AVS 49th International Symposium
    Vacuum Technology Thursday Sessions
       Session VT-ThM

Paper VT-ThM3
Comparison between Monte Carlo and Analytical Calculation of the Conductance of Cylindrical and Conical Tubes

Thursday, November 7, 2002, 9:00 am, Room C-104

Session: Gas Dynamics and Flow
Presenter: J. Gómez-Goñi, Universidad Politécnica de Madrid, Spain
Authors: J. Gómez-Goñi, Universidad Politécnica de Madrid, Spain
P.J. Lobo, Universidad Politécnica de Madrid, Spain
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The accurate calculation of transmission probabilities of ducts in the molecular flow regime has become a need of vacuum standards on the ultra high 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 higher and higher. So it becomes important to compare simulation results with data obtained by other methods to check that random number generators used in the Monte Carlo are not biased. Moreover, with numerical methods we can obtain the density of molecules along the tube. This density is important in molecular beam formation studies. We have applied both a Monte Carlo method and numerical solutions of the Clausing integral equation for cylindrical and conical tubes. In the case of cylinders, we have found very accurate transmission probabilities solving numerically Clausing integral equations. The method consists in an approximation of the Clausing function with Chebyshev polynomials using a subroutine made by the Numerical Algorithm Group (NAG).@footnote 1@ Comparing with other values found in the literature@footnote 2@ made by a variational method, we have obtained values near the upper bound and quite far away from the lower bound. In the case of cones, we obtain values which agree with values found in the Literature@footnote 3@ to a high degree of accuracy. @FootnoteText@ @footnote 1@ NAG Subroutine D05AAF. @footnote 2@ R.J. Cole, J. Inst. Maths. Applics. 20, 107-115 (1977). @footnote 3@ R.P. Iczkowski, J.L Margrave and S.M. Robinson, J. Phys. Chem. 67,229 (1963)