eigen value problem for the given boundary condition. This is the same as in solving
Schrodinger equation, and the K
2 in (4.10.7) is regarded to the kinetic energy, {E-U
(x)}. In (4.10.6), the eigen value is p
2 . With this analogy, it is easy to know the
property of (4.10.2) for more general case.
4.10.2 Nonlinear Saturation of SRS
In analyzing the experimental data, the linear analysis is useful to identify the
instability threshold. It is about 2 Â 10
15 W/cm
2 in experiment. With the phase
velocity shown in Fig. 4.11, the damping rate is evaluated. This damping is mainly
due to wave-particle interaction known as Landau damping to be explained in Vol. 3.
However, in order to explain the rapid growth and saturation of SRS reflectivity
shown in Fig. 4.10, a computer simulation is required. In Fig. 4.10, the simulation
result is plotted with red circles. The simulation could well explain the experimental
data. The nonlinear physics seen in the simulation is as follows.
In Ref. [9], it is insisted that Landau damping is stabilized in higher intensity by
electron trapping in the plasma wave potential. The electrons with velocities near the
phase velocity of the plasma waves directly interact the electrostatic field, and some
are accelerated, and some are decelerated. Landau damping is due to net energy
conversion from the waves to the electrons, because the number of the accelerating
electrons is larger than the decelerated ones in Boltzmann velocity distribution. Once
the wave amplitude becomes large, however, such trapped electrons take bounce
motions in the wave potential, and finally no net energy conversion happens. In
Fig. 4.11, a nonlinear dielectric function is plotted with a solid line by taking into
account the bounce motion by the trapped particle, where a new resonance appears
around the phase velocity 1.5.
For further increase of the laser intensity, it is expected that the wave amplitude
becomes higher, even though the particle trapping is taken place. As seen in the large
amplitude plasma wave, however, the wave-breaking is induced to prevent the
further growth of wave amplitude. It is reasonable to understand that at the intensity
much higher than the threshold one, the particle trapping and wave-breaking are
simultaneously seen, and as a result, a part of the laser energy is converted to the
high-energy electron production. Namely, significant amount of SRS scattering
suggests a production of hot electrons in plasmas.
160
4 Nonlinear Physics of Laser-Plasma Interaction
Schrodinger equation, and the K
2 in (4.10.7) is regarded to the kinetic energy, {E-U
(x)}. In (4.10.6), the eigen value is p
2 . With this analogy, it is easy to know the
property of (4.10.2) for more general case.
4.10.2 Nonlinear Saturation of SRS
In analyzing the experimental data, the linear analysis is useful to identify the
instability threshold. It is about 2 Â 10
15 W/cm
2 in experiment. With the phase
velocity shown in Fig. 4.11, the damping rate is evaluated. This damping is mainly
due to wave-particle interaction known as Landau damping to be explained in Vol. 3.
However, in order to explain the rapid growth and saturation of SRS reflectivity
shown in Fig. 4.10, a computer simulation is required. In Fig. 4.10, the simulation
result is plotted with red circles. The simulation could well explain the experimental
data. The nonlinear physics seen in the simulation is as follows.
In Ref. [9], it is insisted that Landau damping is stabilized in higher intensity by
electron trapping in the plasma wave potential. The electrons with velocities near the
phase velocity of the plasma waves directly interact the electrostatic field, and some
are accelerated, and some are decelerated. Landau damping is due to net energy
conversion from the waves to the electrons, because the number of the accelerating
electrons is larger than the decelerated ones in Boltzmann velocity distribution. Once
the wave amplitude becomes large, however, such trapped electrons take bounce
motions in the wave potential, and finally no net energy conversion happens. In
Fig. 4.11, a nonlinear dielectric function is plotted with a solid line by taking into
account the bounce motion by the trapped particle, where a new resonance appears
around the phase velocity 1.5.
For further increase of the laser intensity, it is expected that the wave amplitude
becomes higher, even though the particle trapping is taken place. As seen in the large
amplitude plasma wave, however, the wave-breaking is induced to prevent the
further growth of wave amplitude. It is reasonable to understand that at the intensity
much higher than the threshold one, the particle trapping and wave-breaking are
simultaneously seen, and as a result, a part of the laser energy is converted to the
high-energy electron production. Namely, significant amount of SRS scattering
suggests a production of hot electrons in plasmas.
160
4 Nonlinear Physics of Laser-Plasma Interaction