Publications

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplified problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other, verifying the method.

This SAND report investigates the electron transport equation in the upper atmosphere and how it relates to auroral light emissions. The electron transport problem is a very stiff boundary value problem, so standard numerical methods such as symmetric collocation and shooting methods will not succeed unless if the boundary conditions are altered with unrealistic assumptions. We show this to be unnecessary and demon- strate a method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method can be verified by showing that under certain restrictive as- sumptions, the electron transport equation has an exact solution that can be written as an integral. The connection between electron transport and the aurora is made explicit and a kinetic model for calculating auroral light emissions is given.

Abstract not provided.