Analytical method for the evaluation of field modulation inside the rf-shielded chamber with a time-dependent dipole magnetic field

A ceramic chamber with Cu stripes is usually used as the vacuum chamber in a rapid cycling synchrotron. The Cu stripes terminate at either end as capacitors, and provide the low impedance for the circulating beam, and the high impedance for the induced current with the frequency components of the external time-dependent magnetic field (for example, injection bump magnets, bending magnets, etc.). It is important to be able to precisely estimate the field modulations inside the chamber when the field is excited, because any such field modulations can cause the beam characteristics to deteriorate. In this paper a theoretical approach to evaluate the field modulations in a quick and precise manner is developed.