Deterministic methods for numerical simulation of high-energy runaway electron avalanches

The possibilities of two deterministic methods for describing the kinetics of high-energy runaway electrons (REs) are analyzed as alternatives to stochastic methods requiring unrealistically large computing resources in problems of numerical simulation of electric discharges in dense gases involving REs. One of the methods being developed in recent years is based on multigroup equations for the moments of the electron distribution function, while the second method, which is conventionally used to solve problems in gas discharges, is based on the diffusion-drift equation. The modern method of multigroup equations allows one to calculate the RE energy distribution and the spatial RE distribution along the electric force, which are close to these distributions obtained by the Monte Carlo method if the number N of energy groups is chosen properly. The diffusion-drift equation does not give the energy distribution, but its advantage is the possibility of obtaining spatial RE distributions using small computing resources not only along but also perpendicular to the electric force, which are close to those calculated by the Monte Carlo method. To simulate discharges by the method of multigroup equations, it is necessary to know a priori the number N of groups providing good accuracy, the characteristic RE multiplication time te, and the energy runaway threshold εth as functions of the electric-field overvoltage. The diffusion-drift equation requires the specification, along with te, of the directed RE velocity and longitudinal and transverse diffusion coefficients calculated by the Monte Carlo method.