Transport equation techniques for the deposition of auroral electrons

Auroral electron scattering and energy loss are calculated by using the first time a multiangle equation of transfer at all energies. The results are compared with those obtained by using a Fokker-Planck equation. Both equations have been solved in terms of their eigensolutions. The equation of transfer has also been solved by numerical integration. Fokker-Planck solutions agree well with equation of transfer solutions above 3 keV but deviate increasingly at lower energies. A comparison is made between the present Fokker-Planck results and those of M. Walt at 10 keV, giving good agreement. Energy deposition rates are also found to agree satisfactorily with those obtained previously. The accuracy of integration of the transfer equation is tested by comparing results obtained by the eigenvalue method and the direct integration method. Differences of less than 5% were found at all altitudes, energies, and pitch angles. The predicted backscatter near the upper energy boundary is sensitive to the boundary condition there. Backscatter results for various boundary conditions in energy show both this and the effects of the propagation of the boundary condition toward lower energies. Solutions to the equation of transfer are given between 10 eV and 20 keV, based on a measured auroral electrom spectrum. These solutions are compared with similar results by Banks et al. (1974). The results agree above 3 keV but differ below that energy, a finding which is consistent with our comparisons of solutions of the equation of transfer and the Fokker-Planck equation