Global distribution of proton rings and associated magnetosonic wave instability in the inner magnetosphere

Using the Van Allen Probe A observations, we obtained the global distribution of proton rings and calculated the linear wave growth rate of fast magnetosonic (MS) waves in the region L ~ 3-6. Our statistical and calculated results demonstrate that MS waves can be locally excited on the dayside outside the plasmapause, as well as in the dusk sector inside the plasmapause. The frequency range of unstable MS waves is strongly modulated by the ratio of the proton ring velocity (Vr) to the local Alfv\ en speed (VA). High harmonic MS waves (ω>20ΩH+) can be excited outside the plasmapause where Vr/VA<1 while low harmonic MS waves (ω<10ΩH+) with frequencies less than ~30 Hz are found to be excited both outside and inside the plasmapause where 1