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

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.