Development of self-modulation as a function of plasma length

TL;DR

This paper uses numerical simulations to propose that measuring the halo radius of a proton bunch in plasma can accurately determine the self-modulation saturation length, aiding experimental diagnostics.

Contribution

It introduces a method to estimate the self-modulation saturation length by analyzing the proton halo radius in plasma wakefield experiments.

Findings

Maximum transverse momentum of protons correlates with saturation length.

Halo radius measurement can serve as a diagnostic for saturation length.

Results support using halo radius as an experimental observable.

Abstract

We use numerical simulations to determine whether the saturation length of the self-modulation (SM) instability of a long proton bunch in plasma could be determined by measuring the radius of the bunch halo SM produces. Results show that defocused protons acquire their maximum transverse momentum and exit the wakefields at a distance approximately equal to the saturation length of the wakefields. This suggests that measuring the radius of the halo as a function of plasma length in the AWAKE experiment would yield a very good estimate for the saturation length of SM.