# Persistence of precursor waves in two-dimensional relativistic shocks

## TL;DR

This study uses two-dimensional particle-in-cell simulations to analyze the persistence and efficiency of precursor electromagnetic waves in relativistic shocks, revealing their potential role in electron acceleration.

## Contribution

It demonstrates that precursor wave emission persists in 2D shocks even at low magnetizations, contrasting with 1D results, and explores implications for wakefield acceleration.

## Key findings

- Precursor waves persist at low magnetization in 2D simulations.
- Wave amplitudes are smaller than in 1D but still significant.
- Electromagnetic waves disturb upstream medium, forming density structures.

## Abstract

We investigated the efficiency of coherent upstream large-amplitude electromagnetic wave emission via synchrotron maser instability at relativistic magnetized shocks by using two-dimensional particle-in-cell simulations. We considered the purely perpendicular shock in an electron-positron plasma. The coherent wave emission efficiency was measured as a function of the magnetization parameter {\sigma}, which is defined by the ratio of the Poynting flux to the kinetic energy flux. The wave amplitude was systematically smaller than that observed in one-dimensional simulations. However, it continued to persist, even at a considerably low magnetization rate, where the Weibel instability dominated the shock transition. The emitted electromagnetic waves were sufficiently strong to disturb the upstream medium, and transverse filamentary density structures of substantial amplitude were produced. Based on this result, we discuss the possibility of the wakefield acceleration model for the production of non-thermal electrons in a relativistic magnetized ion-electron shock.