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Accurate numerical calculations of molecular flow transmission probabilities and density distributions of tubes are important to the benchmark problems of Monte Carlo solutions, dynamic expansion vacuum gauge calibration systems, and molecular beam formation studies. Although Nawyn and Meyer [published by van Essen and Heerens. J Vac Sci Technol 1976; 13:1183] have solved cylindrical tube problems by using the numerical method based on Clausing's equations, perhaps the calculated results still lack sufficient accuracy. In this paper, we propose a modified method that could achieve calculation accuracies of transmission probabilities as high as 10−11–10−13 in the range of L′/R ≤ 100 (where L′ is the tube length, R is the tube radius), which are more accurate than the results recently reported by Mohan et al. [J Vac Sci Technol A 2007; 25:758] and Gomez-Goni et al. [J Vac Sci Technol A 2003; 21:1452]. |
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