NONLINEAR SHEAR ALFVEN RESONANCES IN A DIPOLAR MAGNETIC-FIELD

The effect of the ponderomotive force (PF) on the temporal evolution o f shear Alfven field line resonances (FLRs) is considered for a magnet ic dipole geometry appropriate to the Earth's magnetosphere. We derive a set of equations which describes the coupling of shear Alfven and s low mode waves and show that in a dipole field, the PF initiates a spe ctrum of standing slow mode waves, rather than just the fundamental mo de that arises in a Cartesian box model magnetosphere. Magnetic field aligned slow mode density perturbations lead to a nonlinear temporal p hase shift between the compressional driver and shear Alfven wave. Thi s results in nonlinear saturation of the wave fields of FLRs and may o ccur well in advance of linear saturation as a result of ionospheric d issipation. We derive expressions for the nonlinear frequency shifts c aused by the slow mode spectrum and determine the timescale for nonlin ear saturation of the shear Alfven wave fields. Finally, we compare ou r results with previous estimates made in a box model magnetosphere an d show that our main conclusions remain valid.