A Simple Model for the Energy Loss of a Bunched Beam Traversing a Cavity

Based on a simple model of the field pattern, an analytical formula for the energy loss of a relativistic bunched beam traversing a cavity is derived, for a range of parameters where the field lines do not spread and where reflections from the cavity walls are absent. The parameters of the formula are the beam tube radius (a), the gap length (g), the bunch length (σ), and if necessary, a nose cone angle (θ). The formula is applied to several cavities with various shapes, for which accurate data from computer programs are available. It is found that this model agrees with the data within an accuracy of 30 % for 0.2 < σ/a < 2.0 when g/σ >
₂
and σ is less that half the outer radius of the cavity.