Transport theoretic solutions for auroral proton and H atom fluxes and related quantities

In this paper we show that linear transport theory may be used to solve for the auroral proton and H atom fluxes in plane-parallel geometry in the forward scattering and average discrete energy loss approximations. In this approximation, inelastic scattering is taken into account, but elastic scattering drops out and the solutions are approximations to the fluxes in the downward hemisphere. Using the multiple scattering method, we obtain the particle fluxes are finite sums of anlaytic functions of altitude, energy, and pitch angle. Closed form expressions are also found for the hemispherically averaged fluxes and the energy deposition and ionization rates. The notion of pseudoparticles is discussed and used to approximate the sums that occur in the above formulae. Results are presented for incident isotropic-Maxwellian proton fluxes