No abstract

We present a numerical method of calculating the pressure profile of a large ultra-high vacuum (UHV) system using finite-element analysis (FEA) that exploits the continuity of gas flow. In this study, we introduce a modified FEA (MFEA) that excludes the redundant count of aperture conductance of the element by the Oatley method and uses a correction factor compensating the beaming effect. Along with the correction and by choosing an appropriate length of the element, we improve the result for a cylindrical tube to show a small difference of 5% or less from that of the test particle Monte Carlo (TPMC) simulation. As an example of a practical application, we calculate the pressure profile of an accelerator vacuum system with a split chamber using the MFEA, and the result is validated by comparison with the TPMC. The MFEA method will be useful to design a large UHV system at an early stage that requires design iteration using a simple and fast calculation procedure.

The concept of transmission conductance is required to describe phenomena occurring in a tube with wall pumping. This is because the gas flow is not constant along the length of the tube but decreases, which implies that the geometric conductance determined by dimensional parameters of the tube cannot be further used. In one of the previous studies, the transmission conductance of a cylindrical tube was analytically derived using the particle balance equation based on the continuity principle. However, the calculated results well agreed with those of the test particle Monte Carlo (TPMC) simulation only when the sticking coefficient was less than 0.1. This is due to the intrinsic limitation of the analytical method, in which the constant conductance of a tube of unit length with uniform wall pumping was used. In this study, we introduced another analytical method based on the cosine law and finite element analysis using the conductance of the tube of unit length as a function of the position in the tube, considering the beaming effect. Using both methods, the relative difference in transmission conductance with TPMC considerably decreased compared to the previous study when the sticking coefficient was greater than 0.1. The results can be used in the design of a non-evaporable getter coated tube or a cryogenic water pump using an adsorbing wall to determine characteristic dimensions. Furthermore, this can be employed in a windowless vacuum coupling or a distributed pumping system for various light source systems.