Analytic and quasi-analytic solutions of wake-fields

The analysis of wake-fields generated by moving charges in the vicinity of dielectric and metallic bodies is essential for the design of the next generation of optical acceleration structures. Recently, we have investigated analytically the wake-field associated with three different geometries. I. In the case of an electron bunch moving parallel to a dielectric cylinder, it was shown that for the relativistic regime (gamma much greater than 1) the circular harmonic of order zero contributes a decelerating force inversely proportional to gamma, whereas the circular harmonics of nonzero order contribute a gamma-independent force. II. For a line charge moving in the vicinity of a dielectric cylinder, it was shown that the emitted energy increases logarithmically with the kinetic energy (gamma-1) of the line charge and its transverse kick is inversely proportional to the kinetic energy for the ultra-relativistic case. III. When an electron-bunch traverses a geometric discontinuity a time-domain method was developed for the evaluation of the wake-field employing the independence of the exponential functions, that control the temporal behavior of the field.