Previous studies of scattering effects have involved either ad hoc physical assumptions or Monte Carlo techniques requiring very costly computer programs. In this new theory of scattering, a transport equation is derived that governs the evolution in time of the electron velocity distribution function from the initial Compton production distribution function under the influence of the earth's magnetic field, energy loss processes, and atmospheric scattering. This differential equation is solved analytically by an expansion to third order in the ratio of spatial spreading to velocity spreading, thus providing sufficient accuracy to cover the significant duration of the pulse. The current and ionization are then calculated as integrals over the velocity distribution function. After the integrals are carried out as far as possible, rapid computer programs are employed. Results show that scattering produces major reductions in the current.