Relativistic theory of particles in a scattering flow – II. Viscosity, electrical conductivity, and heating

We use the theory developed in Achterberg & Norman (Paper 1) to calculate the transport, viscosity, and electrical conductivity of a population of charged particles in a relativistic flow that scatters them elastically. We show that the energy-momentum tensor of these particles takes the form proposed by Eckart. We also show that, when adopting the diffusion approximation for particle transport, no terms associated with bulk viscosity appear: We only find the terms describing shear (dynamic) viscosity and heat flow terms in our expression for the energy-momentum tensor. Using the same techniques we find the general transport equation for the scattered particles, generalizing and unifying earlier results of Skilling, Webb, and Williams & Jokipii, extending them to the fully relativistic case. In this way we can calculate both the effects of adiabatic heating and of irreversible (diffusive) heating and Joule heating.