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* 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 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 *

Overview of NDCX-II Physics Design and Comments on final beam-lines for a driver *

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Overview of NDCX-II Physics Design and Comments 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. - PowerPoint PPT Presentation

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Page 1: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

* 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*

Page 2: 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

Page 3: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 4: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 5: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 6: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 7: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 8: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 9: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 10: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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).

Page 11: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 12: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 13: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 14: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 15: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 16: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 17: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 18: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 19: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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.

Page 20: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 21: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 22: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 23: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 24: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 25: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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.

Page 26: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 26The Heavy Ion Fusion Science

Virtual National Laboratory

Comments on final beam-lines

for a driver

Page 27: Overview of NDCX-II Physics Design  and 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

Page 28: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 29: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 30: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 31: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 32: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 33: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 34: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 35: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 36: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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 …

Page 37: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 38: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 38The Heavy Ion Fusion Science

Virtual National Laboratory

EXTRAS – NDCX-II misc

Page 39: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 40: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 40The Heavy Ion Fusion Science

Virtual National Laboratory

EXTRAS – ASP code

Page 41: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 42: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 43: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 43The Heavy Ion Fusion Science

Virtual National Laboratory

EXTRAS – Warp code

Page 44: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 45: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 46: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 47: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 48: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 49: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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)

Page 50: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 51: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 52: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 52The Heavy Ion Fusion Science

Virtual National Laboratory

Slides from October 2003

w/ UMER group

Page 53: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

Slide 53The Heavy Ion Fusion Science

Virtual National Laboratory

The high energy part of a driver consists mostly of accelerating modules (“gaps”)

Page 54: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 55: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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

Page 56: Overview of NDCX-II Physics Design  and Comments on final beam-lines for a driver *

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”)