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

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Self consistent simulations of the interaction of electron clouds and beams with warp posinst

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


Self consistent simulations of the interaction of electron clouds and beams with warp posinst

  • 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


Self consistent simulations of the interaction of electron clouds and beams with warp posinst

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).


    Self consistent simulations of the interaction of electron clouds and beams with warp posinst

    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


    Self consistent simulations of the interaction of electron clouds and beams with warp posinst

    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.


    Self consistent simulations of the interaction of electron clouds and beams with warp posinst

    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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