Collisionless energy absorption in nanoplasma layer in regular and stochastic regimes.

Abstract
Collisionless energy absorption in 1D nanoplasma is considered. Straightforward classical calculation of the absorption
rate in action-angle variables is presented. In regular regime the result obtained is the same as in [4], but deeper insight is
possible now due to the technique used. Chirikov criterion of the chaotic absorption regime is written out. Collisionless
energy absorption rate in nanoplasma layer is calculated in stochastic regime.
1 Collisionless absorption in regular regime.
One of the novel problems of laser-matter interaction is the problem of energy absorption in nanometer targets subjected to
an ultrashort (up to few picosecond) intence (1013 − 1017W/cm2) laser fields. During such interaction hot (up to several keV
energy) classical plasma bounded in nanoscale volume is produced, which has a life time of about hundreds of femtoseconds.
This is dense plasma with the electron density of 1023cm−3 and more. Such systems are used to be called nanoplasma since
first experiments of intense short laser interaction with three-dimensional nanobodies (atomic Van-der-Vaals clusters) were
hold in 1996 [1].
Nanobodies are known to absorb much more compared to traditional targets like gas or even bulk. The great amount
of energy contained in tiny volume results in breakdown, birth of energetic particles and high harmonics generation [2,
3]. Different mechanisms of absorption were suggested to explain such phenomena. They are inner ionization, inverse
bremsstrahlung effect, vacuum heating, collisionless heating and some others a bit more sophisticated.
As far as nanoplasma is a strongly bounded system with the width much less than laser wave length, the most interesting
mechanism of energy absorption in it is collisionless heating in self-consistent potential. It was considered recently in onedimensional
systems corresponded to irradiated films and more deeply in three-dimesional systems which correspond to
nanoclusters; the important role of it in the absorption process was evidently shown (for 1D situation see [4]).
The problem of collisionless energy absorption in thin films irradiated by intence short laser pulse was considered in
[4] in the frames of the following model. First, the incompressible liquid approximation for the electronic cloud was used1
and both the self-consistent potential and distribution function were taken as if they are known function slowly changing
on times of the laser pulse duration. This means that the self-consisted system of Boltsman and Laplace equations was
supposed to be solved elsewhere. Then, in [4] dipole aproximation2 and the perturbation theory on the small parameter of
the dimensionless oscillation amplitude of the electron cloud3 was used. Here we use the same model. The calculation of
the rate of collisionless absorption presented in [4] was based on quantum-mechanical approach in quasiclassical limit. Note,
that the system considered is classical, and the final result in [4] does not contain Plank constant. Althogh this method is
non-contradictory, it hides some classical features of the system. The present paper has the aim to make the same calculation
for this system in the frames of classical mechanics and to learn more about it possible behaviour.
Let the particle is bounded.

In this expression all resonance levels take part in the absorption process simultaneously. Moreover, in such a situation
particle with arbitrary energy should gain energy from the external field. Formula (29) is the main result of the present work.
It describes the collisionless heating in 1D classical nanoplasma layer when the field strength is enough for chaotic regime to
take place, according to (23).
Author wish to thank S.V. Popruzhenko, D.F. Zaretsky, I.Yu. Kostyukov for fruitful discussions. The work was done with
the financial support of RFBR.
References
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[2] Jasapara J., Nampoothiri A. V. V., Rudolph W., Ristau D., Starke K., 2001, Phys. Rev.B 63, 045117
[3] Tom H.W.K., Wood O.R.II, Aumiller G.D., Rosen M.D. In: Springer series in chemical physics, Ultrafast phenomena
VII (Berlin, Heidelberg, Springer-Verlag, 1990, v.53, p.107-109).
[4] D.F. Zaretsky, Ph.A. Korneev, S.V. Popruzhenko and W. Becker, Journal of Physics B: Atomic, Molecular and Optical
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[5] Landau L D and Lifshitz E M 1979 Mechanics. (Oxford: Pergamon)
[6] Regular and Chaotic Dynamics, 2nd Edition; A.J. Lichtenberg, M.A. Lieberman, Springer Verlag, 1992
[7] Chirikov B.V., Phys. Reports, Vol.52, p.265 (1979)
[8] G.M. Zaslavsky, ”Stochasticity of the dynamical systems”, Moscow, ”Nauka”, 1984 (in russian).

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