# Relativistic electron streaming instabilities modulate proton beams accelerated in laser-plasma interactions

## TL;DR

This study provides experimental evidence that relativistic electron streaming instabilities generate strong electromagnetic fields, modulating proton beams in laser-plasma interactions, with implications for optimizing proton acceleration.

## Contribution

The paper demonstrates the role of Weibel instability in electromagnetic field amplification affecting proton beam modulation in laser-driven plasma experiments.

## Key findings

- Electromagnetic fields exceeding 10 MG and 0.1 MV/μm are generated during proton acceleration.
- Proton modulation correlates with the development of filamentary electromagnetic fields.
- Results agree with 3D particle-in-cell simulations and analytical models.

## Abstract

We report experimental evidence that multi-MeV protons accelerated in relativistic laser-plasma interactions are modulated by strong filamentary electromagnetic fields. Modulations are observed when a preplasma is developed on the rear side of a $\mu$m-scale solid-density hydrogen target. Under such conditions, electromagnetic fields are amplified by the relativistic electron Weibel instability and are maximized at the critical density region of the target. The analysis of the spatial profile of the protons indicates the generation of $B>$10 MG and $E>$0.1 MV/$\mu$m fields with a $\mu$m-scale wavelength. These results are in good agreement with three-dimensional particle-in-cell simulations and analytical estimates, which further confirm that this process is dominant for different target materials provided that a preplasma is formed on the rear side with scale length $\gtrsim 0.13 \lambda_0 \sqrt{a_0}$. These findings impose important constraints on the preplasma levels required for high-quality proton acceleration for multi-purpose applications.