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.

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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


  • 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) Electron-Clouds and Beams with WARP-POSINSTgoal 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. Electron-Clouds and Beams with WARP-POSINST

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 Electron-Clouds and Beams with WARP-POSINST-

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 Electron-Clouds and Beams with WARP-POSINST

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 Electron-Clouds and Beams with WARP-POSINST

  • 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 Electron-Clouds and Beams with WARP-POSINST-/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. Electron-Clouds and Beams with WARP-POSINST

    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. Electron-Clouds and Beams with WARP-POSINST

    • 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 Electron-Clouds and Beams with WARP-POSINST

    (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 Electron-Clouds and Beams with WARP-POSINSTon

    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) Electron-Clouds and Beams with WARP-POSINST

    (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 Electron-Clouds and Beams with WARP-POSINST

    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 Electron-Clouds and Beams with WARP-POSINST

    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, Electron-Clouds and Beams with WARP-POSINSTY

    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


    y Electron-Clouds and Beams with WARP-POSINST

    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 Electron-Clouds and Beams with WARP-POSINST

    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 Electron-Clouds and Beams with WARP-POSINST ≈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.


    Boosted frame calculation sample Electron-Clouds and Beams with WARP-POSINSTproton 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 Electron-Clouds and Beams with WARP-POSINST

    • 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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