1.5.2 Relativistic Laser and Solid Interaction
For the purpose of applications, many experiments have been done in the last two
decades by irradiating a variety of solid targets with relativistic lasers. Many papers
have been published by varying mainly the laser intensity and target conditions.
Most of the data have been analyzed with use of Particle-in-Cell (PIC) simulations.
One-, two-, and three-dimensional simulations have been carried out to explain the
corresponding experimental results. It is surprising that in most of cases, good
agreement with the experimental data is obtained. However, there are limited cases
where the effort aims to clarify the physics and propose some model equation. In the
early time of research, the experimental results were dependent on the condition of
each laser. One of the big issues giving the laser dependence is the so-called the
pedestal accompanying the main ultra-short pulse. The duration of the pedestal
pulse is in the range of nanosecond.
Even if the intensity ratio of the pedestal to the main pulse is about 10 orders of
magnitude different, the solid surface is melted, and pre-formed plasma is formed.
The density of pre-formed plasma is usually lower than the cut-off density, and the
relativistic laser dominantly interacts with the pre-formed plasma. For example, the
intensity dependence of laser absorption fraction strongly depends on the energy
ratio of the pedestal to the main pulse. Such a fact has been clarified as phenomena
after comparison of experiments among different facilities. Review of the result of
such interaction experiments is given in Chap. 7. A brief survey is also given about
the structured targets widely used recently.
1.5.3 Theory of Chaotic and Stochastic Heating
Final Chaps. 8 and 9 are devoted to theoretical study of electron acceleration by
relativistic Lorentz force in low-density plasma. In the case where laser linearly
polarized in the y-direction is propagating to the x-direction, it is shown that an
electron momentum normalized by mc is obtained analytically after solving (1.3.8).
p y ¼ a 0 sin kx À ωt
ð
Þþβ
ð1:5:1Þ
p x ¼γ À α
¼
1
2α
p
2
y þ 1 À α
2
,
ð1:5:2Þ
where α and β are integration constants, and the first term on RHS in (1.5.1) is the
vector potential of laser with the normalized amplitude defined in (1.3.11).
The constants are given from the initial condition, and β ¼ 0 is assumed without
loss of generality. The value of the constant α (>0) is very important for efficient
acceleration of electrons. High-energy acceleration is expected if some way can
1.5 Relativistic Laser-Plasma Interaction
21
For the purpose of applications, many experiments have been done in the last two
decades by irradiating a variety of solid targets with relativistic lasers. Many papers
have been published by varying mainly the laser intensity and target conditions.
Most of the data have been analyzed with use of Particle-in-Cell (PIC) simulations.
One-, two-, and three-dimensional simulations have been carried out to explain the
corresponding experimental results. It is surprising that in most of cases, good
agreement with the experimental data is obtained. However, there are limited cases
where the effort aims to clarify the physics and propose some model equation. In the
early time of research, the experimental results were dependent on the condition of
each laser. One of the big issues giving the laser dependence is the so-called the
pedestal accompanying the main ultra-short pulse. The duration of the pedestal
pulse is in the range of nanosecond.
Even if the intensity ratio of the pedestal to the main pulse is about 10 orders of
magnitude different, the solid surface is melted, and pre-formed plasma is formed.
The density of pre-formed plasma is usually lower than the cut-off density, and the
relativistic laser dominantly interacts with the pre-formed plasma. For example, the
intensity dependence of laser absorption fraction strongly depends on the energy
ratio of the pedestal to the main pulse. Such a fact has been clarified as phenomena
after comparison of experiments among different facilities. Review of the result of
such interaction experiments is given in Chap. 7. A brief survey is also given about
the structured targets widely used recently.
1.5.3 Theory of Chaotic and Stochastic Heating
Final Chaps. 8 and 9 are devoted to theoretical study of electron acceleration by
relativistic Lorentz force in low-density plasma. In the case where laser linearly
polarized in the y-direction is propagating to the x-direction, it is shown that an
electron momentum normalized by mc is obtained analytically after solving (1.3.8).
p y ¼ a 0 sin kx À ωt
ð
Þþβ
ð1:5:1Þ
p x ¼γ À α
¼
1
2α
p
2
y þ 1 À α
2
,
ð1:5:2Þ
where α and β are integration constants, and the first term on RHS in (1.5.1) is the
vector potential of laser with the normalized amplitude defined in (1.3.11).
The constants are given from the initial condition, and β ¼ 0 is assumed without
loss of generality. The value of the constant α (>0) is very important for efficient
acceleration of electrons. High-energy acceleration is expected if some way can
1.5 Relativistic Laser-Plasma Interaction
21