Steady-state response of the electron distribution function to an applied electric field

Steady-state solutions to the linearized Fokker–Planck equation have been numerically investigated using two models. The Kulsrud model, in which the electron-electron collision term is simplified by evaluating the integrals using a Maxwellian distribution, is considered first. It is shown that steady-state solutions of the Kulsrud model, obtained by long time integrations of the time dependent equation, can be obtained more easily by considering a separable solution. A more physically reasonable steady-state model, which consistently describes both the thermal and runaway regimes and is readily solved numerically, is developed. The resistivity, in agreement with Spitzer and Härm, and runaway production rates, in agreement with the Kulsrud model, are obtained.