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Self-Consistent Simulations of the Interaction of Electron-Clouds and Beams with WARP-POSINST

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Self-Consistent Simulations of the Interaction of Electron-Clouds and Beams with WARP-POSINST

Jean-Luc Vay

Lawrence Berkeley National Laboratory

Heavy Ion Fusion Science Virtual National Laboratory

E-cloud 07, 9-12 April 2007, Daegu, Korea

- Collaborators

- M. A. Furman, C. M. Celata, P. A. Seidl, K. Sonnad
- 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. Veitzer
- Tech-X Corporation
- J. P. Verboncoeur
- University of California - Berkeley

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

Artist view of a

Heavy Ion Fusion driver

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

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

Which elevates the probability of halo ions hitting structures.

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

e-

g

e-

e-

i+

halo

i+

g

e-

e-

e-

e-

e-

- i+= ion
- e-= electron
- g = gas
- = photon
= instability

Positive

Ion Beam

Pipe

- Ionization of
- background gas
- desorbed gas

Primary:

Secondary:

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

- photo-emission from synchrotron radiation (HEP)

- secondary emission from electron-wall collisions

End-to-End 3-Dself-consistent time-dependent simulations of beam, electrons and gas with self-field + external field (dipole, quadrupole, …).

Note: for Heavy Ion Fusion

accelerators studies,

self-consistent is a necessity!

HCX

Electrons

200mA

K+

From source…

WARP-3D

T = 4.65s

…to target.

- 3-D accelerator PIC code
- Geometry:3D, (x,y), or (r,z)
- Field solvers:FFT, capacity matrix, multigrid
- Boundaries:“cut-cell” --- no restriction to “Legos”
- Bends: “warped” coordinates; no “reference orbit”
- Lattice: general; takes MAD input
- solenoids, dipoles, quads, sextupoles, …
- arbitrary fields, acceleration

+ new e-/gas modules

quad

beam

1

2

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

+ Novel e- mover

+ Adaptive Mesh Refinement

Allows large time step greater than cyclotron period with smooth transition from magnetized to non-magnetized regions

concentrates resolution only where it is needed

R

Speed-up

x10-104

e- motion in a quad

Speed-up x10-100

3

4

Z

merge of WARP & POSINST

POSINST provides advanced SEY model.

Monte-Carlo generation of electrons with energy and angular dependence.

Three components of emitted electrons:

backscattered:

rediffused:

true secondaries:

I0

Ie

Ir

Its

re-diffused

true sec.

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

back-scattered

elastic

- ion-induced electron emission and cross-sections from the TxPhysics* module from Tech-X corporation (http://www.txcorp.com/technologies/TxPhysics),
- ion-induced neutral emission developed by J. Verboncoeur (UC-Berkeley).

Benchmarked against dedicated experiment on HCX

(b)

(c)

(a)

Q1

Q2

Q3

Q4

Location of Current

Gas/Electron Experiments

MATCHING

SECTION

ELECTROSTATIC

QUADRUPOLES

INJECTOR

MAGNETIC

QUADRUPOLES

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

Retarding Field Analyser (RFA)

Clearing electrodes

Capacitive

Probe (qf4)

Suppressor

GESD

e-

K+

End plate

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

Suppressor on

Suppressor off

experiment

200mA K+

e-

(a)

(b)

(c)

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

- Time-dependent beam loading in WARP from moments history from HCX data:
- current
- energy
- reconstructed distributionfrom XY, XX', YY' slit-plate measurements

simulation

measurement

reconstruction

Good semi quantitative agreement.

(a)

(b)

(c)

Simulation

Experiment

Simulation

Experiment

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

Potential contours

WARP-3D

T = 4.65s

e-

200mA K+

Q1

Q2

Q3

Q4

WARP-3D

T = 4.65s

Electrons

200mA

K+

Electrons

bunching

Importance of secondaries - if secondary electron emission turned off:

run time ~3 days

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

Beam ions hit end plate

0.

-20.

-40.

Oscillations

I (mA)

(c)

I (mA)

0.

-20.

-40.

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

0. 2. time (s) 6.

(c)

0. 2. time (s) 6.

AMR essential

X103-104 speed-up!

- LARP funding: simulation of e-cloud in LHC
Proof of principle simulation:

- Fermilab: study of e-cloud in MI upgrade (K. Sonnad)
- ILC: study of e-cloud in positron damping ring wigglers (C. Celata)

Quadrupoles

Drifts

Bends

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

WARP/POSINST-3D - t = 300.5ns

quad

drift

bend

drift

2-D slab of electrons

s

3-D beam

s0

lattice

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.

WARP-QSM X,Y

HEADTAIL X,Y

WARP-QSM X,Y

HEADTAIL X,Y

1 station/turn

Emittances X/Y

(-mm-mrad)

Time (ms)

2 stations/turn

Emittances X/Y

(-mm-mrad)

Time (ms)

Note: WARP-QSM now parallel

y

y

x

x

How can FSC compete with QS? Recent key observation:range of space and time scales is not a Lorentz invariant*

- same event (two objects crossing) in two frames
Consequences

- there exists an optimum frame which minimizes ranges,
- for first-principle simulations (PIC), costT/t ~2 (L/l*T/t ~ 4 w/o moving window),

= (L/l, T/t)

F0-center of mass frame FB-rest frame of “B”

0

space

0

0

0

space+time

0

Range of space/time scales =(L/l,T/t) vary continuously as 2

for large, potential savings are HUGE!

*J.-L. Vay, PRL 98, 130405 (2007)

Laser-plasma acceleration

In laboratory frame.

longitudinal scale x1000/x1000000…

Free electron lasers

x1000

3cm

1m

… so-called“multiscale”problems

= very challenging to model!

Use of approximations

(quasi-static, eikonal, …).

3cm/1m=30,000.

HEP accelerators (e-cloud)

x1000000

x1000

10km

10m

1nm

10cm

10km/10cm=100,000.

10m/1nm=10,000,000,000.

frame ≈19

3cm

1.6mm

1m

30m

Hendrik Lorentz

compaction

x560

3cm/1m=30,000.

1.6mm/30m=53.

frame ≈22

frame ≈4000

2.5mm

450m

10km

10m

1nm

1nm

4m

10cm

4.5m

compaction

x103

compaction

x3.107

450m/4.5m=100.

10km/10cm=100,000.

10m/1nm=10,000,000,000.

2.5mm/4m=625.

Laser-plasma acceleration

Free electron lasers

HEP accelerators (e-cloud)

Note: of interest only if modeling beam and e-cloud, i.e. for self-consistent calculations.

Boosted frame calculation sampleproton bunch through a given e– cloud

electron

streamlines

beam

- This is a proof-of-principle computation:
- hose instability of a proton bunch
- Proton energy: g=500 in Lab
- L= 5 km, continuous focusing

proton bunch radius vs. z

CPU time:

- lab frame: >2 weeks
- frame with 2=512: <30 min

Speedup x1000

- WARP/POSINST code suite developed for HIF e-cloud studies
- Parallel 3-D AMR-PlC code with accelerator lattice follows beam self-consistently with gas/electrons generation and evolution,

- Benchmarked against HCX
- highly instrumented section dedicated to e-cloud studies,

- Being applied outside HIF/HEDP, to HEP accelerators
- Implemented “quasi-static” mode for direct comparison to HEADTAIL/QUICKPIC,
- fund that cost of self-consistent calculation is greatly reduced in Lorentz boosted frame (with >>1), thanks to relativistic contraction/dilatation bridging space/time scales disparities,
- 1000x speedup demonstrated on proof-of-principle case,
- will apply to LHC, Fermilab MI, ILC,
- assess 3-D effects, gain/complications of calculation in boosted frame.