Improved model for transmission probabilities of membrane bellows based on TPMC simulations

Abstract

Many complex vacuum systems include edge-welded bellows. Their simulation in the molecular flow regime with a Test Particle Monte Carlo (TPMC) code, such as MolFlow+, can take considerable amounts of computing power and time. Therefore we investigated the change of the transmission probability of a bellow compared to a cylindrical tube in TPMC simulations. The results were used to develop an empirical model to simplify the geometry of a bellow in a TPMC model by replacing it with a cylindrical tube of extended length, consequently compensating the reduced conductance of the bellow. The simulated transmission probabilities of a variety of different bellow lengths have been used to fit the parameters of the model. Each bellow geometry simulated with MolFlow+ comprised two cylindrical tubes, one at each end, and the central bellow section. The geometry of each bellow is described by two quantities. The first one is the total length of the geometry model normalized to the inner diameter of the bellow. The second one is the fraction of the bellow section with regard to the total length. Simulating a tube instead of a long bellow reduced the simulation time by a factor of up to 1000, while the error introduced through the replacement of the bellow with a cylindrical tube of modified length was in most cases negligible.