alex friedman hif-vnl, lnll presented at aps-dpp meeting savannah, ga, november 17, 2004
DESCRIPTION
Simulation of space-charge-dominated particle beams *. Alex Friedman HIF-VNL, LNLL Presented at APS-DPP Meeting Savannah, GA, November 17, 2004 Paper HP1.026. Heavy Ion Fusion Virtual National Laboratory. - PowerPoint PPT PresentationTRANSCRIPT
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Alex FriedmanHIF-VNL, LNLL
Presented at APS-DPP MeetingSavannah, GA, November 17,
2004Paper HP1.026
Simulation of space-charge-dominated particle beams*
Heavy Ion Fusion Virtual National Laboratory
*Work performed for U.S. D.O.E. by U.C. LLNL under contract W7405-ENG-48 and by U.C. LBNL under contract DE-AC03-76F00098
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Key question in Heavy Ion Fusion beam science:How do intense ion beams behave as they are accelerated and compressed into a small volume in space and time?Simulation plays a major role in developing the answers
Outline:I. IntroductionII. Present-day experimentsIII. Fundamental beam scienceIV. Future experiments & discussion
… and along the way …New computational methods and models with broad
applicability
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They are collisionless and have “long memories” — must follow ion distribution from source to target
Beam modeling program is~ 2/3 simulation, ~ 1/3 analytic theory;here we discuss the former
“Multiscale, multispecies, multiphysics” - ions encounter:– Good electrons: neutralization by plasma aids
compression, focusing– Bad electrons: stray “electron cloud” and gas can afflict
beam
Beams are non-neutral plasmas with dynamics dominated by long-range space-charge forces
target
beam ions background ions electrons
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Time & length scales in driver & chamber span a wide range
-11-12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
electroncyclotronin magnet pulse
electron driftout of magnet
beamresidence
pb
latticeperiod
betatrondepressedbetatron
pe
transitthru
fringefields
beamresidence
pulse log of timescale (s)
In driver
In chamberpi
pb
Length scales: • electron gyroradius in magnet ~ 10 m• D,beam ~ mm• beam radius ~ cm• lattice period ~ m• beam length ~ 1-10 m• machine length ~ km
Time scales:
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Beam starts with a small 6D phase space volume; applications demand that it grow only modestly• Present-day (e.g., “HCX”) beams, roughly:
– Total ions N ~ 5 x 1012 (K+) in ~ 5 s (0.2 Amperes)– line charge density ~ 0.1 C/m– number density n ~ 1015 m-3
– kinetic energy Ek ~ 1 MeV (v/c ~ 0.005)– temperature Teff ~ 0.2 eV at 5-cm source,
~ 20 eV in transport section– beam radius r ~ 1 cm
• T and r translate to initial transverse phase space area (“normalized emittance”) ~ 0.5 -mm-mr
• Example: at the downstream end of a 2-GeV system: increases ~ 5x in accelerator, then 20x in final
compression– Have “headroom” for phase space area to grow by
~ factor of 10 (less is always better)
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Particle-in-Cell (PIC) is main tool; challenges are addressed by new computational capabilities
• resolution challenges (Adaptive Mesh Refinement-PIC)
• dense plasmas (implicit, hybrid PIC+fluid)• short electron timescales (large-t advance)• electron-cloud & gas interactions (new
“roadmap”)• slowly growing instabilities (f for beams) • beam halo (advanced Vlasov)
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ES / Darwin PIC and moment models EM PIC rad -hydroWARP: 3d, xy, rz, Hermes LSP
EM PIC, f, VasovLSP BEST WARP-SLV
Track beam ions consistently along entire systemStudy instabilities, halo, electrons, ..., via coupled detailed models
HIF-VNL’s approach to self-consistent beam simulation (HEDP & IFE) employs multiple tools
Ion source& injector Accelerator Buncher Final
focusChambertransport Target
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Injector physics
Research on high-brightness sources & injectors uses “test stands”
STS-500 at LLNL
II. Simulations and theory support present-day ion beam experiments
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0.0 0.1 0.2 0.3 0.40.2
0.4
high resolution low resolution + AMR
N (
-mm
.mra
d)
Z (m)
Fine grid patch around source & tracking beam edge
Application to HCX triode in axisymmetric (r,z) geometry
This example:~ 4x savings in computational cost
(in other cases, far greater savings)
WARP simulations of HCX triode illustrate the integration of particle-in-cell (PIC) & adaptive mesh refinement (AMR) methods
(Simulations by J-L. Vay)
r
z (m)
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Adaptive Mesh Refinement requires automatic generation of nested meshes with “guard” regions
Simulation of diode using merged Adaptive Mesh Refinement & PIC
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Rise time
Current (mA) at Faraday cup
ExperimentTheory
Result depends critically on mesh refinement
Phase space at end of diode
Warp simulation Experimental data
(Simulations by I. Haber, J-L. Vay, D. P. Grote)
x (mm)-50 0 50x (mm)
-50 0 50-10
10
x
6
4
2
0
time (s)0 2 4
WARP simulations of STS-500 experiments clarify our understanding of short-rise-time beam generation
5-cm-radius K+ alumino-silicate
source
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J. Kwan poster Monday PM described this work
Einzel lens plates
Free drift
Novel compact injector, based on merging of many bright beamlets, is being studied
0. 1.5-7.5
7.5
0.5 1.0Z (m)
X (mm)
• Now: high-gradient experiment with parallel beamlets
• Soon: “curved-plate” exp’t: 119 beamlets, 0.07 A total, 400 keV
x (m)
y (m)
Simulation Experiment
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ESQ injector
Marx
matching
10 ES quads
diagnostics
diagnostics
ESQ injector
10 Electrostatic quads
diagnostics
4 Magnetic quads
K+ Beam~ 0.2 - 0.5 A1 - 1.7 MeV~ 5 s
The High Current Experiment enables studies of beam dynamics and stray-electron physics
HCX
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Time-dependent 3D simulations of HCX electrostatic quadrupole injector reveal beam-head behavior
From a WARP movie by J-L. Vay; see http://hif.lbl.gov/theory/simulation_movies.html
Much recent HCX work has focused on electron-cloud; see below
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“Optical slit” diagnostic is yielding unprecedented information about the HCX beam particle distribution
Isosurface upon which ƒ(x,y,x) = 0.3 ƒmax
face-on (xy) view rotated to right
shadow of “bridge” across slit
• This scanner measures f(x,y,x)• Another such scanner at right
angles measures f(x,y,y)• Using both, suitably remapped to
a common longitudinal plane, one can tomographically “synthesize” an approximation to the 4-D f(x,y,x,y)
• Ref: A. Friedman et al., PAC 2003:
http://accelconf.web.cern.ch/accelconf/p03/PAPERS/TOPB006.PDF xu
vyScintillatorSlit
C. M. Celata poster CP1.119 (Monday afternoon) showed use of such a “synthesized” 4-D f as initial conditions for PIC simulations
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4 magneticquadrupoles
MEVVA source (plasma plug)
RF source(volumetric)
Scintillating glass diagnostic
The Neutralized Transport Experiment (NTX) enables studies of beam neutralization and focusing
Non-neutralized
Plasma plug +volume plasma
FWHM = 6.6 mm
FWHM = 1.5 mm
NTX
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265keV
283keV
Vertical
Horizontal
Vertical
5mm diameter aperture, 265keV vertical profile
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
-30 -20 -10 0 10 20 30mm
slit-integrated intensity
Experimental Optical 040206021
Theoretical
5mm diameter aperture, 283keV vertical profile
0
5000
10000
15000
20000
25000
30000
35000
-30 -20 -10 0 10 20 30mm
Slit-integrated intensity
Experimental Optical 040206022
Theoretical
1.5 mA beam
Horizontal densityprofile
5mm diameter aperture, 283keV horizontal profile
0
5000
10000
15000
20000
25000
30000
35000
-30 -20 -10 0 10 20 30mm
Slit-integrated intensity
Experimental Optical 040206022
Theoretical
5mm diameter aperture, 265keV horizontal profile
0
10000
20000
30000
40000
50000
60000
-30 -20 -10 0 10 20 30 40mm
Slit-integrated intensity
Experimental Optical 040206021
Theoretical
Slit-
inte
grat
ed in
tens
itySl
it-in
tegr
ated
inte
nsity
After 4 magnetic focusing quads, data & WARP-generated density profiles agree well, except for halo (which originated upstream)
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0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5
FLUENCE (a.u.)
R(mm)
LSP simulations of NTX agree with data at focal plane for different neutralization methods (within error bars)
(radius containing half the current)
With plasma plugand RF Plasma
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5
FLUENCE (a.u.)
R(mm)
MEASUREMENTSIMULATION
1.1 1.4 mm
Linearcolor scale
With plasma plug
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5
FLUENCE (a.u.)
R(mm)
MEASUREMENTSIMULATION
1.3 1.7 mm
7 mm
“No space charge”
MEASUREMENTSIMULATION
0.8
1.0 mm
DATA
LSP
Carsten Thoma, et al.
•EM, 3D cylindrical geom., 8 azimuthal spokes
•3 eV plug 3x109 cm-3, volume plasma 1010 cm-3
•6 mA, 10 mm initial radius
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University of Maryland Electron Ring will study long-path transport physics
UMER
Q1 Q3 Q4The rings are due to edge lensing
Experiment
WARP
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Electrons cantrap into beam space-charge and quadrupolemagnetic fields
Electron lifetime ~ time to drift out the end of a magnetic quadrupole
Gas, electron source diagnostic for number and energy of electrons and gas molecules produced per incident ion
BeamTiltabl
e target
electron cloud
beam
Experiments and simulations explore sources, sinks, and dynamics of stray electrons
A. Molvik’s poster Tues. AM
III. Fundamental beam science studies: “afflictions and avoidance thereof”
R. Cohen inv. talk Wed. AM & poster Wed. PM
quad
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We are following a road map toward self-consistent e-cloud and gas modeling in WARP
WARP ion PIC, I/O, field solve
fbeam, , geom.
electron dynamics(full orbit; drift)
wall electron source
volumetric (ionization)
electron source
gas module
penetration from walls ambient
charge exch.ioniz.
nb, vb
fb,wall
fb,wall
sinks
ne
ions
Reflectedions
fb,wall
Key: operational; implemented and undergoing testing; partially implemented; active offline development
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Self-consistent WARP3d simulations of electrons and ions in 4th HCX magnet help validate large-t electron mover
small t new mover, t 10x larger Boris/Parker-Birdsall
ions
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Nonlinear f simulations reveal properties of electrostatic anisotropy-driven mode
• When T > T, free energy is available for a Harris-like instability• Earlier work (1990 …) used WARP• Simulations using BEST f model (above) show that the mode
saturates quasilinearly before equipartitioning; final v v / 3 • BEST was also applied to Weibel; that mode appears
unimportant for energy isotropization• BEST, LSP, and WARP are being applied to 2-stream
Instabilities
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• 4D Vlasov testbed (with constant focusing) showed halo structure down to extremely low densities
Solution of Vlasov equation on a grid in phase space offers low noise, large dynamic range
x
px 10-5
10-4
10-3
10-2
10-1
1
Evolved state of density-mismatched axisymmetric thermal beam with tune depression 0.5, showing halo
Halo
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New ideas include moving grid in phase space to model quadrupoles, adaptive mesh to resolve fine structures
moving phase-space grid, based on non-splitsemi-Lagrangian advance
adaptive meshin phase space
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HI-driven IFE will require matter in the “High Energy Density Physics” (HEDP) regime; ion-driven strongly-coupled 1-eV plasmas (“Warm Dense Matter”) will come first
• HEDP regime is 1011 J/m3 (NRC)• Must produce the beam, compress it longitudinally, focus it• Approach for “Neutralized Drift Compression Experiments”:
- “Accel-decel” or other short-pulse injector- Neutralization to allow drift compression in short distance
- Final focusing system with large chromatic acceptance
NDCX
J. Barnard poster Monday afternoon covered this in detail
IV. Simulations enable exploration of future
experiments
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Strategy: maximize uniformity and efficient use of beam energy by placing center of foil at Bragg peak
In simplest example, beam impinges on a foil of solid or “foam” metal
Enter foilExit foil
dE/dX T
log-log plot fractionalenergy loss can be highand uniformity also highif operating at Bragg peak(Larry Grisham, PPPL)
Ion beam
€
−1Z 2dEdX
Energyloss rate
Energy/Ion mass
(MeV/mg cm2)
(MeV/amu)(dE/dX figure from L.C Northcliffeand R.F.Schilling, Nuclear Data Tables,A7, 233 (1970))
Example beam: He+, 10 A, 2 MeV, rspot = 1 mm, p 1 ns(pulse duration hydrodynamic
disassembly time)
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NDCX-1 has 3 stages over next ~2 years; will study neutralized compression by factors of 10-100
1a - Neut. Drift Compr.; starting ~ now1b - solenoid transport; start June 051c - accel-decel / load & fire; start Oct. 05
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GunAccel.column
Solenoidtransport
WARP simulation of a novel high line charge density injector based on the accel-decel / load-and-fire principle
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As simulated:• Axial compression 120
X• Radial compression to
1/e focal spot radius < 1 mm
• Beam intensity on target increases by 50,000 X.
R(cm
)
3.9T solenoid
Z(cm)
LSP simulations of neutralized drift and focusing show possibility of strong compression in NDCX-1
(simulations by Welch, Rose, Henestroza, Yu)
Ramped 220-390 keV, K+, 24 mA ion beam injected into a 1.4-m long plasma column with density 10 x beam density.
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vb = c/2; lb = 7.5 c/p;c=5p; rb = 1.5 c/p; nb = np/2
2D EM PIC code in XY slab geometry, comoving frame, beam & plasma ions fixed
Analytic theory & simulation by Igor Kaganovich
ne/npelectron density
contours
y (c/p)
x (c
/p)
electron flow past beam
EDPIC simulation of ion pulse neutralization: waves induced in plasma are modified by a uniform axial magnetic field
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• Traveling Wave Accelerator is based on slow-wave structure (helix)
• Beam “surfs” on traveling pulse of Ez (moving at ~ 0.01 c in first stage)
• One possible configuration:
NDCX experiments may employ a novel accelerating method based on broadband Traveling Wave Accelerator
Accel-decel injector with “load-and-fire” column
Broadband Traveling Wave Accelerator
Energy ramping
Neutralized Drift Compression
CL
Vs(t) from Pulse Forming Network
ion pulse
Insulator column 3-D FDTD calculations of EM pulse propagation are underway (S. Nelson)
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Knowledge gained on NDCX-1 and on bench tests of slow-wave structures opens up new NDCX-2 opportunity•Adds helical line to NDCX-1 (still uses K+)•20 MeV < Bragg peak (~ 50 MeV), but deposition only down ~10-15%
•~ 8 meters long, < $2M for full 5 T solenoid system•Rbeam = 2 cm, ahelix = 4 cm, bwall = 10 cm•+/- 450 kV drive (not all usable for beam)•Beam 15-20 cm •Voltage ramps over 30 cm acceleration at 3 MV/m
•3 helix segments, each w/ tapered line tracking ~2x gain in velocity
•Longitudinal blow-up controlled by “tilt” and “inertia” (rapid accel)
•Target heating to ~ 1eV if focus to rspot < ~ 1 mm
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Program needs drive us toward “multiscale, multispecies, multiphysics” modeling
• e-Cloud and Gas:– merging capabilities of WARP and POSINST; adding new
models– new method for bridging disparate e & i timescales
• Plasma interactions:– LSP already implicit, hybrid, with collisions, ionization,
… now with improved one-pass implicit EM solver– Darwin model development (W. Lee et. al.;
Sonnendrucker)
• New HEDP mission changes path to IFE; models must evolve too– Non-stagnating pulse compression– Plasmas early and often– Modular approach a natural complement
• Injectors– Merging beamlet approach is “multiscale”– Plasma-based sources (FAR-Tech SBIR)
Discussion
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While simulations for Heavy Ion Fusion are at the forefront in terms of the relative strength of the space charge forces, a wide range of beam applications are pushing for higher intensity, and will benefit from this workMFE applications may also benefit from AMR-PIC, Vlasov, e-mover, …
This talk drew on material from quite a few people - thanks to all!
Closing thoughts …