The radial and latitudinal dependence of the cosmic ray diffusion tensor in the heliosphere

Abstract

The radial and latitudinal dependence of the cosmic ray diffusion tensor is investigated on the basis of a recently developed model of magnetohydrodynamic turbulence in the expanding solar wind [ Zank et al. , 1996a,b; Matthaeus et al. , 1996]. In the ecliptic plane, decaying magnetohydrodynamic turbulence is assumed to be replenished in situ by turbulence generated through the interaction of streams (both shear and compressional effects) and by the creation of pickup ions. In the polar region, at least during solar minimum, stream interaction driven turbulence is neglected and only pickup ion driven turbulence is included. To model the perpendicular and drift elements of the cosmic ray diffusion tensor, we employ both a quasi‐linear theory (QLT) and a newly developed nonperturbative theory (NPT) to describe the field line wandering which drives perpendicular transport. A resonant quasi‐linear description is applied to the parallel component. For the QLT approach, we find that in the solar wind ecliptic plane (1) the radial diffusive length scale or mean free path (mfp) is very nearly constant until some 10 AU, after which it experiences some variation with increasing heliocentric distance; (2) the radial mfp is dominated at all radial distances by the component parallel to the mean magnetic field and the perpendicular component is completely unimportant; (3) the length scale associated with the drift component of the cosmic ray diffusion tensor is only comparable to the radial mfp beyond ∼ 10 AU; and (4) the rigidity P dependence of the radial mfp within 10 – 20 AU is weak and proportional to P 1/3 , but in the far outer heliosphere it is proportional to P 2 . For the QLT model in the polar region of the solar wind, we find that the radial cosmic ray mfp is much greater than the corresponding mfp in the ecliptic region, consistent with observed mfps for pickup ions reported by Gloeckler et al. [1995]. The polar models are, however, preliminary and assume vanishing cross‐helicity. The polar radial mfp is dominated by the parallel component, and drift length scales are never comparable to the radial mfp in the high polar latitudes. By using instead a nonperturbative model for the perpendicular and drift components of the cosmic ray diffusion tensor, it was found that the mfps for these coefficients could be significantly larger than their QLT counterparts. The increased perpendicular mfp was found to be important in the radial mfp only beyond ∼ 20 AU, which remains dominated by the parallel diffusion within this distance. Within the ecliptic, the nonperturbative model yields a radial mfp for cosmic rays that is almost constant with heliocentric distance. Similar order of magnitude differences between the radial mfps in the ecliptic and polar regions of the solar wind are found with the nonperturbative models.