Electron-beam-seeded self-modulation with plasma density ... Electron-beam-seeded self-modulation...

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Transcript of Electron-beam-seeded self-modulation with plasma density ... Electron-beam-seeded self-modulation...

  • Electron-beam-seeded self-modulation with plasma

    density steps

    Konstantin Lotov, Vladimir Minakov, 09.04.2020

    Two options for the electron beam:

    low-energy (as in Run I):

    charge: 500 pC

    length σz: 660 μm (2.2 ps)

    emittance: 4 mm mrad (normalized)

    radius σr: 250 μm

    energy: 18 MeV

    high-energy (discussed for Run II):

    charge: 100 pC

    length σz: 60 μm (200 fs)

    emittance: 2 mm mrad (normalized)

    radius σr: 200 μm (= 1 c/ωp)

    energy: 160 MeV

    Proton beam (with longitudinal compression):

    population: 3 1011 particles

    length σz: 7 cm

    emittance: 2.2 mm mrad (normalized)

    radius σr: 200 μm

    energy: 400 GeV

    We study whether (and how) it is possible to freeze self-modulation with plasma

    density ramps, if SSM is seeded by an electron beam

    Two plasma densities:

    low 2 1014 cm-3

    high 7 1014 cm-3

    Plasma radius is 1.5 mm

    Propagation length is 20 m

    Single cell (gap neglected)

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    What we take into account:

    wide simulation window for correct simulation of escaping plasma electrons

    p-beam e-beam

    e-beam evolution at

    the plasma entrance

    can be important, so

    we simulate a

    smooth density

    increase here

    position

    length height

    We optimize 3 parameters for

    strongest wakefield at 20 m

    (to be exact, for maximum

    wakefield potential)

    s2

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    The result:

    1250 MV/m

    660 MV/m

    655 MV/m

    885 MV/m

    Strong fields are possible

    Gradual density growth over several meters

    (not a sharp density step)

    18 MeV seed is better than 160 MeV (!)

    The field stabilizes after ~10 m

    in dimensional

    units:

    s3

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    Is the wakefield phase locked to the seed bunch? Yes:

    s6

    We vary the distance between e- and p-beams.

    The wave pattern (measured relative to the proton

    beam head) changes correspondingly.

    Points show locations of field zeros (Ez = 0, Ez’

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    More details about self-modulation:

    s7

    General picture of self-modulation is similar to that of laser-seeded SM. Most part of the beam is

    micro-bunched and contributes to wakefield drive.

    At z = 20 m:

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    Technical details: optimum search

    s5

    18 MeV, 2e14 cm-3

    18 MeV, 7e14 cm-3

    160 MeV, 2e14 cm-3160 MeV, 7e14 cm-3

    Walk on 3d grid; maximum found -> grid refinement

    Each point – 20 m long propagation,

    ~80 core hours at 2e14 cm-3

    ~600 core hours at 7e14 cm-3

    ~100 points to find the maximum

    ~ 120 000 core hours in total

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    Technical details: optimum search

    s5

    18 MeV, 2e14 cm-3

    18 MeV, 7e14 cm-3

    160 MeV, 2e14 cm-3160 MeV, 7e14 cm-3

    Walk on 3d grid; maximum found -> grid refinement

    Each point – 20 m long propagation,

    ~80 core hours at 2e14 cm-3

    ~600 core hours at 7e14 cm-3

    ~100 points to find the maximum

    ~ 120 000 core hours in total

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    Technical details: e-beam initial evolution and substepping

    Quasi-static codes (LCODE) work fast, if the timescale of

    beam evolution is large.

    For 400 GeV proton beam, we can calculate plasma fields

    as rarely as every 4 cm.

    Low energy electron beam evolves much faster, making the

    quasi-static approach inefficient.

    However, a trick with beam substepping helps us to speed

    up simulations.

    We simulate the initial stage of electron beam evolution in a

    small window with a short time step (calculate the plasma

    response every 0.5c/ωp, or 0.1 mm) up to e-beam

    equilibration (at ~20 cm).

    Once electron beam reached the transverse equilibrium, its

    fields change slowly. Then we merge equilibrium electron

    and fresh proton beams and follow their evolution with long

    steps (calculate plasma fields every 200c/ωp ,or 4 cm).

    With beam substepping,

    individual electrons are

    propagated in these fields

    with time step 0.5/ωp or

    even shorter.

    s4

    -2 mm z-ct 0

    127 MV/m

    0

    Ez, Φ

  • Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020

    To conclude:

    Proper longitudinal density profile can freeze self-modulation seeded by an electron bunch at the

    level ~0.5 E0.

    Proper profile means a gradual density growth over several meters (not a sharp density step)

    Lower energy seed (18 MeV) produce higher wakefield than the high-energy one (160 MeV).

    The required length of self-modulation section is ~10 m.

    The “frozen” wakefield is phase-stable and phase-locked to the seed bunch.

    How we can proceed with this study? We want to write a paper. Any objections?

    How can we present more details? PEB could be an option, but the nearest one was cancelled.

    This study relies on new concept of electron beam seeding and parameters of 160 MeV electron beam.

    Are there any publications about this other than SPSC report (CERN-SPSC-2019-037 / SPSC-SR-258)?