A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.