The left figure is, on the other hand, the same electric field profile observed in 2D
PIC simulation for realistic plasma. Since the cutoff density surface is deformed by
the ponderomotive force and the conductivity of the over dense region is not perfect,
the reflected laser profile is strongly modified compared to the right figure. Typical
particle trajectories are also shown with thin black lines in both cases. It is clear that
in the ideal case, most of electrons are accelerated by the reflected laser field toward
the laser incident direction by following the relation (8.2.4), while in the real plasma,
the phase shift and self-generated magnetic field confine the trajectories, and the
electron acceleration is boosted.
It is very hard to study quantitatively the physics of coupling and hot electron
generation of the structured targets shown in Chap. 7. In order to know a part of
multi-dimensional effect, it is useful to introduce the following 2D PIC simulation
result. Surface-corrugated solid target is used to simulate the effect of the surface
irregularity for the case with laser intensity of 4.65 Â 10
19 W/cm
2 at λ ¼ 0.53 μm
with linear polarization in the z-direction. The pulse duration is 200 fs.
The target parameter is changed from flat to the sinusoidal surface with the
amplitude of H ¼ λ and the wavelength of Λ ¼ 2 λ. It is concluded that the
absorption efficiency ~5% for the flat target has been increased to ~50% with such
surface corrugation. Almost static magnetic field generation is concluded to play an
important role in absorption enhancement and stochastic heating of electrons, where
the random reflection of the laser also enhances the stochastic of the electron
acceleration as seen above.
8.7 Electron Motion in Two Counter-Propagating
Relativistic Lasers
There are more general cases where the incidence of relativistic laser induces chaotic
motion of electrons in under-dense plasma. As seen in Chap. 7, substantial fraction
of incident laser is reflected. It is, therefore, more natural to consider the electron
motions in both of incident and reflected relativistic laser field. Of course, depending
on the incident condition to a target, there is freedom about the combination of field
polarizations, propagating directions, intensity difference, etc. Let us consider the
case that the incident and reflected relativistic lasers are counter-propagating in the xand –x-directions, respectively.
The stochasticity of charged particles in plasma has been studied for a long time.
The pioneering work is done by Boris Chirikov in 1959 to study the stability of
plasma confinement by open magnetic device, so-called mirror machine [17]. Such
chaos appears in many cases in plasma physics, for example, magnetic island in
toroidal configurations, ion heating by lower-hybrid waves, wave instability saturated via harmonic generation, etc. In laser-produced plasmas, hot electron generations observed experiment with relativistic lasers are mostly because of the
stochastic heating of electrons as see below. It is noted that paying attention to the
322
8 Chaos due to Relativistic Effect
PIC simulation for realistic plasma. Since the cutoff density surface is deformed by
the ponderomotive force and the conductivity of the over dense region is not perfect,
the reflected laser profile is strongly modified compared to the right figure. Typical
particle trajectories are also shown with thin black lines in both cases. It is clear that
in the ideal case, most of electrons are accelerated by the reflected laser field toward
the laser incident direction by following the relation (8.2.4), while in the real plasma,
the phase shift and self-generated magnetic field confine the trajectories, and the
electron acceleration is boosted.
It is very hard to study quantitatively the physics of coupling and hot electron
generation of the structured targets shown in Chap. 7. In order to know a part of
multi-dimensional effect, it is useful to introduce the following 2D PIC simulation
result. Surface-corrugated solid target is used to simulate the effect of the surface
irregularity for the case with laser intensity of 4.65 Â 10
19 W/cm
2 at λ ¼ 0.53 μm
with linear polarization in the z-direction. The pulse duration is 200 fs.
The target parameter is changed from flat to the sinusoidal surface with the
amplitude of H ¼ λ and the wavelength of Λ ¼ 2 λ. It is concluded that the
absorption efficiency ~5% for the flat target has been increased to ~50% with such
surface corrugation. Almost static magnetic field generation is concluded to play an
important role in absorption enhancement and stochastic heating of electrons, where
the random reflection of the laser also enhances the stochastic of the electron
acceleration as seen above.
8.7 Electron Motion in Two Counter-Propagating
Relativistic Lasers
There are more general cases where the incidence of relativistic laser induces chaotic
motion of electrons in under-dense plasma. As seen in Chap. 7, substantial fraction
of incident laser is reflected. It is, therefore, more natural to consider the electron
motions in both of incident and reflected relativistic laser field. Of course, depending
on the incident condition to a target, there is freedom about the combination of field
polarizations, propagating directions, intensity difference, etc. Let us consider the
case that the incident and reflected relativistic lasers are counter-propagating in the xand –x-directions, respectively.
The stochasticity of charged particles in plasma has been studied for a long time.
The pioneering work is done by Boris Chirikov in 1959 to study the stability of
plasma confinement by open magnetic device, so-called mirror machine [17]. Such
chaos appears in many cases in plasma physics, for example, magnetic island in
toroidal configurations, ion heating by lower-hybrid waves, wave instability saturated via harmonic generation, etc. In laser-produced plasmas, hot electron generations observed experiment with relativistic lasers are mostly because of the
stochastic heating of electrons as see below. It is noted that paying attention to the
322
8 Chaos due to Relativistic Effect