Toward a realistic diffusion tensor for galactic cosmic rays

We present analytical expressions for the mean free path parallel to the background magnetic field, calculated from quasi-linear theory for a composite slab/two-dimensional geometry model of turbulence. Diffusion perpendicular to the field is assumed to be anisotropic and proportional to parallel diffusion. For the variation in the magnetic field and the correlation length throughout the heliosphere, recent results of Zank et al. are used. We emphasize the role of the power spectrum of magnetic field fluctuations in determining the rigidity dependence of the parallel diffusion coefficient, and show that this rigidity dependence is unlikely to remain constant throughout the heliosphere. While we concentrate on Galactic protons at medium to high rigidities, we briefly discuss electron parallel mean free paths at low rigidities. Drifts are also included in the numerical modulation model, the results of which are compared with Ulysses, IMP 8, and Pioneer 10 measurements. Good agreement is found for energy spectra and latitudinal gradients in the inner heliosphere, but not for radial gradients farther away from the Sun in the ecliptic plane. We suggest that the combination of a turbulence, a scattering, and a modulation model presents a formalism that should prove useful for further studies.