An efficient and positivity‐preserving layer method is introduced to solve the radiation belt diffusion equation and is applied to study the bounce resonance interaction between relativistic electrons and magnetosonic waves. The layer method with linear interpolation, denoted by LM‐L (layer method‐linear), requires the use of a large number of grid points to ensure accurate solutions. We introduce a monotonicity‐ and positivity‐preserving cubic interpolation method to be used with the Milstein‐Tretyakov layer method. The resulting method, called LM‐MC (layer method‐monotone cubic), can be used to solve the radiation belt diffusion equation with a much smaller number of grid points than LM‐L while still being able to preserve the positivity of the solution. We suggest that LM‐MC can be used to study long‐term dynamics of radiation belts. We then develop a 2‐D LM‐MC code and use it to investigate the bounce resonance diffusion of radiation belt electrons by magnetosonic waves. Using a previously published magnetosonic wave model, we demonstrate that bounce resonance with magnetosonic waves is as important as gyroresonance; both can cause several orders of magnitude increase of MeV electron fluxes within 1 day. We conclude that bounce resonance with magnetosonic waves should be taken into consideration together with gyroresonance.

A new 3‐D diffusion code using a recently published layer method has been developed to analyze radiation belt electron dynamics. The code guarantees the positivity of the solution even when mixed diffusion terms are included. Unlike most of the previous codes, our 3‐D code is developed directly in equatorial pitch angle (α0), momentum (p), and L shell coordinates; this eliminates the need to transform back and forth between (α0,p) coordinates and adiabatic invariant coordinates. Using (α0,p,L) is also convenient for direct comparison with satellite data. The new code has been validated by various numerical tests, and we apply the 3‐D code to model the rapid electron flux enhancement following the geomagnetic storm on 17 March 2013, which is one of the Geospace Environment Modeling Focus Group challenge events. An event‐specific global chorus wave model, an AL‐dependent statistical plasmaspheric hiss wave model, and a recently published radial diffusion coefficient formula from Time History of Events and Macroscale Interactions during Substorms (THEMIS) statistics are used. The simulation results show good agreement with satellite observations, in general, supporting the scenario that the rapid enhancement of radiation belt electron flux for this event results from an increased level of the seed population by radial diffusion, with subsequent acceleration by chorus waves. Our results prove that the layer method can be readily used to model global radiation belt dynamics in three dimensions.

[1] We examine the strength of the electron source associated with dipolarization at the outer boundary of the radiation belts using multisatellite observations from THEMIS. This topic is relevant to the determination on the relative roles of inward radial diffusion versus internal local acceleration for the origin of the relativistic electrons in the outer radiation belt. We focus on the electron phase space density (PSD) as a function of the first adiabatic invariant (m) for equatorially mirroring population over a broad energy range. It is found that the source strength associated with dipolarization for non-storm periods at the outer boundary of the radiation belts can be well above the observed fluxes of relativistic electrons inside the outer radiation belt. The PSD change due to the magnetic field strength variation dominates over PSD change from the energy flux increase with dipolarization, resulting in a strong anticorrelation between magnetic field strength and PSD values at a given m. If observations from closely spaced satellites during the same event can be used to indicate radial transport of electrons with dipolarization, then the observed PSD at these satellites indicates frequent occurrence of non-adiabatic process during their radial transport.