Conduction heat loss scaling in open field line geometries

A scaling law governing the cooling of a finite-length column due to electron thermal conduction loss at the column ends, where the magnetic field lines are intercepted by a cold material wall, is derived. In addition to the electron temperature, both the electron number density and the magnetic field strength are allowed to vary along the field lines. It is shown that the cooling of the column is not very sensitive to moderate spatial variations of number density and magnetic field strength and is well represented by a characteristic cooling time given by τ0= (5/2) nL2/K0, where L is the column half-length and n and K0 are the number density and coefficient of thermal conductivity at the midplane.