* 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.
The Heavy Ion Fusion Science Virtual National Laboratory
Alex FriedmanFusion Energy Program, LLNL
andHeavy 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 2The Heavy Ion Fusion Science
Virtual National Laboratory
Overview of NDCX-II Physics Design
Beam traversing an acceleration gap
Slide 3The 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:
vz
z
vz
z
vz
z
vz
z
(in beam frame)
Slide 4The 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
injectapply
tiltdrift 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
Slide 5The 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 6The 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 7The 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 8The 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 9The 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 10The 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-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. Plasmas 17, 056704 (2010).
Slide 11The Heavy Ion Fusion Science
Virtual National Laboratory
Steps in development of the NDCX-II physics design …
0
10 cm
40g-12
extractor117 kV
emitter130 kV
accel20 kV
second, carry out a time-dependent r-z simulation from the source with Warp
1 mA/cm2 Li+ ion source
z (m)
V (kV)
50
100
00 1
10
0
r (m
)
first, use Warp steady-flow “gun” mode to design the injector for a nearly laminar flow
Slide 12The Heavy Ion Fusion Science
Virtual National Laboratory
Steps in development of the NDCX-II physics design …
perveance beam 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 13The Heavy Ion Fusion Science
Virtual National Laboratory
Steps in development of the NDCX-II physics design …
200 kV “ramp” measured waveformfrom test stand
“shaped” to equalize beam energy after injection
“shaped” for initial bunch compression (scaled from measured waveforms)
250 kV “flat-top” measured waveformfrom test stand
40g.002-12
fourth, pass the waveforms back to Warp and verify with time-dependent r-z simulation
Slide 14The 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.002-12
Slide 15The Heavy Ion Fusion Science
Virtual National Laboratory
Steps in development of the NDCX-II physics design …
40g.002-12
fifth, adjust transverse focusing to maintain nearly constant radius
center of mass z position (m)
edge
radi
us (c
m)
3
2
1
00 2 4 6 8
Slide 16The 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 17The 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 18The 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-nsnominal
jitter
sixth, test sensitivity to random timing error in acceleration waveforms
Slide 19The 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-mmnominal
misalignment
seventh, test sensitivity to random solenoid misalignments
Beam “steering” via dipole magnets will center beam and minimize “corkscrew” distortion.
Slide 20The 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 (m
m)
J/cm2
x (mm)
y (m
m)
J/cm2
x (mm)
y (m
m)
J/cm2
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 21The 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 923 1100
tail 1082 1300
• 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.
ASP 0-D
Slide 22The 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 23The 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/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
–
Slide 24The 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 species K+ (A=39) Li+ (A=7)
Total charge 15 nC 50 nC
Ion kinetic energy 0.3 MeV 1.25 MeV
Focal radius (containing 50% of beam) 2 mm 0.6 mm
Bunch duration (FWHM) 2 ns 0.6 ns
Peak current 3 A 38 A
Peak fluence (time integrated) 0.03 J/cm2 8.6 J/cm2
Fluence within a 0.1 mm diameter spot 0.03 J/cm2 (50 ns window)
5.3 J/cm2 (0.57 ns window)
Fluence within 50% focal radius and
FWHM duration (Ekinetic x I x t / area)
0.014 J/cm2 1.0 J/cm2
* 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)
Slide 25The Heavy Ion Fusion Science
Virtual National LaboratoryHeavy Ion Fusion Science Virtual National Laboratory
NDCX-II will be a unique user facility for HIF-relevant physics.
Slide 26The Heavy Ion Fusion Science
Virtual National Laboratory
Comments on final beam-lines
for a driver
Slide 27The Heavy Ion Fusion Science
Virtual National Laboratory
Schematic of final beamlines for ion indirect drive
finalfocus
(only representative beamlines are shown)
axis
fromaccelerator
Slide 28The Heavy Ion Fusion Science
Virtual National Laboratory
Schematic of final beamlines for ion direct drive
fromaccelerator
finalfocus
(only representative beamlines are shown)
axis
Slide 29The 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
indirectdrive
directdrive
Slide 30The 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 31The 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 footkinetic energy speed at higher speed beams of foot arrive beams first
main pulse beams boost main beams targetdrift at lower speed (delay) to final energy
main
foot
z = 0 z1 z2 z3 z4
Slide 32The Heavy Ion Fusion Science
Virtual National Laboratory
z2
z3
A single linac with common arcs could drive a 2-sided target
footmain
z1z = 0
acceleration
drift (with ears, corrections
apply tiltrearrangedrift-compress
z4
Slide 33The Heavy Ion Fusion Science
Virtual National Laboratory
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
accel to intermediate boost foot beams drift footkinetic energy speed at higher speed beams of foot arrive beams first
main pulse beams boost main beams targetdrift at lower speed (delay) to final energy
main
foot
z = 0 z1 z2 z3 z4
z1 = 0.167 km
z2 = 0.542 km
z3 = 1.042 km
z4 = 1.242 km
Slide 34The Heavy Ion Fusion Science
Virtual National Laboratory
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
accel to intermediate boost foot beams drift footkinetic energy speed at higher speed beams of foot arrive beams first
main pulse beams boost main beams targetdrift at lower speed (delay) to final energy
main
foot
z = 0 z1 z2 z3 z4
z1 = 0.333 km
z2 = 0.433 km
z3 = 0.767 km
z4 = 1.067 km
Slide 35The 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:
vz
z
vz
z
vz
z
vz
z
(in beam frame)
Slide 36The 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)
fromaccelerator
finalfocus
target
non-neutral drift compression line(magnetic quads & dipoles)In a driver …
On NDCX-II, two configurations to test …
Slide 37The 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 vz profile Final line-charge profile
J. W-K. Mark, et al., AIP Conf. Proc 152, 227 (1986)
Slide 38The Heavy Ion Fusion Science
Virtual National Laboratory
EXTRAS – NDCX-II misc
NDCX-II performance for typical cases in 12-21 cell configurations
NDCX-I(bunched
beam)
NDCX-II
12-cell 15-cell 18-cell 21-cell
Ion species K+ (A=39) Li+ (A=7) Li+ (A=7) Li+ (A=7) Li+ (A=7)
Charge 15 nC 50 nC total25 2xFWHM
50 nC total25 2xFWHM
50 nC total25 2xFWHM
50 nC total30 2xFWHM
Ion kinetic energy 0.3 MeV 1.2 MeV 1.7 MeV 2.4 MeV 3.1 MeV
Focal radius (50% of beam) 2 mm 0.6 mm 0.6 mm 0.6 mm 0.7 mm
Duration (bi-parabolic measure = √2 FWHM) 2.8 ns 0.9 ns 0.4 ns 0.3 ns 0.4 ns
Peak current 3 A 36 A 73 A 93 A 86 A
Peak fluence (time integrated) 0.03 J/cm2 13 J/cm2 19 J/cm2 14 J/cm2 22 J/cm2
Fluence w/in 0.1 mm diameter, w/in duration 8 J/cm2 11 J/cm2 10 J/cm2 17 J/cm2
Max. central pressure in Al target 0.07 Mbar 0.18 Mbar 0.17 Mbar 0.23 Mbar
Max. central pressure in Au target 0.18 Mbar 0.48 Mbar 0.48 Mbar 0.64 Mbar
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)
Slide 40The Heavy Ion Fusion Science
Virtual National Laboratory
EXTRAS – ASP code
Slide 41The Heavy Ion Fusion Science
Virtual National Laboratory
1-D PIC code ASP (“Acceleration Schedule Program”)
• Follows (z,vz) 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, 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)
Slide 42The Heavy Ion Fusion Science
Virtual National Laboratory
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, /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
Slide 43The 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 45The 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.
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-3DT = 4.65s
Beam ions hit end plate
(a) (b) (c)
HCX beam line
Q4Q3Q2Q1
200mA K+ Beam
electronbunching oscillations
(c)
0. 2. time (s) 6.
Simulation Experiment0.
-20.
-40.
I (m
A)
Slide 46The 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 47The Heavy Ion Fusion Science
Virtual National Laboratory
Time and length scales span a wide range
Length scales:
-11-12 -10 -9 -8 -7 -6 -5 -4
electron cyclotron in magnet
pulse
electron drift out of magnet
beam residence
pb
latticeperiod
betatrondepressed betatron
transit thru
fringe fields
log (seconds)
machine length
Time scales:
-5 -4 -3 -2 -1 0 1 2 3
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 49The Heavy Ion Fusion Science
Virtual National Laboratory
Electrostatic AMR simulation of ion source with the PIC code Warp: speedup x10
Run Grid size Nb particles
Low res. 56x640 ~1M
Medium res. 112x1280 ~4M
High res. 224x2560 ~16M
Low res. + AMR 56x640 ~1M
R (
m)
Z (m) Z (m)Refinement of gradients: emitting area,
beam edge and front.
Z (m)
R (
m)
zoom
0.0 0.1 0.2 0.3 0.40.2
0.4
0.6
0.8
1.0 Low res. Medium res. High res. Low res. + AMR
Em
itta
nce
(mm
.mra
d)
Z(m)
Slide 50The Heavy Ion Fusion Science
Virtual National Laboratory
delta-f, continuum Vlasov, EM PIC
electrostatic / magnetoinductive PIC EM PIC rad. 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 51The 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 52The Heavy Ion Fusion Science
Virtual National Laboratory
Slides from October 2003
w/ UMER group
Slide 53The Heavy Ion Fusion Science
Virtual National Laboratory
The high energy part of a driver consists mostly of accelerating modules (“gaps”)
Slide 54The 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 Nbeams
• Longitudinal waves obey vwave = 1/2 g1/2p (a0b0)1/2; g = 1/(40)log(rw
2/a0b0)
• 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 beamsnear center of cluster (destabilizing)
– But spread in wave speed amongbeams is probably stabilizing
– Also stabilize by capacitance, feedforward– May have to avoid g < 0 on any beam
obs
erv
ing
sta
t ion
time in beam frame
Slide 55The 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 N2 ~ 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 10-8 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 56The 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 Ez 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”)