Moment-based Formulae for the Transport Coefficients

Abstract The coefficients of the transport equations that describe propagation features are particularly important in astrophysics, interplanetary physics, and experimental plasma physics. In this paper, using the momentum transport equations, we find that the coefficients are related to statistical quantities, and some of these relations are new. In addition, these coefficients take logarithmic forms that differ from those derived in previous studies. Moreover, we investigate variable-dependent diffusion coefficients in transport equations. For isotropic pitch-angle scattering, we also obtain a formula that has a logarithmic form. For fractional transport equations, the coefficients expressed in terms of the moments are obtained from the governing equations.