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
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
3
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
4
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:
5
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)
6
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)
7
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
8
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
9
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)
10
Adaptive Mesh Refinement requires automatic generation of nested meshes with “guard” regions
Simulation of diode using merged Adaptive Mesh Refinement & PIC
11
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
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
13
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
14
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
“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
16
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
17
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
19
University of Maryland Electron Ring will study long-path transport physics
UMER
Q1 Q3 Q4The rings are due to edge lensing
Experiment
WARP
20
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
21
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
22
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
23
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
24
• 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
25
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
26
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
27
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)
28
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
29
GunAccel.column
Solenoidtransport
WARP simulation of a novel high line charge density injector based on the accel-decel / load-and-fire principle
30
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.
31
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
• 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)
33
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
34
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
35
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 …
