Radiation Losses Due to the Interaction of Charged Particles with Conducting Bodies

When particle bunches travel near perfectly conducting bodies, an electromagnetic field is induced which modifies the energy of the particles. In this paper we discuss the interaction of cylindrical bunches and toroidal perfectly conducting bodies. This problem is treated in terms of electromagnetic wave scattering As a matter of fact, when the electromagnetic waves that travels together with the bunch, illuminates the obstacle, a scattered electromagnetic field appears, which modifies the energy of the bunch particles. This scattering problem is treated directly in the time domain, using space-time integral equations and solved by a time stepping approach. From the knowledge of the scattered field on the bunch axis, a transient potential seen by every particle is determined and the total energy loss of the bunch can be deduced. A numerical application for the case of toroidal obstacles with circular cross-section is presented. The transient potential obtained by beam-obstacle interaction is relevant to the determination of the bunch longitudinal equilibrium distribution. Particularly in high energy storage rings this potential (as well as the beam cavity interaction potential) can modify the bunch shape and involve current limitations.