Analytic solutions of wake-fields

The analysis of wake-fields generated by moving charges in the vicinity of dielectric bodies is essential for the design of the next generation of optical acceleration structures. We present here analytic expressions for the wake-field in two different configurations where dielectric structures are involved. In the first case, the wake-field of an electron bunch moving parallel to a dielectric cylinder is considered. In the second, the radiation characteristics generated by a relativistic line charge moving in the vicinity of a dielectric cylinder is determined. The analysis in both cases relies on two assumptions: firstly, all external force is acting on the moving charge, keeping its velocity constant, or equivalently the energy transferred to radiation is negligible compared to the initial kinetic energy of the bunch. Secondly, the transverse motion of the moving charge is neglected. In the section that follows, a general approach for achieving analytic or quasi-analytic solutions is presented. This is followed by a presentation of the main analytic results.