Formation of power law energy distribution via stochastic process in a relativistic laser-driven bouncer*

Non-Maxwellian energy distributions are ubiquitous in nature, many of which are considered to be generated via non-thermal stochastic interactions.The well-known example is the power law energy distribution of cosmic rays described by the Fermi acceleration [1]. We found that picosecond (ps) relativistic laser-foil interactions can result a stochastic electron acceleration [2] which resembles the Fermi acceleration described by the bouncer model [3]. In the ps interaction, superthermal electrons increase especially after the transition from the hole boring to the plasma blowout [4]. Based on the Fokker-Planck equation, we developed a theory of power law electron spectrum formation in the laser-foil system. We found that the p² difference between acceleration (diffusion) and dissipation in the blowout phase leads a power law distribution with index given by the ratio of the dissipation and diffusion coefficients. The kJ-class laser experiments thus can be a platform for investigating energy distribution formation in collisionless plasmas. 

[1] E. Fermi, Phys. Rev. 75, 1169 (1949), [2] N. Iwata et al., Phys. Plasmas 24, 073111 (2017),[3] A. J. Lichtenberg, et al., Physica 1D, 291 (1980),[4] N. Iwata et al., Nat. Commun. 9, 623 (2018).