* 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-AC02-76CH The Heavy Ion Fusion Science Virtual National Laboratory 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 Overview of NDCX-II Physics Design and Comments on final beam-lines for a driver *

Slide 2 The Heavy Ion Fusion Science Virtual National Laboratory Overview of NDCX-II Physics Design Beam traversing an acceleration gap

Slide 3 The Heavy Ion Fusion Science Virtual National Laboratory 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: In neutralized drift compression, the space charge force is eliminated, resulting in a shorter pulse but a larger velocity spread: vzvz z   vzvz z vzvz z   vzvz z   (in beam frame)

Slide 4 The Heavy Ion Fusion Science Virtual National Laboratory 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 driftaccelerate 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 n plasma > n beam for this to work well

Slide 5 The Heavy Ion Fusion Science Virtual National Laboratory 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

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

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

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

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

Slide 10 The Heavy Ion Fusion Science Virtual National Laboratory Simulations enabled development of the NDCX-II physics design ASP is a purpose-built, fast 1-D (z) particle-in-cell code 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 ω c Δt) –emission, ionization, secondaries, Coulomb collisions... –parallel processing A. Friedman, et al., Phys. Plasmas 17, (2010).

Slide 11 The Heavy Ion Fusion Science Virtual National Laboratory Steps in development of the NDCX-II physics design … 0 10 cm 40g-12 extractor 117 kV emitter 130 kV accel 20 kV second, carry out a time-dependent r-z simulation from the source with Warp 1 mA/cm 2 Li + ion source z (m) V (kV) r (m) first, use Warp steady-flow “gun” mode to design the injector for a nearly laminar flow

Slide 12 The Heavy Ion Fusion Science Virtual National Laboratory Steps in development of the NDCX-II physics design … perveancebeam length beam length (m) center of mass z position (m) third, iterate with ASP to find an acceleration schedule that delivers a beam with an acceptable final phase-space distribution neutral - maximum - average center of mass z position (m)

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

Slide 14 The Heavy Ion Fusion Science Virtual National Laboratory -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 center of mass z position (m) Pulse duration vs. z: the finite length of the gap field folds in 40g

Slide 15 The Heavy Ion Fusion Science Virtual National Laboratory Steps in development of the NDCX-II physics design … 40g fifth, adjust transverse focusing to maintain nearly constant radius center of mass z position (m) edge radius (cm)

Slide 16 The Heavy Ion Fusion Science Virtual National Laboratory Snapshots from a Warp (r,z) simulation Beam appears long because we plot many particles … … but current profile shows that it is short compressing approaching maximum compression exiting at focus 40g-12

Slide 17 The Heavy Ion Fusion Science Virtual National Laboratory 3-D Warp simulation with perfectly aligned solenoids 40ga24-12 simulation and movie from D P Grote

Slide 18 The Heavy Ion Fusion Science Virtual National Laboratory Steps in development of the NDCX-II physics design … 40g-12 with random timing shifts in acceleration voltage pulses voltage jitter 2-ns nominal jitter sixth, test sensitivity to random timing error in acceleration waveforms

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

Slide 20 The Heavy Ion Fusion Science Virtual National Laboratory Warp runs illustrate effects of solenoid alignment errors 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 x (mm) y (mm) J/cm 2 x (mm) y (mm) J/cm 2 x (mm) y (mm) J/cm 2 ASP and Warp runs show that steering can improve intensity and stabilize spot location see Y-J Chen, et al., Nucl. Inst. Meth. in Phys. Res. A 292, 455 (1990)

Slide 21 The Heavy Ion Fusion Science Virtual National Laboratory 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 0-D ASP head tail 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. ASP0-D

Slide 22 The Heavy Ion Fusion Science Virtual National Laboratory 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)

Slide 23 The Heavy Ion Fusion Science Virtual National Laboratory “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/cm 2 –Simulations show a usable beam at 0.5 mA/cm 2 –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 –

Slide 24 The Heavy Ion Fusion Science Virtual National Laboratory NDCX-II, when mature, should be far more capable than NDCX-I NDCX-I (typical bunched beam) NDCX-II 12-cell (ideal*) Ion speciesK + (A=39)Li + (A=7) Total charge15 nC50 nC Ion kinetic energy0.3 MeV1.25 MeV Focal radius (containing 50% of beam)2 mm0.6 mm Bunch duration (FWHM)2 ns0.6 ns Peak current3 A38 A Peak fluence (time integrated)0.03 J/cm J/cm 2 Fluence within a 0.1 mm diameter spot0.03 J/cm 2 (50 ns window) 5.3 J/cm 2 (0.57 ns window) Fluence within 50% focal radius and FWHM duration (E kinetic x I x t / area) J/cm J/cm 2 *NDCX-II estimates of ideal performance are from (r,z) Warp runs (no misalignments), and assume uniform 1 mA/cm 2 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)

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

Slide 26 The Heavy Ion Fusion Science Virtual National Laboratory Comments on final beam-lines for a driver

Slide 27 The Heavy Ion Fusion Science Virtual National Laboratory Schematic of final beamlines for ion indirect drive final focus (only representative beamlines are shown) axis from accelerator

Slide 28 The Heavy Ion Fusion Science Virtual National Laboratory Schematic of final beamlines for ion direct drive from accelerator final focus (only representative beamlines are shown) axis

Slide 29 The Heavy Ion Fusion Science Virtual National Laboratory 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. or indirect drive direct drive

Slide 30 The Heavy Ion Fusion Science Virtual National Laboratory 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)

Slide 31 The Heavy Ion Fusion Science Virtual National Laboratory 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) accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot z = 0 z 1 z 2 z 3 z 4

Slide 32 The Heavy Ion Fusion Science Virtual National Laboratory z2z2 z3z3 A single linac with common arcs could drive a 2-sided target foot main z1z1 z = 0 acceleration drift (with ears, corrections apply tilt rearrange drift-compress z4z4

Slide 33 The Heavy Ion Fusion Science Virtual National Laboratory Example: for an indirect-drive target requiring two beam energies Aion = amu Accelgradient = 3.0 MV/m Int. Vz = m/us, beta = Foot Vz = m/us, beta = Main Vz = m/us, beta = Int. Ek = 2.5 GeV Foot Ek = 3.0 GeV Main Ek = 4.0 GeV t1foot = ns t1main = ns t2foot = ns t2main = ns t3foot = ns t3main = ns t4foot = ns t4main = ns delay = ns accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot z = 0 z 1 z 2 z 3 z 4 z1 = km z2 = km z3 = km z4 = km

Slide 34 The Heavy Ion Fusion Science Virtual National Laboratory Example: for an X-target requiring a single beam energy Aion = amu Accelgradient = 3.0 MV/m Int. Vz = m/us, beta = Foot Vz = m/us, beta = Main Vz = m/us, beta = Int. Ek = 12.0 GeV Foot Ek = 13.0 GeV Main Ek = 13.0 GeV t1foot = ns t1main = ns t2foot = ns t2main = ns t3foot = ns t3main = ns t4foot = ns t4main = ns delay = ns accel to intermediate boost foot beams drift foot kinetic energy speed at higher speed beams of foot arrive beams first main pulse beams boost main beams target drift at lower speed (delay) to final energy main foot z = 0 z 1 z 2 z 3 z 4 z1 = km z2 = km z3 = km z4 = km

Slide 35 The Heavy Ion Fusion Science Virtual National Laboratory 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: In neutralized drift compression, the space charge force is eliminated, resulting in a shorter pulse but a larger velocity spread: vzvz z   vzvz z vzvz z   vzvz z   (in beam frame)

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

Slide 37 The Heavy Ion Fusion Science Virtual National Laboratory 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? Most dimensionless parameters (perveance, “tune depression,” compression ratio, etc.) will be similar to, or more aggressive than, those in a driver. Initial v z profile Final line-charge profile J. W-K. Mark, et al., AIP Conf. Proc 152, 227 (1986)

Slide 38 The Heavy Ion Fusion Science Virtual National Laboratory EXTRAS – NDCX-II misc

NDCX-II performance for typical cases in cell configurations NDCX-I (bunched beam) NDCX-II 12-cell15-cell18-cell21-cell Ion speciesK + (A=39)Li + (A=7) Charge15 nC 50 nC total 25 2xFWHM 50 nC total 25 2xFWHM 50 nC total 25 2xFWHM 50 nC total 30 2xFWHM Ion kinetic energy0.3 MeV1.2 MeV1.7 MeV2.4 MeV3.1 MeV Focal radius (50% of beam) 2 mm0.6 mm 0.7 mm Duration (bi-parabolic measure = √2 FWHM) 2.8 ns0.9 ns0.4 ns0.3 ns0.4 ns Peak current3 A36 A73 A93 A86 A Peak fluence (time integrated) 0.03 J/cm 2 13 J/cm 2 19 J/cm 2 14 J/cm 2 22 J/cm 2 Fluence w/in 0.1 mm diameter, w/in duration 8 J/cm 2 11 J/cm 2 10 J/cm 2 17 J/cm 2 Max. central pressure in Al target 0.07 Mbar0.18 Mbar0.17 Mbar0.23 Mbar Max. central pressure in Au target 0.18 Mbar0.48 Mbar 0.64 Mbar NDCX-II estimates are from (r,z) Warp runs (no misalignments), and assume uniform 1 mA/cm 2 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)

Slide 40 The Heavy Ion Fusion Science Virtual National Laboratory EXTRAS – ASP code

Slide 41 The Heavy Ion Fusion Science Virtual National Laboratory 1-D PIC code ASP (“Acceleration Schedule Program”) Follows (z,v z ) phase space using a few hundred particles (“slices”) Accumulates line charge density (z) on a grid via particle-in-cell Space-charge field via Poisson equation with finite-radius correction term Here,  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)

Slide 42 The Heavy Ion Fusion Science Virtual National Laboratory The field model in ASP yields the correct long-wavelength limit For hard-edged beam of radius r b in pipe of radius r w, 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, / r b 2 ≈ const.; find: For an emittance-dominated beam r b ≈ 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 r b more nearly constant; In practice we tune  to obtain agreement with Warp results

Slide 43 The Heavy Ion Fusion Science Virtual National Laboratory EXTRAS – Warp code

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

Slide 45 The Heavy Ion Fusion Science Virtual National Laboratory 6-MHz oscillations were seen first in simulations; then they were sought and measured at station (c) in experiments. The Warp code includes e-cloud & gas models; here, we modeled and tested deliberate e-cloud generation on HCX WARP-3D T = 4.65  s Beam ions hit end plate (a)(b)(c) HCX beam line Q4Q3Q2Q1 200mA K + Beam electron bunching oscillations (c) time (  s) 6. Simulation Experiment I (mA)

Slide 46 The Heavy Ion Fusion Science Virtual National Laboratory 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) Warp 3D EM/PIC on Franklin 32,768 cores Z (m) R (m)

Slide 47 The Heavy Ion Fusion Science Virtual National Laboratory Time and length scales span a wide range Length scales: electron cyclotron in magnet pulse electron drift out of magnet beam residence  pb  lattice period betatron depressed betatron transit thru fringe fields log (seconds) machine length Time scales: log (meters) electron gyroradius in magnet D,beam beam radius

large  t=5./  c Standard Boris mover (fails in this regime) 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* Magnetic quadrupole Sample electron motion in a quad beam quad * R. Cohen et. al., Phys. Plasmas, May 2005 small  t=0.25/  c Standard Boris mover (reference case) large  t=5./  c New interpolated mover Test: Magnetized two-stream instability

Slide 49 The Heavy Ion Fusion Science Virtual National Laboratory Electrostatic AMR simulation of ion source with the PIC code Warp: speedup x10 RunGrid sizeNb particles Low res.56x640~1M Medium res.112x1280~4M High res.224x2560~16M Low res. + AMR56x640~1M R (m) Z (m) Refinement of gradients: emitting area, beam edge and front. Z (m) R (m) zoom Low res. Medium res. High res. Low res. + AMR Emittance (mm.mrad) Z(m)

Slide 50 The Heavy Ion Fusion Science Virtual National Laboratory delta-f, continuum Vlasov, EM PIC electrostatic / magnetoinductive PICEM PICrad. hydro delta-f “main sequence” tracks beam ions consistently along entire system instabilities, halo, electrons,... are studied via coupled detailed models Approach to end-to-end simulation of a fusion system

Slide 51 The Heavy Ion Fusion Science Virtual National Laboratory 51 Warp Warp is a state-of-the-art 3-D parallel multi-physics code and framework –modeling of beams in accelerators, plasmas, laser-plasma systems, non-neutral plasma traps, sources, etc. –unique features: ES/EM solvers, cut-cells, AMR, particles pushers, python interface, etc. Contribution to projects –HIFS-VNL (LBNL,LLNL,PPPL): work-horse code; design and support expts. –VENUS ion source (LBNL): modeling of beam transport –LOASIS (LBNL ): modeling of LWFA in a boosted frame –FEL/CSR (LBNL) : modeling of free e- lasers & coherent synch. radiation in boosted frame –Anti H- trap (LBNL/U. Berkeley): simulation of model of anti H- trap –U. Maryland: modeling of UMER sources and beam transport; teaching –Ferroelectric plasma source (Technion, U. Maryland): modeling of source –Fast ignition (LLNL): modeling physics of filamentation –E-cloud for HEP (LHC, SPS, ILC, Cesr-TA, FNAL-MI): see slide on Warp-Posinst –Laser Isotope Separation (LLNL): now defunct –PLIA (CU Hong Kong): modeling of beam transport in pulsed line ion accelerator –Laser driven ions source (TU Darmstadt): modeling of source Benchmarking –Heavily benchmarked against various experiments: MBE4, ESQ ion source, HCX, multibeamlet ion source, UMER, NDCXI, etc.; codes: IGUN, LSP; theory: beam transport and plasma analytic theory

Slide 52 The Heavy Ion Fusion Science Virtual National Laboratory Slides from October 2003 w/ UMER group

Slide 53 The Heavy Ion Fusion Science Virtual National Laboratory The high energy part of a driver consists mostly of accelerating modules (“gaps”)

Slide 54 The Heavy Ion Fusion Science Virtual National Laboratory Multiple beams in driver introduce significant new physics Transverse deflections arise from self-fields in accelerating gaps –Can shield transverse electric field via plates-with-holes –But plates allow cavity modes to develop; use wires (?) –Magnetic forces may be comparable for large N beams Longitudinal waves obey v wave = 1/2 g 1/2  p ( a 0 b 0 ) 1/2 ; g = 1/(4  0 )log(r w 2 /a 0 b 0 ) They can be driven unstable by module impedance (“resistive wall”) –Convective growth, head-to-tail –Inductive field in multi-beam system slows space-charge waves on beams near center of cluster (destabilizing) –But spread in wave speed among beams is probably stabilizing –Also stabilize by capacitance, feedforward –May have to avoid g < 0 on any beam observing station time in beam frame

Slide 55 The Heavy Ion Fusion Science Virtual National Laboratory Considerations for a scaled multi-beam experiment using electrons Goal would be to explore transverse deflections & wave propagation in a regime where magnetic and inductive effects are significant UMER is 10 kV (  = 0.2), 100 mA, a ~ 0.5 cm, 32 cm LP, 40 ns = 2.4 m, 36 LP’s total; could go up to  = 0.4 w/ upgrade Magnetic forces are down from electric forces by  2 but are not shielded by plates-with-holes; so are comparable when N  2 ~ 1 This implies need for ~12 to 25 UMER beams Waves propagate ~ 1 beam diameter / period; could shorten beam, so to propagate ~ 1 m would require ~ 3x UMER length Vacuum of needed to avoid poisoning K  challenging pumping Resolving 10 cm wavelength (~ tip?) implies that diagnostics need ~ 2ns time resolution Crude cost estimate; if UMER was ~ $3M, then cost might be: $3M x (15 beams) x (multibeam savings 1/3) x (length factor 3)  $45M with very large error bars

Slide 56 The Heavy Ion Fusion Science Virtual National Laboratory Further considerations Emittance –Transverse emittance (tune depression) is OK; beams resemble UMER –In a driver, longitudinal thermal pressure is << space charge force. In a scaled electron experiment, T || may be too high (what is it in UMER?); but this may not matter much, since the interesting inductive E z is of opposite sign to the electrostatic and pressure terms Small total current ~1-2 A would not offer beam loading of accel modules; and module impedance effect is unlikely to be “driver-like” –May be able to use smart electronics to simulate these effects –Could scale the beams to somewhat larger a and for higher current; but the aspect ratio would become too “fat” well before the kA range There are also possible “tech” experiments –A “real” driver-scale induction module, for measuring impedances –It might be “tickled” and/or “loaded” by pulsed electron beams (with head, noise); a wire won't work because it shorts the cavity –The gap could have removable plates-with-holes (or “chicken-wire-with- holes” or “wires-parallel-to-x-axis,” to minimize “rf cavities”)