Monte-Carlo approach to calculate the proton stopping in warm dense matter within particle-in-cell simulations

TL;DR

This paper introduces a Monte-Carlo method integrated into particle-in-cell simulations to accurately model proton stopping in warm dense matter, capturing effects of electron ionization and temperature-dependent stopping power.

Contribution

The novel Monte-Carlo approach accounts for bound and free electron contributions, improving the realism of proton stopping simulations in warm dense matter.

Findings

Converges to Bethe-Bloch predictions at low temperatures.

Matches experimental data for increased stopping power at moderate temperatures.

Shows decreased stopping power at high ionization levels due to collision suppression.

Abstract

A Monte-Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. The model is based on multiple binary-collisions among electron-electron, electron-ion and ion-ion, taking into account contributions from both free and bound electrons, and allows to calculate particle stopping in much more natural manner. At low temperature limit, when ``all'' electron are bounded at the nucleus, the stopping power converges to the predictions of Bethe-Bloch theory, which shows good consistency with data provided by the NIST. With the rising of temperatures, more and more bound electron are ionized, thus giving rise to an increased stopping power to cold matter, which is consistent with the report of a recently experimental measurement [Phys. Rev. Lett. 114, 215002 (2015)]. When temperature is further increased, with ionizations reaching the maximum, lowered stopping power is observed, which is due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.