8.4 Chaotic Motion due to External Force
Let us consider the physics of generation of hot electrons by stochastic process of
electron motion in laser field instead of the ponderomotive force we mentioned
before. It became clear in Chap. 7 that the laser absorption is high and hot electron
temperature is also high in general for the case with pre-formed plasmas. Pre-formed
plasma is beneficial to enhance the laser-electron interaction; consequently better
coupling is expected. This is the reason for the use of foam layered or structured
targets for higher energy conversion of laser to plasmas. We did not study so far the
physical mechanism of enhanced absorption in low-density plasma region. In the
relativistic laser and plasma interaction, the chaotic heating of electrons becomes
most dominant mechanism. Note that this process is in general not seen in the case of
non-relativistic laser interaction. Electron orbits in non-relativistic laser are generally
stable because it is a simple linear motion, and there is a threshold for the chaotic
heating as seen below.
8.4.1 Simple Example [1] (Random Force)
In this section, a brief introduction to the concept of chaos is given for a particle in an
external random force given by the equation:
Fig. 8.11 Time history of energy partition in laser-generated electrons, showing sustained absorption of up to 80% (absorbed laser energy flux through z ¼ 0 plane, dashed line) into relativistic
electrons (total electron energy flux projected on z, solid black line); also shown are contributions
from particles with energies E 1.5Ep ¼ 7 MeV and > 7 MeV; all values are normalized to peak
laser power P L 1.3 PW. [Figure 4 in Ref. 4]
8.4 Chaotic Motion due to External Force
305
Let us consider the physics of generation of hot electrons by stochastic process of
electron motion in laser field instead of the ponderomotive force we mentioned
before. It became clear in Chap. 7 that the laser absorption is high and hot electron
temperature is also high in general for the case with pre-formed plasmas. Pre-formed
plasma is beneficial to enhance the laser-electron interaction; consequently better
coupling is expected. This is the reason for the use of foam layered or structured
targets for higher energy conversion of laser to plasmas. We did not study so far the
physical mechanism of enhanced absorption in low-density plasma region. In the
relativistic laser and plasma interaction, the chaotic heating of electrons becomes
most dominant mechanism. Note that this process is in general not seen in the case of
non-relativistic laser interaction. Electron orbits in non-relativistic laser are generally
stable because it is a simple linear motion, and there is a threshold for the chaotic
heating as seen below.
8.4.1 Simple Example [1] (Random Force)
In this section, a brief introduction to the concept of chaos is given for a particle in an
external random force given by the equation:
Fig. 8.11 Time history of energy partition in laser-generated electrons, showing sustained absorption of up to 80% (absorbed laser energy flux through z ¼ 0 plane, dashed line) into relativistic
electrons (total electron energy flux projected on z, solid black line); also shown are contributions
from particles with energies E 1.5Ep ¼ 7 MeV and > 7 MeV; all values are normalized to peak
laser power P L 1.3 PW. [Figure 4 in Ref. 4]
8.4 Chaotic Motion due to External Force
305