Toward an Ab Initio Theory of the Solar Modulation of Cosmic Rays

Abstract

Recent efforts to improve and complete modulation theory are described, emphasizing factors that arise in attempts to understand the diffusion tensor based on turbulence theory and the theory of charged particle scattering. Direct numerical solutions of the transport equations are used to illustrate several sensitive factors affecting modulation that are difficult to understand either observationally or physically. First, the nature of perpendicular diffusion is still poorly understood. We introduce a new perpendicular diffusion formalism that can smoothly vary between the field line random walk limit and a recent treatment based on the Taylor-Green-Kubo equation. Second, this new perpendicular diffusion coefficient is shown to be sensitive to an outer scale of turbulence, the ultrascale, which we know almost nothing about. Third, the radial variation of the ordinary correlation length is still poorly characterized, in part owing to the uncertain impact of pickup ion-driven turbulence in the outer heliosphere. These three factors encompass a very diverse set of possible solutions of the modulation equation, only a small part of which even remotely resembles available observations.