Relativistic Langevin equation for runaway electrons

The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations [V.I. Tikhonov and M.A. Mironov, Markovian Processes (1977). Soviet Radio, Moscow]. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past [I. Fernández-Gómez et al., Phys. Plasmas 19 (2012) 102504].