MHD wave interactions in space plasmas and Noether’s theorem

Abstract

The interaction of magnetohydrodynamic (MHD) waves in space plasmas can be investigated by Lagrangian and Hamiltonian methods. In this paper, we discuss the propagation of non‐WKB waves in a non‐uniform background plasma flow such as the solar wind, by using Lagrangian variational principles for MHD plasmas developed by Newcomb. The Lagrangian methods for the propagation of WKB waves in a non‐uniform background plasma flow developed by Dewar are extended to the case of of non‐WKB waves in a non‐uniform background flow. As part of the analysis, we obtain Noether’s theorem for the combined system of waves and background plasma. This effectively generalizes the form of Noether’s theorem for Lagrangian MHD used by Padhye and Morrison and Padhye in their analysis of Lagrangian, fluid re‐labelling symmetries. Examples of the use of Noether’s theorem, are the derivation of the energy and momentum conservation laws for the total system of waves and background plasma, corresponding respectively to the case of time and space translation symmetries.