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

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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 σ z : 660 μm (2.2 ps) emittance: 4 mm mrad (normalized) radius σ r : 250 μm energy: 18 MeV high-energy (discussed for Run II): charge: 100 pC length σ z : 60 μm (200 fs) emittance: 2 mm mrad (normalized) radius σ r : 200 μm (= 1 c/ω p ) energy: 160 MeV Proton beam (with longitudinal compression): population: 3 10 11 particles length σ z : 7 cm emittance: 2.2 mm mrad (normalized) radius σ r : 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 10 14 cm -3 high 7 10 14 cm -3 Plasma radius is 1.5 mm Propagation length is 20 m Single cell (gap neglected)

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

Page 1: Electron-beam-seeded self-modulation with plasma density …...Electron-beam-seeded self-modulation with plasma density steps, K.Lotov & V.Minakov, 09.04.2020 Technical details: optimum

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)

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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

lengthheight

We optimize 3 parameters for

strongest wakefield at 20 m

(to be exact, for maximum

wakefield potential)

s2

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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

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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:

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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’<0)

For this task, we reduced the number of macro-

particles in the proton beam (and increase their

size) to increase the noise. The required noise

level is taken from simulations of laser-seeded

SSM (M. Baistrukov). For 3.3M macro-particles

in the beam, the wave is phase-locked to the

seed laser pulse if the pulse is 1.8σz ahead of

the proton beam center.

Lines are horizontal after 10 m, good for acceleration Wave amplitude is insensitive to e-beam position

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

More details about self-modulation:

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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:

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

Technical details: optimum search

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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

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

Technical details: optimum search

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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

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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

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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)?