Magnetospheric cavity modes: Some nonlinear effects

Abstract

Linear models of magnetospheric cavity modes are unlikely to be directly applicable to events generated by, for example, large solar wind pressure pulses. To determine basic nonlinear effects, we apply a two‐dimensional, nonlinear hydromagnetic computer code to the problem of pure fast mode cavity resonances in the simplest possible box model of the magnetosphere, stimulated by a magnetopause compression and relaxation with maximum velocity ν0, normalized against the Alfvén speed at the magnetopause boundary. The results show that significant nonlinear effects can occur for ν0 ∼ 0.2. The initial impulse develops into a relatively weak shock as it propagates into the magnetosphere. After cavity modes are set up, their temporal development is very different from the corresponding linear modes. In particular, the cavity mode frequencies are reduced, and the temporal structure of the modes is apparently not well represented by sinusoidal functions. Much of the change in behavior can be attributed to a large distortion of the background plasma mass density, which we consider to be an effect of the ponderomotive force (PMF). We develop expressions for the PMF as it applies to small but finite amplitude cavity modes in our box model and show that these expressions are consistent with the simulation results. For a cold plasma, extreme density enhancements occur at and near the magnetospheric equator. We consider such large enhancements to be unlikely, but enhancements of the order of 100% can occur in a warm plasma, accompanied by adiabatic heating within the enhancements, increasing the plasma temperature by a factor of about 2. The density enhancements are limited by the propagation of slow magnetosonic perturbations away from the positions of maximum density. This leads to quasi‐cyclic density structures as the perturbations reflect from the ionospheric boundaries, the quasi‐period depending on the sound speed and therefore the plasma parameter β. Complex density structures appear to evolve rapidly when β is of the order of 0.05. We consider that mass transport by the PMF is likely to occur in the magnetosphere when relatively large ULF wave fields exist, regardless of the exact driving mechanism.