Radiation Belt Modeling: Implementation Issues When Solving Three-dimensional Diffusion Equations

Details Radiation Belt Modeling: Implementation Issues When Solving Three-dimensional Diffusion Equations Radiation Belt Modeling: Implementation Issues When Solving Three-dimensional Diffusion Equations

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufmsm42c0617g&link_type=abstract

American Geophysical Union, Fall Meeting 2003, abstract #SM42C-0617

Other

2720 Energetic Particles, Trapped, 2722 Forecasting, 2753 Numerical Modeling

Scientific paper

The Diffusion in I, L, and B Energetic Radiation Tracker (DILBERT) is being developed by AFRL to model radiation belt dynamics on both radial and pitch-angle diffusive time-scales with a realistic magnetic field model in three dimensions, where one of the dimensions is parameterized by the L shell. Large spatial variations in the pitch-angle (Dα α ), energy (DEE) and cross-term (D{α E}) quasi-linear diffusion coefficients make the calculations challenging. Two basic aspects of the calculation will be considered here, the variable sub-space in which the diffusion is computed, i.e pitch angle--energy, \{α eq,E\}, or adiabatic invariant, \{μ ,J\}, and constraints on the grid size. In the \{α eq,E\} space the coefficients compare to each other as |Dα α |>>|D{α E}|>>|DEE|, while in \{μ ,J\} space, the coefficients Dμ μ , D{μ J} and DJJ, have the relation, |Dμ μ | ˜|D{μ J}| ˜|DJJ|. Pitch angle--energy space is attractive in two dimensions because the dominance of Dα α makes the calculation almost one dimensional. Complications are introduced, however, by including the third dimension and it is argued that adiabatic invariant space is the better choice. Large spatial gradients in the coefficients in either variable space cause ``convective'' behavior in the numerical formulation of the equations. Based on estimated timescales for the ``convective'' and ``diffusive'' components of the equation constraints are derived on the grid resolution and it is shown that the required grid spacing varies by orders of magnitude.

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