Azimuthal phase speeds of field line resonances driven by Kelvin-Helmholtzunstable waveguide modes

A model for the coupling of Kelvin-Helmholtz unstable fast cavity modes to field line resonances (FLRs) is presented. We consider a bounded, nonunifor m magnetospheric flank separated from a semi-infinite, field-free, flowing magnetosheath by an infinitely thin magnetopause. Fast cavity modes may bec ome unstable for sufficiently high flow speeds, and we find that for any fl ow speed there is a common phase speed at which all the harmonics have thei r maximum growth rate. The common phase speed is less dependent on the equi librium structure within the magnetosphere than on the local structure of d ensity ratio and relative velocity jump at the magnetopause. We perform a l ocal analysis of the reflection and transmission of modes at the magnetopau se. By requiring the spontaneous radiation of modes from the magnetopause, we may predict a phase speed at which we would expect the maximum growth ra te to occur for any set of parameters. These predicted phase speeds are fou nd to be in agreement with both those found by our model and observations o f FLRs that are observed simultaneously at different latitudes.