Atmospheric spreading of protons in auroral arcs

A model is developed to calculate the effect of atmospheric spreading on the flux and angular distribution of protons in homogeneous auroral arcs. An expression is derived that indicates the angular distribution in the atmosphere as a function of distance from arc center, neutral scale height, arc width, and initial angular distribution. The results of the model agree favorably with those based on Monte-Carlo calculations. From these results the enhancement factors needed to compute the original proton current above the atmosphere are obtained. A technique is indicated for determining the incident angular distribution from rocket-based measurements of the arc width and angular distribution.