Generation mechanism of power law energy distribution in an expanding thin-foil plasma irradiated by intense lasers

Power law energy spectra consisting of high energy particles have been observed ubiquitously in nature such as cosmic rays in astrophysical plasmas, and are considered to be generated via multiple-scattering processes in electric/magnetic/electromagnetic fields. However, the critical details of the acceleration, diffusion and relaxation processes that lead to the observed superthermal distributions have not understood completely. In intense laser-produced plasmas, the strong laser field in the intensity level exceeding $10^{18}$ W/cm$^{2}$ and self-generated fields play a role in stochastic multiple-scattering which dominates the electron acceleration and heating [1, 2]. In this study, by using the particle-in-cell simulation, we found that the high energy tail of the electron energy spectrum becomes power law distribution, so called the ‘kappa distribution’ [3], in the interaction between a thin-foil plasma and a multi-picosecond high intensity laser. We discuss the generation mechanism of the power law tail relating to the multiple-scattering of electrons in the expanding foil plasma in details. [1] Y. Sentoku et al., Phys. Rev. Lett. 90, 155001 (2003). [2] N. Iwata et al., Phys. Plasmas 24, 073111 (2017). [3] A. Hasegawa et al., Phys. Rev. Lett. 54, 2608 (1985).