The Nature of Elsässer Variables in Compressible MHD

Abstract

The Elsässer variables are often used in studies of plasma turbulence, in helping differentiate between MHD waves propagating parallel or antiparallel to the main magnetic field. While for pure Alfvén waves in a homogeneous plasma the method is strictly valid, we show that compressible, magnetoacoustic waves are in general described by both Elsässer variables. Furthermore, in a compressible and inhomogeneous plasma, the pure MHD waves (Alfvén, fast and slow) are no longer normal modes, but waves become linearly coupled or display mixed properties of Alfvén and magnetoacoustic nature. These waves are necessarily described by both Elsässer variables, and therefore the Elsässer formalism cannot be used to strictly separate parallel and antiparallel propagating waves. Nevertheless, even in an inhomogeneous plasma, for a highly Alfvénic wave the Elsässer variable corresponding to the propagation direction appears still dominating. We suggest that for Alfvénic waves, the relative amplitude of Elsässer variables depends on the local degree of inhomogeneity and other plasma and wave properties. This finding has implications for turbulence studies in inhomogeneous and compressible plasmas, such as the solar corona and solar wind.