Generation of particle beams and Xrays in ultrarelativistic laserplasmas'

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Generation of particle beams and X-rays in
ultra-relativistic laser-plasmas.
A. Pukhov1, S. Gordienko1,2, T. Baeva1,
O.Shorokhov1, S. Kiselev1 1Institut für
Theoretische Physik Universität
Düsseldorf 2L.D.Landau Institute for Theoretical
Physics, Moscow
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Outline

• Ultra-relativistic similarity theory
• Origin of the ponderomotive scalingsfor
  electron temperatures
• Experimental observation of Weibel instability
• High harmonics from plasma surfaces the
  universal power-law spectra up to X-raysand
  coherent focusing

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S-Similarity for Ultra-Relativistic Plasmas,
Il2?1018 Wmm2/cm2
Gordienko, Pukhov Phys. Plasmas 12, 043109 (2005)
The similarity parameter (S-number)
Valid for the Vlasov-Maxwell electron dynamics,
a02?1
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S-Similarity for Ultra-Relativistic Plasmas,
Il2?1018 Wmm2/cm2
Gordienko, Pukhov Phys. Plasmas 12, 043109 (2005)
The similarity parameter (S-number)
Dynamics of plasmas with Sconst is similar.
Electrons move along the same trajectories,
their momenta scale as
The S-number has the role of relativistically
corrected plasma density.It separates
relativistically overdense plasmas,
Sgtgt1, from relativistically underdense ones,
Sltlt1.
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Scalability of laser-plasmas, Sconst
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Similarity in Fast Ignition contextponderomotiv
e temperatures
Why these scalings?
Electron energies scale as I1/2 a.Electron
numbers scale as I1/2 a.
Interaction regime is quite complex and clearly
non-ponderomotive
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Ponderomotive temperaturesin exponential
preplasmas
Ponderomotive scalings are in fact similarity
scalings!
Interaction is automatically self-similar,
because laser pulses are always reflectedat the
relativistic critical density, S 1.
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The RAL Experiment
R. Jung, et al. Phys. Rev. Lett. 94, 195001 (2005)
VULCAN Laser Energy 350 J duration 750 fs
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The RAL Experiment Electron Spectra
R. Jung, et al. Phys. Rev. Lett. 94, 195001 (2005)
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Experimental observation of the Weibel
Instability
R. Jung, J. Osterholz, K. Lowenbruck, S. Kiselev,
G. Pretzler, A. Pukhov, O. Willi, S. Kar, M.
Borghesi, W. Nazarov, S. Karsch, R. Clarke, D.
Neely Phys. Rev. Lett. 94, 195001 (2005)
Laser 350 J, 750 fs
Second harmonic emission from rear surface of
250 µm foam target.
Two concentric circles of filaments
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Nonlinear Weibel Instability
2D PIC simulations by Honda et al., Phys. Rev.
Lett. (2000).
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Filamentation, 3D PIC Simulation
()
(?)
(?) Transverse cuts of electron
density () The x-component of the
quasi-static magnetic field.
10µm
()
(?)
20µm
(?)
()
Two rings of filaments
100µm
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Harmonics from plasma surfacesthe analytical
theory
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 93, 115002 (2004).
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 94, 103903 (2004).
Relativistically oscillatingapparent reflection
point E?(X(t))0.
X(t), g(t)
Ion boundary
The reflected pulse contains high harmonics
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Analytical Form of the Universal Spectrum
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 94, 103903 (2004).
Similarity theory states that g ? a if S const.
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Reflected radiation spectra in 1D PIC simulations
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 93, 115002 (2004).
I w-2.5
The Gaussian laser pulse aa0exp-(t/t)2cosw0t
is incident onto an overdense plasma layer with
n30nc, wt4p. The color lines correspond to
laser amplitudes a05,10,20.The broken line
marks the analytical scaling I w-2.5.
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Temporal profile of the reflected radiation
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 93, 115002 (2004).
Unfiltered signal train of attosecond pulses
Harmonics with nlt300 filtered out train of
zeptosecond pulses
Reflected signal intensity, a.u.
the 300-zeptosecond pulse zoomed
wt / 2p
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Characteristics of the plasma harmonics

• The spectrum is the universal slow-decaying power
  law Iw w-2.5.
• The cut-off frequency scales fast with the plasma
  g-factor wc / w0 8g3max
• The shortest pulse duration scales as
  t1/wc1/8g3max
• The harmonics are coherent and phase-locked

References 1. S. Gordienko, A. Pukhov, O.
Shorokhov, T. Baeva, submitted (2004).
2. L. Plaja, L. Roso, K. Rzazewski,
M. Lewenstein, J. Opt. Soc. Am. B 7, 1904
(1998). 3. R. Lichters,
J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3,
3425 (1996). 4. S. V.
Bulanov, N. M. Naumova, F. Pegoraro, Phys.
Plasmas 1, 745 (1994). 5.
I. Watts, M.Zepf, et al, Phys. Rev. Lett. 88,
155001-1 (2002).
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Coherent Harmonics Focusing
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva,
Phys. Rev. Lett. 94, 103903 (2004).
Because all the harmonics are phase locked, their
fields in the focus interfere constructively
leading to an enormous intensity boost
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3D PIC Simulation of CHF
CHF
Laser pulse with a03 is reflected from a concave
plasma surface with n/nc5, focal distance R04l.
Linear focusing
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The CHF Intensity Scaling from 1D PIC Simulations
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Summary

• Ultra-relativistic laser-plasmas are
  characterized by the similarity number S ne /
  anc
• Spectra with ponderomotive temperatures are in
  fact due to the S-similarity scalings
• Weibel instability has been observed
  experimentally
• Harmonics from plasma surfaces are phase-locked,
  coherent and have universal power-law spectra
• The Coherent Harmonics Focusing may boost the
  intensity above the vacuum breakdown threshold