Production of high quality electron beams in numerical simulations of LWFA with controlled injection

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Production of high quality electron beams in
numerical simulations of LWFA with controlled
injection
P. Tomassini1, F. Pegoraro2, L. Labate1,3 M.
Galimberti1, A. Giulietti1, D. Giulietti1,2, L.A.
Gizzi1
1Intense Laser Irradiation Laboratory - IPCF CNR
Pisa (Italy), 2Dip. Fisica, Unità INFM,
Università di Pisa 3Dip. Fisica, Università di
Bologna (Italy)
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Wave breaking due to density transition 1

• The idea was introduced by S. Bulanov, N.
  Naumova, F. Pegoraro and J. Sakai in 1998 PRE
  58, 5 R5257-5260. In a 1D wave the local
  pulsation w and wavevector k satisfy the relation
  
  
• so that a Langmuir wave excited in a plasma
  presenting an electron density which decreases
  along the laser pulse propagation has a local
  wavenumber which increases in time.
• The corresponding local phase speed vph w /k
  then decreases and when it equals the Langmuir
  quiver velocity vq a portion of the wave breaks,
  thus injecting electrons in the accelerating
  phase.

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Wave breaking due to density transition 2

• If the quivering of the electrons in the Langmuir
  wave is nonrelativistic bq vq/cltlt1, their
  motion is linear in Lagrange coordinates
• If the wave number increases (as in the case of a
  density decrease), the phase speed vf w/k
  decreases and when kxM 1 the quiver velocity vq
  equals the phase velocity so that the crest of
  the wave starts to break.
• In the case of a gentle density transition,
  i.e. with a transition scalelength Lgtgtlp, an
  energy-balance argument shows that the relative
  density of the injected electrons is

S. Bulanov et al., PRE 58, 5 R5257.
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Transverse effects

• In a 3D geometry a concurring transverse breaking
  occurs. Transverse wave breaking (i.e.
  self-intersection in the transverse direction of
  the electron trajectories) is generated by the
  dependence of the plasma frequency on the radial
  coordinate S. Bulanov, F. Pegoraro, A. Pukhov
  and A. Sakharov, PRL 78 22 4205 (1997).
• If w(r) increases with r e.g. because of the
  relativistic effects of the pulse, plasma
  inhomogeinity or pulse generated magnetic fields
  the wake develops a characteristic horseshoe
  shape leading to transverse breaking after a
  number of crests Nb
• where and w
  is the laser pulse waist.
• In a plasma with a decreasing density
  distribution the plasma frequency decreases, thus
  lowering the threshold for transverse wave
  breaking.

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Related works

• S. Bulanov, N. Naumova, F. Pegoraro and J. Sakai,
  PRE 58, 5 R5257 (1998). The main idea of
  controlled injection with longitudinal nonlinear
  wave-breaking in 1D LWFA, supported by both PIC
  and theoretical results.
• H. Suk, N. Barow, J.B. Rosenzweig and E. Esarey,
  PRL 86 6, 1011-1014 (2001). PWFA in which the
  plasma density presents a sharp density
  transition. Supported by both 2D PIC and 1D
  theoretical results.
• R.J. England, J.B. Rosenzweig and N. Barov, PRE
  66 6, 016501 (2002). PWFA in which the plasma
  density presents a sharp density transition.
  Supported by both Lagrangian analysis and 1D PIC
  simulations.
• R.G. Hemker, N.M. Hafz and M. Uesaka, PRE-ST Acc.
  and beams 5, 041301 (2002). LWFA regime with two
  gas-jets studied with 2D PIC simulations. The
  particles are injected at the downramp of the
  density of the first gas-jet because of
  TRANSVERSE wave breaking and accelerated in the
  second gas-jet.
• T. Hosokai et al., PRE 67, 036407 (2003). First
  experimental paper of LWFA with injection by
  density decrease. The density transition was
  obtained with a gas-jet system heated by the ASE
  of the main pulse which produces a shock-wave.
• Such a breaking can inject particles in the
  accelerating phase, although in an uncontrolled
  way see R.G. Hemker, N.M. Hafz and M. Uesaka,
  Phys. Rev. ST 5, 041301b (2002).

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2.5D PIC results 1

• We report the results of a simulation (3D in the
  fields and 2D in the coordinates) performed with
  a full relativistic PIC code developed by H.
  Ruhl, which runs on 32 processors of a SP4 system
  at CINECA, Bologna (Italy).
• A p-polarized, plane wave laser pulse of duration
  T 17fs, waist w0 20 mm, intensity I
  2.5.1018 W/cm2 and wavelength lL 1 mm (a0
  1.3) impinges onto a preformed plasma whose
  density profile presents two plateaux separated
  by a steep transition

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2.5D PIC results 2

• About 108 macro-particles move in a simulation
  box of 40x150mm2 with a spatial resolution of
  0.05 ll
• The plasma density was chosen in order to fit the
  quasi-resonance criterium for LWF cT5.1
  mmlp/2.
• The density transition was sharp (L2 mm ltlt
  lp).
• The laser pulse intensity was tuned in order to
  produce in Zone I a wakefield far from
  wavebreaking (either nonlinear and
  relativistic).
• The pulse waist was chosen in order to assure
  that longitudinal effects do dominate over
  transverse effects.

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2.5D PIC results 3
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2.5D PIC results 4

• The wake behind the pulse is well
• developed in Zone I

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2.5D PIC results 5

• The Langmuir wave in Zone I is
• far from nonlinear wave-breaking.
• The phase speed is very close to c
• and the maximum quiver velocity is
• Accordingly, the amplitude of the quivering
  can be estimated by the maximum momentum of the
  particles
• so that

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2.5D PIC results 6

• At a later time the crest behind
• the pulse starts to brake at the
• density transition

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2.5D PIC results 7
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2.5D PIC results 8

• At the final time of the simulation the
  accelerating and focusing forces acting on the
  first bunch have produced a well collimated and
  quasi-monochromatic bunch.
• A second bunch is generated by the breaking of
  the second crest behind the pulse. It is less
  focused and accelerated than the first bunch.

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2.5D PIC results 9

• Beam quality a beam with a remarkably good
  quality can be produced by selecting the first
  electron bunch (e. g. with a bending magnet).

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Conclusions

• We have investigated by means of a 2.5D PIC code
  developed by H. Ruhl the interaction of an
  ultrashort laser pulse with a preformed plasma
  whose electron density presents a sharp density
  transition.
• There is a clear evidence of the longitudinal
  breaking of the Langmuir wave which injected
  about 108 electrons in the accelerating phase.
• The number of electrons is well below the number
  that can be estimated in a gentle transition
  condition (109)
• The produced electron bunch has a very good beam
  quality
• Future work
• Systematic study of the dependence of the beam
  charge and quality on the density transition
  amplitude and scalelength.
• Explore the relativistic quivering regime
• Experimental study of the injection and
  acceleration processes.

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2.5D PIC results