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 at time t given by U (t) approx. =U/subs/(t-tau), where U/subs/ 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. The predicted spectra reproduce most of the features of the so-called hysteresis effect when values of V=360 km/s, R=60 AU, and K varying between 1.3 x 10/sup 22/ cm/sup 2//s at solar maximum and 3.5 x 10/sup 22/ cm/sup 2//s at solar minimum are used. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations. (AIP)