On the Causality Problem in Focused Particle Transport

Abstract

Abstract When perpendicular diffusion is included into the focused transport equation, certain assumptions of the perpendicular diffusion coefficient (including the well-known fieldline random walk limit) clearly lead to faster-than-light motion for relativistic particles, and transport that does not preserve causality in general. In this work we show that this discrepancy can be solved by including the effect of turbulence on particle drifts, especially the streaming term present in the focused transport equation, leading to a so-called drift reduction factor. We discuss this drift reduction factor, how it solves the above-mentioned causality problem, and its general implications for particle transport. Under certain simplifying assumptions we show the interplay between particle streaming (as a drift process) and perpendicular diffusion, and how these processes can be consistently coupled through the turbulent magnetic field.