Comparison between Monte Carlo and analytical calculation of the conductance of cylindrical and conical tubes

The accurate calculation of transmission probabilities of ducts in the molecular flow regime has become a need of vacuum standards on the ultrahigh vacuum region. The usual approach is to simulate a molecular flow of molecules with a Monte Carlo method, because of the difficulties that arise trying to find a solution of the Clausing integral equation in a system of a given geometry. As modern computers increase their speed, the accuracy of Monte Carlo methods is getting higher. It is therefore important to compare simulation results with data obtained by other methods to check that pseudorandom numbers generated are uniformly distributed and not correlated. We have applied both a Monte Carlo method and numerical methods to solve the Clausing integral equation for cylindrical and conical tubes. Both Monte Carlo and numerical methods are consistent within estimated uncertainties. In the case of conical ducts, we obtain values which agree very well with values found in the literature and with uncertainties several orders of magnitude smaller. In the case of cylinders, very accurate transmission probabilities are obtained solving numerically the Clausing integral equation. Comparing with other values found in the literature using a variational method, our values are near the upper bound and quite far away from the lower bound.