An efficient energy-conserving numerical model for the electron energy distribution function in the presence of electron–electron collisions

An efficient algorithm to calculate the contribution of electron–electron collisions in the Boltzmann equation for free electrons, in the two-term approximation is presented. The electron–electron collision term must be energy-conserving, while, due to non-linearity, commonly used algorithms do not satisfy this requirement. The efficiency of the algorithm make feasible the use of a non-linear iterative solver to conserve electron energy in electron–electron collisions. The performance of the proposed algorithm has been compared with standard numerical schemes obtaining: 1) considerable gain in computational time; 2) the conservation of the total electron energy density in e–e collisions under the required tolerance.