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
lengthheight
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’<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
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)?
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