A new analytical model for axi-symmetric cavities

In this paper we derive a general off-axis expansion valid for axi-symmetrical EM fields. With the application of general arguments a new method to determine analytically off-axis field components is presented, starting with the knowledge of the on-axis distribution of the longitudinal field component. Analytical and numerical EM fields off-axis are compared, in the case of RF monopole modes in a cavity, showing very good agreement up to a radial off-axis position which is comparable to the wavelength. The relevance of the method on applications in analytical study of particles dynamics is discussed and a calculation of the transverse momentum imparted by the field to a relativistic particle is reported: this is of interest for dark current, beam halo and RF injector analysis. Another kind of application in cavity design is mentioned.