Transport theoretic solutions for the beam‐spreading effect in the proton‐hydrogen aurora

In this paper, we give matched asymptotic solutions for the particle fluxes in the Earth's proton‐hydrogen aurora. The proton (Φ P ) and hydrogen atom (Φ H ) fluxes are functions of two spatial and three velocity variables. These results are new and are given in closed form to the lowest order in the expansion parameter, which is the ratio of the proton gyroradius to the atmospheric scale height, and show a pronounced lateral, beam‐spreading effect. Numerical calculations for Φ P and Φ H where no approximations are made are also given and found to agree reasonably well with the matched asymptotic solutions.