# Physics of relativistic collisionless shocks: II Dynamics of the background plasma

## TL;DR

This paper investigates the dynamics of background plasma in relativistic collisionless shocks, modeling its deceleration and heating through microturbulence interactions and validating the model with PIC simulations.

## Contribution

It introduces a combined fluid and kinetic model to describe plasma deceleration and heating, matching simulation results and providing a microscopic understanding of shock transition.

## Key findings

- The deceleration law relates Lorentz factor to beam pressure as γ_p ∼ ξ_b^(-1/2).
- The kinetic model reproduces plasma heating and deceleration observed in PIC simulations.
- The combined approach offers a successful 1D microscopic description of shock transition.

## Abstract

In this second paper of a series, we discuss the dynamics of a plasma entering the precursor of an unmagnetized, relativistic collisionless pair shock. We discuss how this background plasma is decelerated and heated through its interaction with a microturbulence that results from the growth of a current filamentation instability (CFI) in the shock precursor. We make use, in particular, of the reference frame $\mathcal R_{\rm w}$ in which the turbulence is mostly magnetic. This frame moves at relativistic velocities towards the shock front at rest, decelerating gradually from the far to the near precursor. In a first part, we construct a fluid model to derive the deceleration law of the background plasma expected from the scattering of suprathermal particles off the microturbulence. This law leads to the relationship $\gamma_{\rm p}\,\sim\,\xi_{\rm b}^{-1/2}$ between the background plasma Lorentz factor $\gamma_{\rm p}$ and the normalized pressure of the beam $\xi_{\rm b}$; it is found to match nicely the spatial profiles observed in large-scale 2D3V particle-in-cell simulations. In a second part, we model the dynamics of the background plasma at the kinetic level, incorporating the inertial effects associated with the deceleration of $\mathcal R_{\rm w}$ into a Vlasov-Fokker-Planck equation for pitch-angle diffusion. We show how the effective gravity in $\mathcal R_{\rm w}$ drives the background plasma particles through friction on the microturbulence, leading to efficient plasma heating. Finally, we compare a Monte Carlo simulation of our model with dedicated PIC simulations and conclude that it can satisfactorily reproduce both the heating and the deceleration of the background plasma in the shock precursor, thereby providing a successful 1D description of the shock transition at the microscopic level.