Conductive electron heat flow along magnetic field lines

Abstract

In this work, a unified closure for the conductive electron heat flux along magnetic field lines is derived and examined. Both free-streaming and collisional pitch-angle scattering of electrons are present in the drift kinetic equation which is solved using an expansion in pitch-angle eigenfunctions (Legendre polynomials). The closure takes the form of a generic integral operator involving the electron temperature variation along a magnetic field line and the electron speed. Derived for arbitrary collisionality, the heat flux closure may be written in forms resembling previous collisional and collisionless expressions. Electrons with two to three times the thermal speed are shown to carry heat for all collisionalities and thermal electrons make an important contribution to the heat flow in regimes of moderate to low collisionality. As a practical application, the flow of electron heat along a chaotic magnetic field is calculated in order to highlight the nonlocal nature of the closure which allows for heat to flow against local temperature gradients.