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

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