Modern, multi-modular plasma modeling requires accurate and versatile methods for the determination of the electron velocity distribution function from which rate coefficients of electron impact processes as well as electron transport quantities are determined. In this paper we propose as a solution a modified version of a strongly overlooked method developed in the early 90s, namely, Monte Carlo Flux (MCF). The improvement lies in a criterion for the otherwise somewhat empirical selection of the time-step used in the method. We show that an MCF based code highlights and overcomes the limitations of two-terms codes such as BOLSIG+ and it is much faster than a conventional Monte Carlo. Moreover, MCF is in excellent agreement with the multi-term method for a wide range of reduced electric fields, being at the same time much simpler to implement and to extend to more general cases than the latter. Explicit illustrations of the Markov matrices representing short-time kinetics are presented to gain insight into the method. The two-dimensional velocity distribution and its expansion into Legendre polynomials are discussed for electrons in argon.
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