A note on the theory of transverse diffusion in shock particle acceleration

TL;DR

This paper explores how the form of the spatial diffusion coefficient influences shock acceleration of particles, demonstrating that non-classical, Levy flight diffusion aligns well with simulation results in high-Mach shocks.

Contribution

It provides a theoretical and numerical analysis showing non-classical diffusion, specifically Levy flights, governs particle acceleration in collisionless shocks.

Findings

Diffusion coefficients match theoretical predictions

Diffusion is non-classical and Levy flight-like

Diffusion is weakly time-dependent

Abstract

We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock population in quasi-perpendicualr high-Mach number collisionless shocks to which we apply the theory, we demonstrate that the inferred diffusion coefficients are in excellent agreement with the requirements of the theory and its predictions. Diffusion in the collisionless regime turns out to be non-classical Gibbsian (L\'evy flight), time-dependent though weak.