Three-dimensional Radiation Belt Simulations in Terms of Adiabatic Invariants Using Only One Grid

Details Three-dimensional Radiation Belt Simulations in Terms of Adiabatic Invariants Using Only One Grid Three-dimensional Radiation Belt Simulations in Terms of Adiabatic Invariants Using Only One Grid

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsm13b2076s&link_type=abstract

American Geophysical Union, Fall Meeting 2011, abstract #SM13B-2076

Physics

[2753] Magnetospheric Physics / Numerical Modeling, [2774] Magnetospheric Physics / Radiation Belts

Scientific paper

Highly energetic electrons in the Earth's radiation belts are hazardous for satellite equipments. The evolution of relativistic electron fluxes in the radiation belts is described by the 3-D Fokker-Plank equation in terms of the radial distance, energy and equatorial pitch angle. Previously, two grids were used by the VERB code to solve the Fokker-Planck equation, the first grid for radial diffusion that keeps constant first and second adiabatic invariants, and the second grid for energy, pitch-angle and mixed scattering at each fixed radial distance. We present a new numerical method for the solution of the 3-D Fokker-Planck equation that uses only one computational grid written in terms of adiabatic invariants. The new method transforms the Fokker-Planck equation and the diffusion coefficients into a new coordinate system which allows for an efficient one-grid solution. The new one-grid method eliminates time-consuming interpolation between different grids and prevents possible interpolation-related numerical instabilities. We validate the method by comparing results with previous simulations that use the two-grid numerical scheme. The solution in terms of adiabatic invariants makes it straightforward to use any realistic magnetic field configuration while simultaneously accounting for adiabatic magnetic field fluctuations. The one-grid method can be naturally extended to MLT-dependent 4-D solution.

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