Electron Heat Transport down Steep Temperature Gradients

Electron heat transport is studied by numerically solving the Fokker-Planck equation, with a spherical harmonic representation of the distribution function. The first two terms ($f_0, f_1$) suffice, even in steep temperature gradients. Deviations from the Spitzer-Härm law appear for $\frac{\lambda }{L_T}\left[\right(\mathrm{mean}\mathrm{free}\mathrm{path})/(\mathrm{temperature}\mathrm{gradient}\mathrm{length}\left)\right]\gtrsim 0.01$, as a result of non-Maxwellian $f_0$. For $\frac{\lambda }{L_T}\gtrsim 1$, the heat flux is $\frac{1}{3}$ of the free-streaming value. In intermediate cases, a harmonic law describes well the hottest part of the plasma.