Kinetic turbulence in relativistic electron-proton plasmas

We use particle-in-cell simulations to investigate driven turbulence in collisionless, relativistic electron-proton plasmas. We perform a parameter scan across initial temperature that covers the relativistic ($T_p \gg m_p c^2$) and sub-relativistic ($T_p \ll m_p c^2$) proton regimes, while electrons are always relativistic ($T_e \gg m_e c^2$). After turbulence fully develops, we find that the ratio of electron to proton dissipated energies varies from $1$ in the ultra-relativistic regime (where the plasma behaves as a pair plasma) to $\sim 0.1$ in the sub-relativistic regime. We propose an empirical formula to describe the dependence of this electron-proton energy partition on the instantaneous ratio of electron to proton characteristic gyroradii (which is a function of initial temperature and plasma beta). We also find that, whereas both particle species are efficiently accelerated in the relativistic regime, protons exhibit a more substantial nonthermal population than electrons in the sub-relativistic regime. Our results have important implications for the establishment of two-temperature plasmas ($T_p \gg T_e$) in black-hole accretion flows and jets.