Laser ion acceleration in a mass limited target

1
Laser ion acceleration in a mass limited target

• A.A.Andreev1, J.Limpouch2, K.Yu.Platonov1, J.Psik
  al2, V.T.Tikhonchuk3
• 1. ILPh Vavilov State Optical Institute ,
  Russia
• 2. Czech Technical University in Prague, Czechia
• 3. CELIA, Universite Bordeaux 1, France

2
Outline

• Motivation
• Numerical models 1D2D3V PIC
• Theoretical models quasi-neutral expansion of
  cold ions, two sorts of electrons, plane or
  spherical geometry, charged plasma expansion
• Study ion acceleration in mono- and multi-species
  MLT at high laser intensity
• Model ion acceleration at ultra-high intensities
• Conclusion

3
Acceleration of ions by fast electron current
A space charge created by fast electrons pulls
ions from the surface three stages - ionization
- extraction - acceleration
Electric field
4
Why a mass limited targets ?
5
Shapes of a mass limited targets
6
Analytical models of ion acceleration
Positive ions with electron admixture
 (1)2e (1)2i ? (one)two sorts of electrons (of
different temperatures) and (one)two sorts
of ions (of different mass) Rq
(mec2I18/e2ne0)1/2
7
Simulation model of 2.5 PIC calculations
The relativistic, electromagnetic code is used to
calculate the interaction of an intense laser
pulse with an over-dense plasma. The relativistic
equations of motion and the Maxwell equations are
solved for the components x, y, px, py, pz and
Ex, Ey and Bz ?Pj/?t qj(E vxB), ?jmj?r/?t
Pj, ?E/?t - Jj c2 rotB, ?B/?t - rotE .
 Particles
reaching the simulation box boundaries may be
either reflected or frozen at the boundaries. For
thick target special conditions is implemented at
the boundary in the target interior where fast
electrons leaving simulation region are replaced
by thermal electrons carrying the return current
J, Psikal A.Kemp, H.Ruhl.
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Electric field spatial distributions for H foil
and sphere targets
Normalized absolute value of electric field
during interaction of laser of amplitude a0 10,
pulse duration 10T and beam width 4 ? with
homogeneous plasma foil and sphere of initial
size 4 ? and density ne 4nc. The figures are
plotted in moments 5T after laser maximum reaches
the target front side.
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Electron distribution function for laser
interaction with spherical target
Dependence of the hot electron temperature
(average energy) at time t30 ? on laser
dimensionless amplitude for laser pulse duration
10? and beam width 4? and spherical target of
density ne  4nc and diameter 4?.
The electron DF a0 10, t35, tL 5T blue,
10T - green
10
Electric field spatial profiles for spherical H
MLT
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Proton spectra for H MLT of different shapes
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Dependence of ion maximal energy on laser field
amplitude for H spherical target

The maximum ion energy versus normalized laser
amplitude at time instance 50T. Target is plasma
sphere of diameter 4 ? and density ne 4 nc,
pulse duration 5T. Initial electron densities are
4, 4, 12, 36nc and initial temperature 10, 10,
50 200 keV for a 3, 10, 30 and 100
respectively.
13
Laser energy conversion to fast ions
The dependence of laser energy conversion to fast
ions dependence on ratio t_w (target width) to
I_w (laser beam width).
14
Multi-species targets laser interaction with
water micro droplet
15
Interaction with plastic flat foil section and
mono-energetic proton bunch formation
16
Interaction with plastic targets of different
shape and mono-energetic proton bunch formation
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Proton energy spectra versus plastic target shape
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Proton angular distribution and divergence
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Impact of plasma density profile
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Direct acceleration of overdense plasma bunch by
laser pulse of relativistic intensity
t 0, t30T,
t 50T Ion
density distributions calculated for the
different time moments Laser amplitude a0 10,
duration 5T, beam width 4 ? interacts with plasma
sphere of diameter 4 ?, ne 4nc.
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Direct acceleration of overdense plasma bunch by
laser pulse of ultra-relativistic intensity
Conservation lows of energy and impulse in the
lab frame
Piston regime Esirkepov et al.,
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Plasma density profiles at different time of
laser pulse interaction with over-dense plasma
foil target
T 93.3 fs
T 13.3 fs
T 93.3 fs
Laser intensity 3 x1023 W/cm2, spot size 15 mm,
pulse duration 40 fs, H target of solid density.
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Plasma density profiles at different time of
laser pulse interaction with over-dense plasma
sphere target
t 120 fs
t 200 fs
t 253 fs
t 0 fs
Laser intensity 3x1023 W/cm2, spot size 15 mm,
pulse duration 40 fs, hydrogen target of solid
density.
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Plasma density profiles at different time of
laser pulse interaction with semi-sphere foil
segment
T 93.3 fs
T 0 fs
T 120 fs
T 180 fs
T 240 fs
Laser intensity 3x1023 W/cm2, spot size 15 mm,
pulse duration 40 fs, hydrogen target of solid
density.
Maximal proton energy reaches 50 GeV for such
target
25
Dependence of maximal ion energy on laser
intensity for MLT target
Laser beam diameter 4?, pulse duration 10T,
hydrogen sphere of diameter 4?, ne 4nc
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Conclusions

• Mass limited targets enhance ion energy by
  limiting transverse dimension of sheath
• Diffracted light additionally accelerates
  electrons at MLT rear and produced electric field
  enhances ion energy.
• The optimal diameter of laser beam is about of
  target diameter for production of maximal ion
  energy at minimal geometrical losses.
• Droplet targets enhance proton energy but
  increase angular spread
• Multi-species MLT enable generation of
  mono-energetic proton bunches
• Direct acceleration of MLT by ultra-intense laser
  pulse (piston regime) permits to accelerate the
  target up to relativistic velocity and MLT
  propagates together with laser pulse on a long
  length. Laser field protects expansion of plasma
  bunch in transversal direction.
• The optimal shape of a laser piston target is
  hemi-sphere foil segment.
• Maximal proton energy at multi-PW laser power
  reaches 50 GeV for such target.

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CONFERENCE  HONORARY CHAIRS Zhores I. Alferov,
Ioffe Physical-Technical Institute, Russia
Charles H. Townes, Univ. of California, USA
CONFERENCE CHAIR A. A. Mak, Inst. for Laser
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