Plasma transport by carrier electrons: classical coefficients across ionization and magnetization

The classical transport of magnetic field and electron energy in a plasma requires the use of coefficients that depend on plasma ionization $Z$ and magnetization $\chi$. This paper explains these scalings through studying the electron velocities responsible for each transport process. Both electron-electron collisions and magnetization affect higher velocity electron populations preferentially, lowering the carrier velocities; transport carried by a high energy electron population is therefore more suppressed by both electron-electron collisions and magnetization than transport carried by lower velocities. Carrier Hall parameters $\psi =\chi f(Z)$ are defined for each coefficient such that magnetization can be described independent of ionization. An analytic idealized coefficient with a single rigid carrier velocity reproduces many of the characteristics of the coefficients, in particular thermal conductivity, but overestimates plasma magnetization due to magnetization itself lowering the carrier velocity. A single moving carrier model improves agreement, but cannot describe the smoothness of the Righi-Leduc coefficient, which originates from being an average over a range of carrier velocities. This is the first paper in a 3-part series; the subsequent papers will extend the carrier picture to non-local heat-flux (paper 2) and non-local magnetic field evolution (paper 3).