9.5.2 Model Experiments with Relativistic Lasers
The proof of principle experiment can be designed regarding the direct acceleration
of cosmic ray by EM waves in laboratory as a challenging problem of laboratory
astrophysics. When a relativistic laser is injected into low-density plasma like gas jet
plasma, the experimental data of the electron distribution function can be compared
to the theoretical models. If the power law spectra are obtained from the experiment,
we can try to identify the best index of α in (9.4.3) and (9.4.4) to identify the
acceleration physics. The identification of the index α is a big step to study the
anomalous transport in the momentum space in the relativistic fields as has been
done for charged particle transport in Tokamak turbulence to be discussed below.
The advantage of the direct acceleration by EM waves is that the energy conversion rate to cosmic rays is expected higher than the acceleration by the wake field
generated by the EM waves. Analysis of the details of the experiment data of
Figs. 9.10 and 8.22b would be beneficial as the starting point of such research.
Finally, it should be noted that the high-energy electrons are accelerated though the
jumps in many phases of laser field. That is, it should be careful as mentioned in [16]
[Fig. 8.20] that the PIC simulation should be used so as to resolve the fine structure
of laser field distribution. Especially, it is almost impossible to study such Levy-type
acceleration in the simulation shown in Fig. 9.13, because the precise resolution of
the phase of electric and magnetic field in the precursor waves needs a huge number
of computational meshes. The better way is to start with a model simulation with EM
waves.
In Fig. 9.14, 2D PIC simulation result on the time evolution of the ion and
electron energy distributions is plotted [23]. The power law spectra are generated
as the envelope of the tails of the distribution functions. The simulation condition is
that the Lorentz factor of the propagating velocity of the collisionless shock is
γ sh ¼ 15, the mass ratio is 25, and magnetization parameter is σ ¼ 10
À5 . It is
observed that the both distributions are showing the power laws with k ¼ 3.0 (ions)
and k ¼ 2.5 (electrons) as shown in Fig. 9.14. The time evolution of the maximum
energies is also important. It is reported [23] that both ion and electron maximum
energies are proportional to
γ max / t
1=2
ð9:4:17Þ
and Bohm limit in strong magnetic fields is
γ max / t
ð9:4:18Þ
Comparing both time dependences to (9.4.13), it is important to know that the
cosmic ray generation rate is also in the rage of 1/2
C
1in (9.4.13). It is
reasonable to consider that the difference of (9.4.17) and (9.4.18) is due to the
local or nonlocal properties of acceleration corresponding to the difference of
(9.4.17) and (9.4.18), respectively.
9.5 Model Experiment of Cosmic Ray Physics in the Universe
357
The proof of principle experiment can be designed regarding the direct acceleration
of cosmic ray by EM waves in laboratory as a challenging problem of laboratory
astrophysics. When a relativistic laser is injected into low-density plasma like gas jet
plasma, the experimental data of the electron distribution function can be compared
to the theoretical models. If the power law spectra are obtained from the experiment,
we can try to identify the best index of α in (9.4.3) and (9.4.4) to identify the
acceleration physics. The identification of the index α is a big step to study the
anomalous transport in the momentum space in the relativistic fields as has been
done for charged particle transport in Tokamak turbulence to be discussed below.
The advantage of the direct acceleration by EM waves is that the energy conversion rate to cosmic rays is expected higher than the acceleration by the wake field
generated by the EM waves. Analysis of the details of the experiment data of
Figs. 9.10 and 8.22b would be beneficial as the starting point of such research.
Finally, it should be noted that the high-energy electrons are accelerated though the
jumps in many phases of laser field. That is, it should be careful as mentioned in [16]
[Fig. 8.20] that the PIC simulation should be used so as to resolve the fine structure
of laser field distribution. Especially, it is almost impossible to study such Levy-type
acceleration in the simulation shown in Fig. 9.13, because the precise resolution of
the phase of electric and magnetic field in the precursor waves needs a huge number
of computational meshes. The better way is to start with a model simulation with EM
waves.
In Fig. 9.14, 2D PIC simulation result on the time evolution of the ion and
electron energy distributions is plotted [23]. The power law spectra are generated
as the envelope of the tails of the distribution functions. The simulation condition is
that the Lorentz factor of the propagating velocity of the collisionless shock is
γ sh ¼ 15, the mass ratio is 25, and magnetization parameter is σ ¼ 10
À5 . It is
observed that the both distributions are showing the power laws with k ¼ 3.0 (ions)
and k ¼ 2.5 (electrons) as shown in Fig. 9.14. The time evolution of the maximum
energies is also important. It is reported [23] that both ion and electron maximum
energies are proportional to
γ max / t
1=2
ð9:4:17Þ
and Bohm limit in strong magnetic fields is
γ max / t
ð9:4:18Þ
Comparing both time dependences to (9.4.13), it is important to know that the
cosmic ray generation rate is also in the rage of 1/2
C
1in (9.4.13). It is
reasonable to consider that the difference of (9.4.17) and (9.4.18) is due to the
local or nonlocal properties of acceleration corresponding to the difference of
(9.4.17) and (9.4.18), respectively.
9.5 Model Experiment of Cosmic Ray Physics in the Universe
357