Deterministic models of minority neutral particle kinetics close to a catalytic surface, based on the formalism of radiative transfer

The kinetics of neutral particles diluted in a gas or plasma and reacting with a catalytic surface can be calculated accurately only by taking into account the finite value of the mean free path. In reactor models, this problem is usually solved by using reaction-diffusion equations, but this approximation is not always appropriate. As an alternative, Monte Carlo (MC) simulations are used, but they are affected by the noxious problem of statistical error. We propose to address this problem by using the formalism of radiative transfer. A system of integral equations is formulated by generalizing the Schwarzschild-Milne one, in order to take into account several chemical species interacting with a partially catalytic surface, including any kind of backscattering angular distribution. We show that the generalized equations can be easily solved in a computer model using a standard relaxation technique; an excellent agreement with MC simulations is obtained. Applications are discussed.