Temporal variations of cosmic rays in the heliosphere

This thesis investigates temporal variations of cosmic rays in the heliosphere analytically. A perturbation approach is presented to solve the diffusion equation for energetic particle transport in the solar wind. A linear response of the cosmic ray number density to variations in the spatial diffusion coefficient is computed based on the convection-diffusion equation. As the simplest cases to study, the 11-year variation and a Forbush decrease, the assumptions are made (1) that the solar-cycle variation arises from an 11-year sinusoidal variation of the diffusion coefficient at the Sun which propagates out through the heliosphere and (2) a Forbush decrease arises from the passage of an interplanetary traveling disturbance characterized by a sudden decrease of the diffusion coefficient. The predicted solar-cycle variation exhibits a hysteresis effect in which high-energy particles respond before low-energy particles. The predicted Forbush decrease profiles exhibit precursors (the unreasonably large precursors obtained reveal the limitations of one-dimensional and two-dimensional convection-diffusion equations), sudden decreases, and gradual approximately energy-independent recoveries arising from a decay of the propagating disturbance. For high energy particles the time-dependent solution for a Forbush decrease in spherical coordinates is obtained by solving a steady state equation and then substituting the time dependent variation of the diffusion coefficient. It is found that the response function (a measure of the relative modulation effect of disturbances as they propagate outward in the heliosphere) is similar to the Forbush decrease for a $\delta$- function disturbance. Investigation of the response function in terms of the time-dependent Forbush decrease in spherical coordinates results in the determination of the characteristic timescale of its decay, which increases with increasing distance from the Sun