new self-consistent 3-d capabilities of electron clouds simulations jean-luc vay lawrence berkeley...

New self-consistent 3-D capabilities of electron clouds simulations

Jean-Luc VayLawrence Berkeley National Laboratory

Heavy Ion Fusion Science Virtual National Laboratory

CERN - October 5, 2006

2J.-L. Vay - CERN - 10/05/06

Many thanks to collaborators

M. A. Furman, C. M. Celata, P. A. Seidl, M. Venturini

Lawrence Berkeley National Laboratory

R. H. Cohen, A. Friedman, D. P. Grote, M. Kireeff Covo, A. W. Molvik

Lawrence Livermore National Laboratory

P. H. Stoltz, S. VeitzerTech-X Corporation

J. P. Verboncoeur University of California - Berkeley

3J.-L. Vay - CERN - 10/05/06

Outline

1. Who we are and why we care about electron cloud effects2. Our tools and recent selected results3. Application to HEP accelerators4. Future directions and conclusion


4J.-L. Vay - CERN - 10/05/06

The U.S. Heavy Ion Fusion Science Program - Participation

Lawrence Berkeley National Laboratory MITLawrence Livermore National Laboratory Advanced CeramicsPrinceton Plasma Physics Laboratory Allied SignalNaval Research Laboratory National ArnoldLos Alamos National Laboratory HitachiSandia National Laboratory Scientific VossUniversity of Maryland Georgia TechUniversity of Missouri General AtomicStanford Linear Accelerator Center MRTI Advanced Magnet Laboratory Tech-XIdaho National Environmental and SciberQuestEngineering Lab University of California

a. Berkeley b. Los Angeles c. San Diego

Employees of LBNL, LLNL, and PPPL form the U.S. Virtual National Laboratory for Heavy Ion Fusion Sciences

5J.-L. Vay - CERN - 10/05/06

Our near term goal is High-Energy Density Physics (HEDP)...

Heavy Ion Inertial Fusion (HIF) goal is to develop an accelerator that can deliver beams to ignite an inertial fusion target

DT

Target requirements:

3-7 MJ x ~ 10 ns ~ 500 Terawatts

Ion Range: 0.02 - 0.2 g/cm2 1-10 GeV

dictate accelerator requirements:

A~200 ~1016 ions, 100 beams, 1-4 kA/beam

Artist view of a Heavy Ion Fusion driver

6J.-L. Vay - CERN - 10/05/06

High energy density physics (HEDP) is study of matter under extreme temperature, density, and pressure.

• Diverse applications: HED astrophysics, HED laboratory plasmas, ICF, materials science

• Accessible, open facilities with dedicated beam time are needed

• HIFS-VNL workshops, study groups have explored possible contributions; outside collaborators include: R. More, R. Lee (LLNL), M. Murillo (LANL), N. Tahir (and others at GSI)

Dense, strongly coupled plasmas @ 10-2

to 10-1 x solid density are potentially interesting areas to test EOS models.

Aluminum

% disagreement in EOS models

little or no data

7J.-L. Vay - CERN - 10/05/06

Intense heavy ion beams provide an excellent tool to generate homogeneous high energy density matter.

Ion beam

Example: He

Enter foilExit foil

Al target• Warm dense matter (WDM)

– T ~ 1,000 to 100,000 K– ~ 0.01 -1 * solid density– P ~ kbar, Mbar

• Techniques for generating WDM– High explosives– Powerful lasers– Exploding wire (z-pinch)

• Some advantages of intense heavy ion beams– Volumetric heating: uniform physical

conditions– High rep. rate and reproducibility– Any target material

8J.-L. Vay - CERN - 10/05/06

Program Objectives

• OFES/OMB endorses the 2005 Fusion Energy Science Advisory Committee top priority for the heavy ion program:

“How can heavy ion beams be compressed to the intensities required for high energy density physics and fusion?”

• OFES has two targets (objectives) for HIFS-VNL FY06 research:

Priority 1: "Conduct experiments and modeling on combined transverse and longitudinal compression of intense heavy ion beams.”

Priority 2: "Extend electron cloud effects studies to include experiments with mitigation techniques with improved computational models".

9J.-L. Vay - CERN - 10/05/06

Why do we care about electrons?We have a strong economic incentive to fill the pipe.

(from a WARP movie; see http://hif.lbl.gov/theory/simulation_movies.html)

Time-dependent 3D simulations of HCX injector reveal beam ions hitting structure

10J.-L. Vay - CERN - 10/05/06

e-

i+haloe-

• ion induced emission from- expelled ions hitting vacuum wall- beam halo scraping

Sources of electron clouds

Primary:

Secondary:

i+ = ion e- = electrong = gas = photon

= instability

PositiveIon Beam

Pipe

e-

i+

g

g

• Ionization of - background gas - desorbed gas

• secondary emission from electron-wall collisions

e- e-e-

e-e-

• photo-emission from synchrotron radiation (HEP)

11J.-L. Vay - CERN - 10/05/06

Outline



12J.-L. Vay - CERN - 10/05/06

Unique simulation/experimental tools to study ECE

• WARP/POSINST code suite

– Parallel 3-D PlC-AMR code with accelerator lattice follows beam self-consistently with gas/electrons generation and evolution

– collaborative effort - LBNL Center for Beam Physics (M. Furman) - secondary emission

- Tech-X (P. Stoltz, S. Veitzer) - ion-induced electron emission, ionization cross-sections

- UC-Berkeley (J. Verboncoeur) - neutrals generation

• HCX experiment adresses ECE fundamentals relevant to HEP

– trapping potential ~2kV with highly instrumented section dedicated to e-cloud studies

• The combination forms a unique set for careful study of the fundamental physics of ECE and extensive methodical benchmarking

13J.-L. Vay - CERN - 10/05/06

1

WARP-POSINST code suite is unique in four ways

merge of WARP & POSINST

Key: operational; partially implemented (4/28/06)

+ new e-/gas modules

2

+ Adaptive Mesh Refinement

Z

R

concentrates resolution only where it is needed

3Speed-up x10-104

beam

quad

e- motion in a quad

+ New e- moverAllows large time step greater than cyclotron period with smooth transition from magnetized to non-magnetized regions

4 Speed-up x10-100

Monte-Carlo generation of electrons with energy and angular dependence.Three components of emitted electrons:

backscattered:

rediffused:

true secondaries:

true sec.

back-scattered elastic

POSINST provides advanced SEY model.

re-diffused

I0

Its

Ie Ir

Phenomenological model:• based as much as possible on data for and d/dE• not unique (use simplest assumptions whenever data is not available)• many adjustable parameters, fixed by fitting and d/dE to data

15J.-L. Vay - CERN - 10/05/06

We can run WARP/Posinst in different modes.

1. Slice mode (2-D1/2 s-dependent)

2-D beam slab

A 2-D slab of beam (macroparticles) is followed as it progresses forward from station to station evolving self-consistently with its own field + external field (dipole, quadrupole, …) + prescribed additional species, eventually.

benddrift driftquad

s

s0 s0+s0lattice

16J.-L. Vay - CERN - 10/05/06


2. Posinst mode (2-D1/2 time-dependent)

A 2-D slab of electrons (macroparticles) sits at a given station and evolves self-consistently with its own field + kick from beam slabs passing through + external field (dipole, quadrupole, …).

2-D slab of electrons

3-D beam: stack of 2-D slab

benddrift driftquad

s

s0lattice

17J.-L. Vay - CERN - 10/05/06


3. Fully self-consistent (3-D time-dependent)

Beam bunches (macroparticles) and electrons (macroparticles) evolve self-consistently with self-field + external field (dipole, quadrupole, …).

WARP-3DT = 4.65s

200mA K+

Electrons

From source…

…to target.

HCX

18J.-L. Vay - CERN - 10/05/06

(a) (b) (c)CapacitiveProbe (qf4)

Clearing electrodesSuppressor

Q1 Q2 Q3 Q4

K+ e-

Short experiment => need to deliberately amplify electron effects: let beam hit end-plate to generate copious electrons which propagate upstream.

End plate

INJECTOR

MATCHINGSECTION

ELECTROSTATICQUADRUPOLES

MAGNETICQUADRUPOLES

HCX dedicated setup for gas/electron effects studies

Retarding Field Analyser (RFA)

Location of CurrentGas/Electron Experiments

GESD

1 MeV, 0.18 A, t ≈ 5 s, 6x1012 K+/pulse, 2 kV space charge, tune depression ≈ 0.1

19J.-L. Vay - CERN - 10/05/06

Diagnostics in two magnetic quadrupole bores, & what they measure.

MA4MA3

8 “paired” Long flush collectors (FLL): measures capacitive signal + collected or emitted electrons from halo scraping in each quadrant.

3 capacitive probes (BPM); beam capacitive pickup ((nb- ne)/ nb).

2 Short flush collector (FLS); similar to FLL, electrons from wall.

2 Gridded e- collector (GEC); expelled e- after passage of beam

2 Gridded ion collector (GIC): ionized gas expelled from beam

BPM (3)

BPM

FLS(2)

FLS

GIC (2)

GIC

Not in service

FLS

GECGEC

20J.-L. Vay - CERN - 10/05/06

0V 0V 0V V=-10kV, 0V

Time-dependent beam loading in WARP from moments history from HCX data:

• current

• energy• assuming semi-gaussian distribution

RMS envelopes RMS emittances average slopes beam centroids

simulation

May 2005 (PAC conference)

200mA K+

(a) (b) (c)

e-

Suppressor offSuppressor on

experiment

Comparison sim/exp: clearing electrodes and e- supp. on/off

Good qualitative agreement.

21J.-L. Vay - CERN - 10/05/06

simulation

200mA K+ e-

0V 0V 0V V=-10kV, 0V

Suppressor offSuppressor on

experiment

Comparison sim/exp: clearing electrodes and e- supp. on/off

Time-dependent beam loading in WARP from moments history from HCX data:

• current

• energy• reconstructed distribution from XY, XX', YY' slit-plate measurements

(a) (b) (c)

August 2005

Agreement significantly improved!measurement reconstruction

22J.-L. Vay - CERN - 10/05/06

1. Importance of secondaries - if secondary electron emission turned off:

2. simulation run time ~3 days - without new electron mover and MR, run time would be ~1-2 months!

1. Importance of secondaries - if secondary electron emission turned off:

2. simulation run time ~3 days - without new electron mover and MR, run time would be ~1-2 months!

Detailed exploration of dynamics of electrons in quadrupole

WARP-3DT = 4.65s

Oscillations

Beam ions hit end

plate

(a) (b) (c)

e-

0V 0V 0V/+9kV 0V

Q4Q3Q2Q1

200mA K+

200mA K+

Electrons

(c)0. 2. time (s) 6.

Simulation Experiment0.

-20.

-40.

I (m

A)

Potential contours

Simulation Experiment

(c)0. 2. time (s) 6.

I (m

A)

0.

-20.

-40.

Electrons bunching

~6 MHz signal in (C) in simulation AND experiment

WARP-3DT = 4.65s

23J.-L. Vay - CERN - 10/05/06

Outline



24J.-L. Vay - CERN - 10/05/06

WARP/POSINST applied to High-Energy Physics

• LARP funding: simulation of e-cloud in LHC

• Fermilab: study of e-cloud in MI upgrade• ILC: start work in FY07

QuadrupolesDriftsBends

WARP/POSINST-3D - t = 300.5ns

1 LHC FODO cell (~107m) - 5 bunches - periodic BC (04/06)

AMR essentialX103-104 speed-up!

25J.-L. Vay - CERN - 10/05/06

“Quasi-static” mode added for codes comparisons.

A 2-D slab of electrons (macroparticles) is stepped backward (with small time steps) through the beam field and 2-D electron fields are stacked in a 3-D array, that is used to push the 3-D beam ions (with large time steps) using maps (as in HEADTAIL-CERN) or Leap-Frog (as in QUICKPIC-UCLA), allowing direct comparison.

2-D slab of electrons

3-D beam

benddrift driftquad

s

s0 lattice

26J.-L. Vay - CERN - 10/05/06

Time (ms)

Em

ittan

ces

X/Y

(-m

m-m

rad

)

2 stations/turn

Comparison WARP-QSM/HEADTAIL on CERN benchmark

Time (ms)

Em

ittan

ces

X/Y

(-m

m-m

rad

)

1 station/turn

WARP-QSM X,YHEADTAIL X,Y

WARP-QSM X,YHEADTAIL X,Y

27J.-L. Vay - CERN - 10/05/06

Can 3-D self-consistent compete with quasi-static mode?- computational cost of full 3-D run in two frames -

x = x/n; z = min(z,L)/n

t < min[ x/max(vx),z/max(vz) ];

Tmax = NunitsL/Vb

Nop = NeTmax/t

x* = x/n; z* = min(z*,L*)= z

t* < min[ x*/max(vx*),z*/max(vz*) ] = min[ x/(max(vx/), z/vz] = t

T*max = NunitsL*/(Vb-Vf) ~ Tmax /

N*op = NeT*max/t* ~ Nop /

L*z*

zLab frame

Frame

Vb

Vf

Vb

Vb

=> Computational cost greatly reduced in frame

L (1 unit) z

x

28J.-L. Vay - CERN - 10/05/06

Comparison between quasi-static and full 3-D costs.

if z *= S*, =, N*op = Nop,qs

=> cost of full 3-D run in frame = cost of quasi-static mode in lab frame

Quasi-static (HEADTAIL, QUICKPIC): ~ S/z

Nop,qs = Nop/

Frame

z

xLab frame z

Vb

z*-Vf

Vb

S

29J.-L. Vay - CERN - 10/05/06

Application to rings

• In bends, WARP uses warped coordinates with a logically cartesian grid. If solving in a frame moving at constant along s, we need to extend existing algorithm to allow treatment of motion in relativistic rotating frame in bends.

• Meanwhile, in order to study electron cloud effects, including bends, where effects are dominated by the magnitude of the bending field rather than its sign, we propose to substitute a ring by a linear lattice with bends of alternating signs.

• For example, diagram 1 LHC FODO cell ( )

or

or…

quadrupole; bend

30J.-L. Vay - CERN - 10/05/06

Outline



31J.-L. Vay - CERN - 10/05/06

Point source of electrons to simulate synchrotron radiation photoelectrons

Electron current vs. cathode-grid potential at various cathode temperatures

1

10

100

1000

10000

0 500 1000 1500 2000Potential between cathode & grid (V)

Current (mA)

950 C980 C1005 C1035 C1060 C1085 CPower (950 C)Power (980 C)Power (1005 C)Power (1035 C)Power (1060 C)Power (1085 C)

Electron gun operates over range

~10 eV to 2000 eV (cathode & grid indep.)

<1 mA to 1000 mA

Electron gun enables

quantitatively controlled

injection of electrons

32J.-L. Vay - CERN - 10/05/06

Signal from clearing electrode B depends on surface.

(a) (b) (c)

e-

+9kV +9kV 0V 0V

Q4Q3Q2Q1

200mA K+

time (s)

I (m

A)

HCX experimentSim. - stainless steelSim. - copper

Experimental result bracketed by simulation results when using default Posinst SEY parameters for stainless steel and copper.

=> Need to measure SEY for an actual sample.

current in (b)

0. 2. time (s) 6.

Simulation Experiment0.

-20.

-40.

I (m

A)

current in (c)

(a) (b) (c)

e-

+9kV +9kV +9kV 0V

Q4Q3Q2Q1

200mA K+

Case A: all clearing electrodes biased at +9kV

Case B: clearing electrode (C) grounded

Uses default Posinst SEY parameters for stainless steel. Experimental result well recovered.

Nb e- per beam ion: 1.5 (~8. was predicted)Nb H2 per beam ion: 15000. (~7000. was predicted)cross section K+ + H2 => K+ + H2+ + e- : 1.6e-16cm-2

cross section K+ + H2 => K++ + H2 + e- : 6.e-16cm-2

=> Need to measure yields and cross-sections.

Simple 0D model:• electron and neutrals emission• gas ionization• beam stripping• electrons/H(2)+ are collected instantly at the plate

Electron suppressor ring replaced by two plates.

+10kV

Q4

200mA K+ e-

g

-10kV

Q4

200mA K+ i+

g

I (m

A)

I (m

A)

Time (s)

0-D model ExperimentBeam

0-D model ExperimentBeam

34J.-L. Vay - CERN - 10/05/06

Conclusion

• We developed a unique combination of tools to study ECE

• WARP/POSINST code suite– Parallel 3-D PlC-AMR code with accelerator lattice follows beam self-

consistently with gas/electrons generation and evolution,

• HCX experiment adresses ECE fundamentals (HIF/HEDP/HEP)– highly instrumented section dedicated to e-cloud studies,– extensive methodical benchmarking of WARP/POSINST,

• Being applied outside HIF/HEDP, to HEP accelerators– LHC, Fermilab MI, ILC,– Implemented “quasi-static” mode for direct comparison to

HEADTAIL/QUICKPIC,– fund that self-consistent calculation has similar cost than quasi-static

mode if done in moving frame (with >>1), thanks to relativistic contraction/dilatation bridging space/time scales disparities (applies to FEL, laser-plasma acceleration, plasma lens,…).

Backup Slides

36J.-L. Vay - CERN - 10/05/06

Study of virtual cathode using axisymmetric XOOPIC1 model

Ion beam injected from left edge

1 Verboncoeur et al., Comp. Phys. Comm. 87, 199 (1995)

t=200 ns.

v z (

m/s

)

z (m)

t=2000 ns.

v z (

m/s

)

z (m)

z

rBeam - K+, 972 kV, 174 mA, rb=2.2 cm,

emitted electronsreflected electrons

0 26 cm0

11 cm

Phase space hole eventually collapses due to VC oscillations

right boundary:absorbing, with emission of electrons.

left edge: reflects electrons with coefficient R

37J.-L. Vay - CERN - 10/05/06

Spurious oscillations observed when VC is not resolved

Potential in vicinity of virtual cathode region (t=2s, t=0.2ns)

V 24min −=Φ V 2570 min −≤Φ≤−

oscillation

mm 3/1=zmm 55.0=rhigh resolution

(200x780) mm 3/5=zmm 75.2=rlow resolution

(40x156)

Mesh refinement very helpful for modeling of HCX magnetic section!

38J.-L. Vay - CERN - 10/05/06

Quest - nature of oscillations

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.













Z (m)

No secondaries

No secondaries/frozen beam

No secondaries/frozen beam withoutz-dependence

QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.



Progressively removes

possible mechanisms

Not ion-electron two stream

39J.-L. Vay - CERN - 10/05/06

Increasing beam

diameter in direction

of maximum electron

cloud radius, reduces

oscillations.

Vary beam section 0.025

0.

-0.02

5

0.025

0.

-0.02

5

0.025

0.

-0.02

5



0.02

5

0.

-

















X (m) Z (m)




QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.QuickTime™ and a

TIFF (LZW) decompressorare needed to see this picture.

a)

b)

c)

d)




QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.




40J.-L. Vay - CERN - 10/05/06

Replace Q1-4 with 1 quad.

1 s 2 s1 s

Looks like vortices developing and propagating upstream…

R (

m)

V(m/s)

e-200mA K+

41J.-L. Vay - CERN - 10/05/06

Is this a Kelvin-Helmholtz instability?

Fluid velocity vectors (length and color according to magnitude)

Vortices?

Shear flow

42J.-L. Vay - CERN - 10/05/06

Replace quadrupole field by azimuthal field

1 s 2 s

System is axisymmetric: much simpler to study analytically…

43J.-L. Vay - CERN - 10/05/06

Example of application of the quasi-static module

44J.-L. Vay - CERN - 10/05/06

• 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)

We have invented a new “mover” that 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

large t=5./c

Standard Boris mover(fails in this regime)

• Test: Magnetized two-stream instability

45J.-L. Vay - CERN - 10/05/06

code of M. Furman and M. Pivi

Follows slice of electrons at one location along beam line 2-D PIC for e– self forceanalytical kick for force of beam on electrons

Effect of electrons on beam -- minimally modeleddipole wake

Good models for electron production by:synchrotron radiationresidual gas ionizationstray beam particles hitting vacuum wallsecondary electron production (detailed model)

POSINST calculates the evolution of the electron cloud

Under SBIR funding, POSINST SEY module implemented into CMEE library distributed by Tech-X corporation.

POSINST has been used extensively for e-cloud calculations

TxPhysics Library

46J.-L. Vay - CERN - 10/05/06

HEDP: - T regime accessible by beam driven experiments lies square in the interiors of gas planets and low mass stars



Accessibleregion usingbeams in nearterm

Figure adapted from “Frontiers in HEDP: the X-Games of Contemporary Science:”

Terrestialplanet

47J.-L. Vay - CERN - 10/05/06

• Wavelength of ~5 cm, growing from near center of 4th quad. magnet

Array of BPMs in HCX Quad 4 verified WARP simulation results

-23.5 cm -12 Axial Position 0 cm

4.3-2 4.3-1 4.8-3 4.6-3 4.4-3 4.2-3 4.1-3 BPM labels

Centre of 4th magnet

Beam Position Monitor (BPM): electrode capacitively coupled to beam

FFT 1.9-2.9uS averaged over 1-31MHz, Data 26 Jan. 2006, Shot 7

0

200

400

600

800

-5 0 5 10 15 20Axial location from quad center (cm)

RMS Power (pW)

HCX

WARP

upstream

(a) (b) (c)

e-

0V 0V 0V/+9kV 0V

Q4Q3Q2Q1

200mA K+

• Experiment and simulations agree quantitatively on oscillation– frequency

– Wavelength

– amplitude

RM

S P

ow

er (

arb

itra

ry u

nit

s)

ExperimentSimulation

new self-consistent 3-d capabilities of electron clouds simulations jean-luc vay lawrence berkeley...

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