Shock formation in electron-ion plasmas: mechanism and timing

TL;DR

This paper develops a theoretical model for the timing of shock formation in electron-ion plasmas, highlighting the role of filament merging and the extended duration compared to pair shocks.

Contribution

It introduces a new theoretical framework for calculating shock formation time, incorporating filament merging dynamics in electron-ion plasmas.

Findings

Shock formation time scales with sqrt(m_i/m_e) ln(m_i/m_e)

Filament merging significantly delays shock formation

The model aligns with simulation results on shock timing

Abstract

We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account the filament merging in the non-linear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, so that the shock formation is longer by a factor proportional to sqrt(m_i/m_e) ln(m_i/m_e).