On large amplitude MHD waves in high‐beta plasma

Abstract

Downstream of quasi‐parallel shocks, the magnetosheath is often observed as a region of high plasma beta, of the order of 10, with large magnetic field fluctuations and relatively weak thermal pressure fluctuations. Since the wave steepening results from the nonlinearity in the plasma thermal properties, these nonlinear magnetic fluctuations that are accompanied by linear pressure fluctuations in a high‐beta plasma do not necessarily lead to wave steepening. We develop a nonlinear theory based on MHD and observational evidence to describe such a system. We first perturb the MHD equations assuming the reciprocal of beta and the perturbed pressure to be small parameters and retaining nonlinear terms for the magnetic arid velocity perturbations. We then Fourier expand the perturbations and retain terms up to the first order. A nonpropagating mode is present that has the characteristics of a series of tangential discontinuities. A purely incompressible mode is present that propagates obliquely to the background field and is nondispersive and independent of the plasma beta. The field perturbations do not need to be coplanar with the background field and the wave vector. A nonlinear compressible mode is also found. In the limit of small field perturbations, the mode is similar to the linear slow mode in high‐beta plasmas. The first harmonic field perturbation is coplanar with the background field and the wavevector. When the mode propagates along the field, the density and field strength fluctuations are small at the primary frequency of the wave and are significant at a frequency twice the primary frequency. This frequency doubling phenomenon is most severe for parallel propagation. The compressibility of the mode makes it possible to couple the energy across the magnetopause into the magnetosphere. We show observational evidence for the existence of such modes.