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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.

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slide1

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

slide2

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
slide3

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)...

we have a strong economic incentive to fill the pipe
We have a strong economic incentive to fill the pipe.

Which elevates the probability of halo ions hitting structures.

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

sources of electron clouds

e-

g

e-

e-

i+

halo

i+

g

e-

e-

e-

e-

Sources of electron clouds

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
simulation goal predictive capability
Simulation goal - predictive capability

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 = 4.65s

…to target.

warp is our main tool
WARP is our main tool
  • 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
  • Diagnostics: Extensive snapshots and histories
  • Parallel:MPI
  • Python and Fortran: “steerable,” input decks are programs
warp posinst unique features

+ 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

WARP-POSINST unique features

merge of WARP & POSINST

re diffused

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

we use third party modules
We use third-party modules.
  • 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).
slide11

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.

comparison sim exp clearing electrodes and e supp on off

Suppressor on

Suppressor off

experiment

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

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.

detailed exploration of dynamics of electrons in quadrupole

(a)

(b)

(c)

Simulation

Experiment

Simulation

Experiment

Detailed exploration of dynamics of electrons in quadrupole

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

Potential contours

WARP-3D

T = 4.65s

e-

200mA K+

Q1

Q2

Q3

Q4

WARP-3D

T = 4.65s

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.

warp posinst applied to high energy physics

AMR essential

X103-104 speed-up!

WARP/POSINST applied to High-Energy Physics
  • 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

quasi static mode added for codes comparisons

quad

drift

bend

drift

“Quasi-static” mode added for codes comparisons.

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.

comparison warp qsm headtail on cern benchmark

WARP-QSM X,Y

HEADTAIL X,Y

WARP-QSM X,Y

HEADTAIL X,Y

Comparison WARP-QSM/HEADTAIL on CERN benchmark

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

slide17

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), costT/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)

a few systems of interest which might benefit
A few systems of interest which might benefit

Laser-plasma acceleration

In laboratory frame.

longitudinal scale x1000/x1000000…

Free electron lasers

x1000

3cm

1m

… so-called“multiscale”problems

= very challenging to model!

Use of approximations

(quasi-static, eikonal, …).

3cm/1m=30,000.

HEP accelerators (e-cloud)

x1000000

x1000

10km

10m

1nm

10cm

10km/10cm=100,000.

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

lorentz transformation large level of compaction of scales

frame  ≈19

3cm

1.6mm

1m

30m

Hendrik Lorentz

compaction

x560

3cm/1m=30,000.

1.6mm/30m=53.

frame  ≈22

frame  ≈4000

2.5mm

450m

10km

10m

1nm

1nm

4m

10cm

4.5m

compaction

x103

compaction

x3.107

450m/4.5m=100.

10km/10cm=100,000.

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

2.5mm/4m=625.

Lorentz transformation => large level of compaction of scales

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.

slide20

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

summary
Summary
  • 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.
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