alex friedman hif-vnl, lnll presented at aps-dpp meeting savannah, ga, november 17, 2004

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)

18

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 …