# Physics of relativistic collisionless shocks: III The suprathermal particles

## TL;DR

This paper analyzes the physics of accelerated particles in relativistic collisionless shocks, providing theoretical estimates of their scattering length and distribution, validated by PIC simulations, advancing understanding of shock particle acceleration mechanisms.

## Contribution

It offers a new theoretical estimate of particle scattering length in unmagnetized relativistic shocks and compares it with simulation results, enhancing the understanding of particle acceleration.

## Key findings

- The scattering length scales with particle momentum and turbulence parameters.
- Good agreement between theoretical estimates and PIC simulation results.
- Provides a detailed distribution function for accelerated particles.

## Abstract

In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length $l_{scatt}(p)$ in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain $l_{scatt}(p) \simeq (\gamma_p /\epsilon_B)(p/\gamma_{\infty} mc)^2 (c/\omega_p)$, with p the particle momentum in the rest frame of the shock front, $\epsilon_B$ the strength parameter of the microturbulence, $\gamma_p$ the Lorentz factor of the background plasma relative to the shock front and $\gamma_{\infty}$ its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.