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.
Highlights
The modified FEA (MFEA) has been tested in several practical cases, such as vacuum chambers with wall sorption, non-cylindrical tubes with various aspect ratios, and the split chamber of a particle accelerator
The results are summarized as follows: (1) The average pressure of a 1D cylindrical tube calculated by the MFEA is as accurate as that by the test particle Monte Carlo (TPMC), and the relative error is only 5% or less compared to the TPMC for Le/d ≤ 5, which means the length of the element for the finite-element analysis (FEA) calculation is desirable to be selected in the range Le/d ≤ 5
(2) For the non-cylindrical tubes, the relative error is less than 5% for the aspect ratio < 2, and even for the aspect ratio close to 10, it is in the similar range of error as the practical ionization gauge (20%)
Summary
Pressure profile calculation is an important task when designing a large ultra-high vacuum (UHV) system, such as a particle accelerator. The calculated pressure profiles are used to determine the positions and pumping speeds of pumps in the vacuum system and to set parameters for the dimension and shape of tubes.The early techniques of pressure calculation have mainly focused on developing analytical equations, but it is only effective for simple geometries. Numerical methods based on linear kinetic theory or Navier–Stokes equations are studied to simulate gas flow of more complex cases, such as a network geometry consisting of tubes, a cylindrical tube with end-effects, a system with temperature drops, and micro-channels with a sudden expansion or contraction. A direct simulation Monte Carlo (DSMC) is a more flexible numerical method to obtain pressure profiles over the wide range of gas rarefaction, even in micro- or nanochannels.10–13In a free-molecular regime where the interactions between gases are neglected, test particle Monte Carlo (TPMC). Pressure profile calculation is an important task when designing a large ultra-high vacuum (UHV) system, such as a particle accelerator.. The early techniques of pressure calculation have mainly focused on developing analytical equations, but it is only effective for simple geometries.. Numerical methods based on linear kinetic theory or Navier–Stokes equations are studied to simulate gas flow of more complex cases, such as a network geometry consisting of tubes, a cylindrical tube with end-effects, a system with temperature drops, and micro-channels with a sudden expansion or contraction.. A direct simulation Monte Carlo (DSMC) is a more flexible numerical method to obtain pressure profiles over the wide range of gas rarefaction, even in micro- or nanochannels.. In a free-molecular regime where the interactions between gases are neglected, test particle Monte Carlo (TPMC)
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