Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics

Abstract

The magnetized resistivity and electrothermal tensors when substituted into the induction equation lead to electrothermal magnetic field generation, resistive magnetic diffusion, and magnetic field advection due to resistivity gradients, temperature gradients, and currents. The advection terms driven by the temperature gradient and current have cross field components (perpendicular to both the magnetic field and the driving term) that depend on significantly modified versions of Braginskii's transport coefficients [S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205]. The improved fits to Braginskii's coefficients given by Epperlein and Haines [Phys. Fluids 29, 1029 (1986)] and Ji and Held [Phys. Plasmas 13, 042114 (2013)] give physically incorrect results for cross field advection at small Hall parameters (product of cyclotron frequency and collision time). The errors in Epperlein and Haines' fits are particularly severe, giving increasing advection velocities below a Hall parameter of one when they should decrease linearly to zero. Epperlein and Haines' fits can also give erroneous advection terms due to variations in the effective atomic number. The only serious error in Braginskii's fits is an overestimate in advection due to perpendicular resistivity. New fits for the cross field advection terms are obtained from a direct numerical solution of the Fokker–Planck equation and Ji and Held's higher order expansion approach that are continuous functions of the effective atomic number.