Fluctuations in electron-positron plasmas: Linear theory and implications for turbulence

Abstract

Linear kinetic theory of electromagnetic fluctuations in a homogeneous, magnetized, collisionless electron-positron plasma predicts two lightly damped modes propagate at relatively long wavelengths: an Alfvén-like mode with dispersion ωr=k∥ṽA and a magnetosonic-like mode with dispersion ωr≃kṽA if βe⪡1. Here ṽA is the Alfvén speed in an electron-positron plasma and ∥ refers to the direction relative to the background magnetic field Bo. Both modes have phase speeds ωr/k which monotonically decrease with increasing wavenumber. The Alfvén-like fluctuations are almost incompressible, but the magnetosonic-like fluctuations become strongly compressible at short wavelengths and propagation sufficiently oblique to Bo. Using the linear dispersion properties of these modes, scaling relations are derived which predict that turbulence of both modes should be relatively anisotropic, with fluctuating magnetic energy preferentially cascading in directions perpendicular to Bo. Turbulent spectra in the solar wind show two distinct power-law regimes separated by a distinct breakpoint in observed frequency; this characteristic should not be present in electron-positron turbulence because of the absence of whistler-like dispersion. Linear theory properties of the cyclotron and mirror instabilities driven by either electron or positron temperature anisotropies are generally analogous to those of the corresponding instabilities in electron-proton plasmas.