Numerical simulation by a random particle method of Deuterium-Tritium fusion reactions in a plasma

We propose and we justify a Monte-Carlo algorithm which solves a spatially homogeneous kinetic equation of Boltzmann type that models the fusion reaction between a deuterium ion and a tritium ion, and giving an α particle and a neutron. The proposed algorithm is validated with the use of explicit solutions of the kinetic model obtained by replacing the fusion cross-section by a Maxwellian cross section