Effects of VLF transmitter waves on the inner belt and slot region

Signals from VLF transmitters can leak from the Earth-ionosphere wave guide into the inner magnetosphere, where they propagate in the whistler mode and contribute to electron dynamics in the inner radiation belt and slot region. Observations show that the waves from each VLF transmitter are highly localised, peaking on the nightside in the vicinity of the transmitter. In this study we use ~5 years of Van Allen probe observations to construct global statistical models of the bounce-averaged pitch angle diffusion coefficients for each individual VLF transmitter, as a function of L*, Magnetic Local Time ( MLT) and geographic longitude. We construct a 1D pitch-angle diffusion model with implicit longitude and MLT dependence to show that VLF transmitter waves weakly scatter electrons into the drift loss cone. We find that global averages of the wave power, determined by averaging the wave power over MLT and longitude, capture the long-term dynamics of the loss process, despite the highly localised nature of the waves in space. We use our new model to assess the role of VLF transmitters waves, hiss waves, and Coulomb collisions on electron loss in the inner radiation belt and slot region. At moderate relativistic energies, E~500 keV, waves from VLF transmitters reduce electron lifetimes by an order of magnitude or more, down to the order of 200 days near the outer edge of the inner radiation belt. However, VLF transmitter waves are ineffective at removing multi- MeV electrons from either the inner radiation belt or slot region.