on the Convection, Diffusion, and Adiabatic Deceleration of Cosmic Rays in the Solar Wind

We present a generalization and clarification of work on the transport of cosmic rays in the solar system. The general equations for the cosmic-ray density and flux, in the anisotropic-diffusion approximation, are derived in the frame of reference moving with the solar wind, and the transformation to the fixed frame is discussed. Only if the particle density varies smoothly with energy does one obtain a straightforward generalization of equations derived previously for isotropic diffusion. In this approximation we write down, for the first time, the correct differential equations for the particle density and flux for anisotropic diffusion. If the density varies sharply with energy, more complex integro-differential equations arise. We conclude that existing alternative derivations, based on the Boltzmann equation, are in general not adequate for either anisotropic-diffusion or energy transformations.