Viscosity and inertia in cosmic-ray transport: Effects of AN average magnetic field

We derive the equations for cosmic-ray transport in a moving, scattering fluid in the presence of an average background magnetic field which is carried with the fluid. We proceed by expanding the cosmic-ray distribution function about momentum isotropy, keeping three terms. We identify these terms as the isotropic distribution, a streaming flux, and an anisotropic pressure tensor. Relating terms in the pressure tensor to spatial variations of the fluid flow velocity, we find five independent cosmic-ray viscosity coefficients. We present a general discussion of this viscosity and its relation to particle orbits in a magnetic field. Some effects correspond to simple extensions of viscous damping, modified by the magnetic field, but others, which change sign with the magnetic field or particle charge, represent finite gyroradius effects which do not contribute to the damping. We apply the equations to the cases of simple shear in the presence of a magnetic field, and not to the propagation of transverse Alfvén waves. One effect of viscosity which appears not to have been recognized previously is to rotate the polarization plane of a linearly polarized Alfvén wave.