Conductive electron heat flow along an inhomogeneous magnetic field

In this work a general closure for the conductive electron heat flux parallel to an inhomogeneous magnetic field is derived and examined. Free-streaming and collisional effects are present in the drift kinetic equation which is solved using an expansion of eigenfunctions of the bounce-averaged, pitch-angle scattering operator. For bounce times short compared to transit and collision times, the subsequent heat flow closure takes the form of an integral operator acting on electron temperature variations along magnetic field lines. The general closure agrees qualitatively with previous forms for the heat flux in homogeneous magnetic geometry and importantly, predicts a substantial reduction in the heat flow due to the trapping of particles in magnetic wells and the enhanced effect of collisions near the trapped/passing particle boundary.