Reflection and transmission at the boundary between two counterstreaming MHD plasmas – active boundaries or negative-energy waves?

Abstract

A magnetohydrodynamic (MHD) wave, incident on the boundary between two MHD media in relative motion, may be amplified or attenuated by exchanging energy with the kinetic energy of the background flow. The conventional treatment of this problem uses a definition of the wave energy such that energy is conserved at the boundary. An amplified reflected wave then leads to the requirement of a transmitted wave carrying negative energy. Such an approach, while producing correct results, obscures the nature and location of the energy interchange. In this paper, the proper definitions of energy density and flux in a moving plasma are discussed, and the relationship of the group velocity and the energy flow is clarified. The mechanism by which energy is exchanged between streaming plasma and wave is through the work done by the Maxwell and Reynolds stresses on the gradient of velocity at the boundary. The location of the energy exchange is identified as the active boundary, with no need to invoke ideas of negative energy. The relationship between the two approaches is critically discussed.