Adaptive Mesh Refinement R Novel e- mover Z Warp simulates beam injector using “cut cell” boundaries With new electron mover and mesh refinement, run time in an electron cloud problem was reduced from 3 processor-months to 3 processor-days Plasma injection in NDCX e- density (cm-3)

45. The Warp code includes e-cloud & gas models; here, we modeled and tested deliberate e-cloud generation on HCX (a) (b) (c) Simulation Experiment HCX beam line 6-MHz oscillations were seen first in simulations; then they were sought and measured at station (c) in experiments. Q1 Q2 Q3 Q4 WARP-3D T = 4.65s Beam ions hit end plate 200mA K+ Beam electron bunching oscillations 0. -20. -40. I (mA) (c) 0. 2. time (s) 6.

46. Warp: a parallel framework combining features of plasma (Particle-In-Cell) and accelerator codes • Geometry:3D (x,y,z), 2-1/2D (x,y), (x,z) or axisym. (r,z) • Python and Fortran:“steerable,” input decks are programs • Field solvers:Electrostatic - FFT, multigrid; implicit; AMR Electromagnetic - Yee, Cole-Kark.; PML; AMR • Boundaries:“cut-cell” --- no restriction to “Legos” • Applied fields: magnets, electrodes, acceleration gaps, user-set • Bends:“warped” coordinates; no “reference orbit” • Particle movers:Energy- or momentum-conserving; Boris, large time step “drift-Lorentz”, novel relativistic Leapfrog • Surface/volume physics: secondary e- & photo-e- emission, gas emission/tracking/ionization, time-dependent space-charge-limited emission • Parallel:MPI (1, 2 and 3D domain decomposition) R (m) Z (m) Warp 3D EM/PIC on Franklin 32,768 cores

47. Time and length scales span a wide range Time scales: depressed betatron betatron t pb electron drift out of magnet » transit thru fringe fields lattice electron cyclotron in magnet period beam residence pulse log (seconds) -12 -11 -10 -9 -8 -7 -6 -5 -4 Length scales: electron gyroradius in magnet beam radius machine length lD,beam log (meters) -5 -4 -3 -2 -1 0 1 2 3

48. Problem: Electron gyro timescale << other timescales of interest  brute-force integration very slow due to small t Solution*: Interpolation between full-particle dynamics (“Boris mover”) and drift kinetics (motion along B plus drifts) correct gyroradius with New “Drift-Lorentz” mover relaxes the problem of short electron timescales in magnetic field* quad beam large t=5./c Standard Boris mover (fails in this regime) large t=5./c New interpolated mover Magnetic quadrupole Sample electron motion in a quad small t=0.25/c Standard Boris mover (reference case) Test: Magnetized two-stream instability *R. Cohen et. al., Phys. Plasmas, May 2005

49. Electrostatic AMR simulation of ion source with the PIC code Warp: speedup x10 R (m) zoom Z (m) Z (m) Z (m) Refinement of gradients: emitting area, beam edge and front. R (m) 1 . 0 Low res. Medium res. High res. Low res. + AMR 0 . 8 Emittance (mm.mrad) 0 . 6 0 . 4 0 . 2 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 Z ( m )

50. Approach to end-to-end simulation of a fusion system electrostatic / magnetoinductive PIC EM PIC rad. hydro delta-f delta-f, continuum Vlasov, EM PIC “main sequence” tracks beam ions consistently along entire system instabilities, halo, electrons, ... are studied via coupled detailed models