3-D computer simulations of EM fields in the APS vacuum chamber: Part 1, Frequency-domain analysis

The vacuum chamber proposed for the storage ring of the 7-GeV Advanced Photon Source (APS) basically consists of two parts: the beam chamber and the antechamber, connected to each other by a narrow gap. A sector of 1-meter-long chamber with dosed end plates, to which are attached the 1-inch-diameter beampipes centered at the beam chamber, has been built for experimental purposes. The 3-D code MAFIA has been used to simulate the frequency-domain behaviors of EM fields in this setup. The results are summarized in this note and are compared with that previously obtained from 2-D simulations and that from network analyzer measurements. They are in general agreement. A parallel analysis in the time-domain is reported in a separate note. The method of our simulations can be briefly described as follows. The 1-inch diameter beampipes are terminated by conducting walls at a length of 2 cm. The whole geometry can thus be considered as a cavity. The lowest RF modes of this geometry are computed using MAFIA. The eigenfrequencies of these modes are a direct output of the eigenvalue solver E3, whereas the type of each mode is determined by employing the postprocessor P3. The mesh sizes are chosen such that they are small enough for computations in the frequency region in which we are interested (the sampling theorem), while the total number of mesh points is still well within the range that our computer system can cope with