Electron distribution model in a solid sphere for relativistic collisionless plasmas

Abstract

Studying high-energy plasma requires accounting for temperature, one of the primary plasma parameters, along with electron number density. This can be modeled using an adiabatic process through the Poisson-Boltzmann equation. However, variable temperature produces a non-ideal constant adiabatic index, Γ and Λ values.The temperature dependence of the adiabatic index, Γ, is that it decreases with increasing temperature. Γ reaches a value close to the classical, non-relativistic constant 5/3 for low temperatures, while at higher temperatures, it approaches the relativistic ideal gas constant 4/3. As we compare electron density distributions for 1 keV, 10 keV, 100 keV, 1 MeV, and 10 MeV, we find that as temperatures approach relativistic behavior, Γ = 4/3. Furthermore, Λ values closer to one show a more significant deviation from the constant adiabatic indexes. Considering these variances, we can then model more realistic electron-ion interactions in relativistic collisionless plasma.