Two-stage linear filamentation growth of laser-produced proton beams in dense plasmas

We report in this work the current filamentation instability of laser-produced proton beams in a regime where the plasma collision frequency is much smaller than the plasma oscillation frequency but larger than the growth rate of the instability. In this regime, the plasma electron temperature increases significantly due to collisional Ohmic heating during the linear phase of the instability, which leads to a two-stage linear filamentation growth shown in this work. Compared to the collisionless plasma case, a reduced instability growth rate due to plasma collisions is found in the first stage, followed by a second stage with a comparable growth rate. Furthermore, an enhanced magnitude of magnetic fields and wavelength of beam filamentation are observed after instability saturation. The two-stage linear filamentation growth shows agreement with the dispersion relation of the instability and supported by detailed particle-in-cell simulations.