Alex Friedman

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

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

(in beam frame)

• In neutralized drift compression, the space
  charge force is eliminated, resulting in a
  shorter pulse but a larger velocity spread

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

• Final neutralized drift compression onto the
  target
• Electrons in plasma move so as to cancel the
  beams electric field
• Require nplasma gt 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 lt 1 ns
• Kinetic energy 1.2 MeV

6
12-cell NDCX-II baseline layout
7
12-cell NDCX-II baseline layout
8
12-cell NDCX-II baseline layout
9
12-cell NDCX-II baseline layout
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 ?t algorithms (implicit electrostatic,
  large ?c?t)
• emission, ionization, secondaries, Coulomb
  collisions...
• parallel processing

A. Friedman, et al., Phys. Plasmas 17, 056704
(2010).
11
Steps in development of the NDCX-II physics
design
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
Steps in development of the NDCX-II physics
design
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
Steps in development of the NDCX-II physics
design
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 mean energy to
cross finite-length gap time for entire beam to
cross finite-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
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
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

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
well 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-I (typical bunched beam) NDCX-II 12-cell (ideal)
Ion species K (A39) Li (A7)
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)
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 lt 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.

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)

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

z1 0.167 km z2 0.542
km z3 1.042 km
z4 1.242 km
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

z1 0.333 km z2 0.433
km z3 0.767 km
z4 1.067 km
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

(in beam frame)

• In neutralized drift compression, the space
  charge force is eliminated, resulting in a
  shorter pulse but a larger velocity spread

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-energeticbeam
  at the final focus?
• How well can we pulse-shape a beam during drift
  compression (vs. the Robust Point Designs
  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.
38
EXTRAS NDCX-II misc
39
NDCX-II performance for typical cases in 12-21
cell configurations
NDCX-I (bunched beam) NDCX-II NDCX-II NDCX-II NDCX-II
NDCX-I (bunched beam) 12-cell 15-cell 18-cell 21-cell
Ion species K (A39) Li (A7) Li (A7) Li (A7) Li (A7)
Charge 15 nC 50 nC total 25 2xFWHM 50 nC total 25 2xFWHM 50 nC total 25 2xFWHM 50 nC total 30 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 v2 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)
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, a 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 a 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
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
6-MHz oscillations were seen first in
simulations then they were sought and measured
at station (c) in experiments.
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)

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)
-11
-12
-10
-9
-8
-7
-6
-5
-4
Length scales
electron gyroradius in magnet
machine length
beam radius
lD,beam
log (meters)
-5
-4
-3
-2
-1
0
1
2
3
48
New Drift-Lorentz mover relaxes the problem of
short electron timescales in magnetic field
Magnetic quadrupole

• Problem Electron gyro timescale
• ltlt 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

Sample electron motion in a quad
small ?t0.25/?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
Run Grid size Nb particles
Low res. 56x640 1M
Medium res. 112x1280 4M
High res. 224x2560 16M
Low res. AMR 56x640 1M
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
main sequence tracks beam ions consistently
along entire system instabilities, halo,
electrons, ... are studied via coupled detailed
models
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

51
52
Slides from October 2003 w/ UMER group
53
The high energy part of a driver consists mostly
of accelerating modules (gaps)
54
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 g1/2wp
  (a0b0)1/2 g  1/(4??0)log(rw2/a0b0)
• They can be driven unstable by module impedance
  (resistive wall)

• Convective growth, head-to-tail
• Inductive field in multi-beam systemslows
  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 lt 0 on any beam

observing station
time in beam frame
55
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 LPs 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 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

56
Further considerations

• Emittance
• Transverse emittance (tune depression) is OK
  beams resemble UMER
• In a driver, longitudinal thermal pressure is ltlt
  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 l
  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)