A dynamic model for the time evolution of the modulated cosmic ray spectrum

A recently developed model predicts an energy dependent phase lag in the modulated cosmic ray density U(t) given by U(t) approximately equal to US (t - tau) where US is the solution to the Fokker-Planck equation under time independent conditions and tau is the average time spent by particles inside the modulating region. The delay times tau are functions of modulating parameters R (the radius of the modulating cavity), V (the solar wind velocity), and K (the effective average diffusion-coefficient which is a function of energy). This model is applied to predict the time evolution of the modulated cosmic ray proton spectrum over a simulated solar cycle. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations