suggested that the absorption efficiency decreases in proportion to t
-1/2 as shown in
(9.6.4”).
9.4.2 Local and Nonlocal: Gaussian and Lorentzian
Consider that in laser-plasma interaction, filaments of laser shown in Fig. 9.1 induce
not only small phase jumps as modeled by Fokker-Planck equation in (9.2.16), but
also large phase jumps like Levy flights. Then, it is reasonable to consider that the
particle energy is evolved by both stochastic processes, namely, the Gaussian and
Lorentzian probabilities in (9.2.16). In Fig. 9.9, 100% Lorentzian is plotted by blue,
90% Gaussian and 10% Lorentzian is by orange, and 1% Lorentzian is plotted by
green. In Fig. 9.9, Dt ¼ 50 has been assumed.
In real experiment, it is reasonable to consider that the filamentation and modulation instabilities are induced and electrons are stochastically accelerated in the
interaction region. Such an experiment has been reported in Ref. [16], and the
authors insisted that the wake field acceleration is taken place in the laser-focused
capillary to result the accelerated electrons with the power law spectrum. In the
present Levy flight model, it is possible to explain the experimental spectrum with
the assumption that the stochastic probability of 90% local Gaussian diffusion and
10% nonlocal Levy’s flights.
The experimental data of the electron distribution function is given in Fig. 9.10. It
is surprising that the assumption of 10% Levy’s jump can reproduce the experimental spectrum. If this is the case, the physics of electron acceleration changes
completely. The distribution of Fig. 9.9 is obtained by the stochastic heating only
by relativitic laser field. However, the conclusion of Ref. [16] is that the electrons are
accelerated by the wake fields generated by the ponderomotive force by the relativistic lasers. Which one is correct is still open question, but identification of which is
very important in stochastic particle acceleration physics.
Fig. 9.9 The electron
energy distribution obtained
with the combination of
Gaussian and Lorentzian
distributions, where the
percent is the fraction of
Lorentzian one
9.4 Time Evolution of Distribution and Fractal Index α
349
-1/2 as shown in
(9.6.4”).
9.4.2 Local and Nonlocal: Gaussian and Lorentzian
Consider that in laser-plasma interaction, filaments of laser shown in Fig. 9.1 induce
not only small phase jumps as modeled by Fokker-Planck equation in (9.2.16), but
also large phase jumps like Levy flights. Then, it is reasonable to consider that the
particle energy is evolved by both stochastic processes, namely, the Gaussian and
Lorentzian probabilities in (9.2.16). In Fig. 9.9, 100% Lorentzian is plotted by blue,
90% Gaussian and 10% Lorentzian is by orange, and 1% Lorentzian is plotted by
green. In Fig. 9.9, Dt ¼ 50 has been assumed.
In real experiment, it is reasonable to consider that the filamentation and modulation instabilities are induced and electrons are stochastically accelerated in the
interaction region. Such an experiment has been reported in Ref. [16], and the
authors insisted that the wake field acceleration is taken place in the laser-focused
capillary to result the accelerated electrons with the power law spectrum. In the
present Levy flight model, it is possible to explain the experimental spectrum with
the assumption that the stochastic probability of 90% local Gaussian diffusion and
10% nonlocal Levy’s flights.
The experimental data of the electron distribution function is given in Fig. 9.10. It
is surprising that the assumption of 10% Levy’s jump can reproduce the experimental spectrum. If this is the case, the physics of electron acceleration changes
completely. The distribution of Fig. 9.9 is obtained by the stochastic heating only
by relativitic laser field. However, the conclusion of Ref. [16] is that the electrons are
accelerated by the wake fields generated by the ponderomotive force by the relativistic lasers. Which one is correct is still open question, but identification of which is
very important in stochastic particle acceleration physics.
Fig. 9.9 The electron
energy distribution obtained
with the combination of
Gaussian and Lorentzian
distributions, where the
percent is the fraction of
Lorentzian one
9.4 Time Evolution of Distribution and Fractal Index α
349