Nonlinear field line resonances: Dispersive effects

A model is presented which describes the nonlinear interaction of dispersive shear Alfvén wave (SAW) field line resonances (FLRs) and ion acoustic waves (IAWs), with applications to the Earth’s magnetosphere. Two limits are considered: In low-β plasma ${\mathrm{(\beta <m}}_e{\mathrm{/m}}_i\mathrm{),}$ dispersion is dominated by electron inertia (EI), while for higher β it is dominated by the electron thermal effect. In each case, the ponderomotive force steepens the SAW in the radial direction, taken as earthward in the equatorial plane. Following the time of nonlinear steepening, the dynamics strongly depends on dispersion. In the EI case, standing SAWs excited in FLRs exhibit a parametric decay instability (PDI) into secondary SAWs and IAWs. Nonlinearity and dispersion broaden the FLR in the radial direction, leading to rapid density and parallel electric field fluctuations and scale lengths comparable to the EI length. In warm plasmas, SAWs are stable to the PDI, and in this case the FLR emits short perpendicular scale SAW-IAW solitons in the anti-earthward direction. Observational consequences of both scenarios are discussed.