A stochastic view of the solar modulation phenomena of cosmic rays

Abstract

We report on a numerical method for solving the Fokker-Planck equation (FPE) which describes the solar modulation of cosmic rays using Itô's stochastic differential equations (SDEs) and discuss on it's power and profound implications not easily attainable by standard methods. It is shown how easily the modulated energy spectrum of cosmic rays is calculated from the interstellar spectrum utilizing the momentum distribution function obtained by SDE method for particles with a fixed momentum of various values at 1 AU. The resultant modulated spectra are compared with the results by the standard numerical technique using the Crank-Nicholson method to demonstrate the validity of our method. Copyright 1998 by the American Geophysical Union.