Point-to-source path tracing Monte Carlo to compute the Clausing and distribution functions in high-vacuum systems

Abstract

This paper presents an approach to simulate the free molecular flow in vacuum systems by using a Monte Carlo method for solving the Boltzmann particle transport equation with no intermolecular collisions. Sometimes referred to as a point-to-source Monte Carlo path tracing in image rendering, in this paper the name is borrowed from the thermal radiation and heat transfer field, reverse Monte Carlo path tracing. It is shown that this method provides better accuracy and stability when computing the Clausing function when compared to the standard test particle Monte Carlo method used for free molecular flow. The Clausing function leads to the distribution function of positions and velocities from which the particle density map, pressure gradient, energy flux, and other local quantities can be computed. Using reverse path tracing, the particle concentration in a conical segment is computed, and the maximal flow input is determined by calculating the mean free path at the maximum density position.