Whistler-Alfv\'en turbulence in a non-neutral ultrarelativistic pair plasma

Abstract

The large-scale dynamics of most conventional space and astrophysical plasmas are predominantly governed by Alfv\'en modes, which are low-frequency magnetohydrodynamic modes existing in magnetized media. At scales smaller than the ion gyroscale or frequencies exceeding the ion cyclotron frequency, the Alfv\'en modes transform into kinetic-Alfv\'en or whistler modes that significantly contribute to plasma dynamics. However, this scenario reverses in non-neutral pair plasmas, such as those found in the magnetospheres of pulsars and magnetars, around rotating black holes and in their relativistic jets, as well as in certain laboratory plasmas. In these systems, the large-scale dynamics is governed by hybrid whistler-Alfv\'en modes, which transform into pure Alfv\'en modes at smaller scales. We derive the nonlinear equations that describe the dynamics of whistler-Alfv\'en modes in ultrarelativistic non-neutral magnetically dominated pair plasma and discuss the spectrum of turbulence governed by these equations.