not stable, and the kinetic energy of the both currents is converted to the magnetic
field energy, and of course finally the magnetic energy is also converted to the
random motional energy of electrons. This is a thermalize process of statistical
mechanics in collisionless plasmas.
7.10 Multi-dimensional Physics in Pre-formed Plasmas
In Chap. 6, we have discussed the physics of relativistic laser propagation in
low-density plasmas. This is not simple, and still quantitative formulation based
on physics models is still open question. The multi-dimensional effect due to the
focused laser propagating in the pre-formed plasma is essential for the physics of
relativistic laser propagation and the interaction physics, such as laser absorption,
hot electron generation, magnetic field coupling, and so on. The physics of
relativistic laser interaction with plasma will be described in detail later. Let
us here briefly discuss a typical phenomenon seen in the pre-formed plasmas
as multi-dimensional effects, namely, self-focusing, filamentation instability,
magnetic field generation, and hot electron acceleration in the self-focused plasma
channel.
When a relativistic laser with strength a 0 is focused into the subcritical density
pre-formed plasma, its intensity increases toward the focusing point propagating
from the low density to the critical density. In general, the power of laser is much
higher than the critical power for the self-focusing in (6.5.19), and the laser is subject
to self-focus due to the change of the plasma dielectric constants in the laser
propagation path. The growth rate of the self-focusing is given as the solution of
(6.5.27) by setting the size of the laser beam equal to k y . The growth rate for large
beam size is given in (6.5.29), and it is written for the 1 μm wavelength laser in the
form:
1
γ
τ SF ¼ 4
n cr
n 0 a 2
0
fs
½
ð7:10:1Þ
Note that this is a very short time scale compared to the pulse duration for the
subcritical density plasma n 0 ~ n cr and relativistic laser a 0 > 1. For example, in the
case of pre-formed plasma shown with blue line in Fig. 7.2, the main laser intensity
is 10
19 W/cm
2 , and pulse duration is 30 fs. Inserting n 0 ~ n cr and a 0
2 ~ 10, the growth
time of the self-focusing τ SF is τ SF ¼ 0.4 fs. This value is very much shorter than the
laser duration 30 fs.
As clear from such evaluation, the most of the experiments of solid targets
discussed so far can be regarded that the self-focusing and resultant physics
controlled the physical phenomena in the pre-formed plasmas. The self-focusing is
282
7 Relativistic Laser and Solid Target Interactions
field energy, and of course finally the magnetic energy is also converted to the
random motional energy of electrons. This is a thermalize process of statistical
mechanics in collisionless plasmas.
7.10 Multi-dimensional Physics in Pre-formed Plasmas
In Chap. 6, we have discussed the physics of relativistic laser propagation in
low-density plasmas. This is not simple, and still quantitative formulation based
on physics models is still open question. The multi-dimensional effect due to the
focused laser propagating in the pre-formed plasma is essential for the physics of
relativistic laser propagation and the interaction physics, such as laser absorption,
hot electron generation, magnetic field coupling, and so on. The physics of
relativistic laser interaction with plasma will be described in detail later. Let
us here briefly discuss a typical phenomenon seen in the pre-formed plasmas
as multi-dimensional effects, namely, self-focusing, filamentation instability,
magnetic field generation, and hot electron acceleration in the self-focused plasma
channel.
When a relativistic laser with strength a 0 is focused into the subcritical density
pre-formed plasma, its intensity increases toward the focusing point propagating
from the low density to the critical density. In general, the power of laser is much
higher than the critical power for the self-focusing in (6.5.19), and the laser is subject
to self-focus due to the change of the plasma dielectric constants in the laser
propagation path. The growth rate of the self-focusing is given as the solution of
(6.5.27) by setting the size of the laser beam equal to k y . The growth rate for large
beam size is given in (6.5.29), and it is written for the 1 μm wavelength laser in the
form:
1
γ
τ SF ¼ 4
n cr
n 0 a 2
0
fs
½
ð7:10:1Þ
Note that this is a very short time scale compared to the pulse duration for the
subcritical density plasma n 0 ~ n cr and relativistic laser a 0 > 1. For example, in the
case of pre-formed plasma shown with blue line in Fig. 7.2, the main laser intensity
is 10
19 W/cm
2 , and pulse duration is 30 fs. Inserting n 0 ~ n cr and a 0
2 ~ 10, the growth
time of the self-focusing τ SF is τ SF ¼ 0.4 fs. This value is very much shorter than the
laser duration 30 fs.
As clear from such evaluation, the most of the experiments of solid targets
discussed so far can be regarded that the self-focusing and resultant physics
controlled the physical phenomena in the pre-formed plasmas. The self-focusing is
282
7 Relativistic Laser and Solid Target Interactions