Method of solution for the wake field excited by relativistic electron bunch in a dielectric waveguide

The dielectric waveguide is one of the simplest slow-wave structures, and therefore an experimental wake field excited by a relativistic electron bunch in a dielectric waveguide is of interest. Zhang et al. (1997) have determined the fields in a flat two dimensional dielectric slow-wave structure. It was revealed that due to multimode interaction in a dielectric slab with a large value of dielectric constant (ε=10), the spatial distribution of the wake field is formed by narrow periodically located maxima. The latter propagate along the structure axis with the phase velocity equal to the velocity of the bunch. Such fields can be used both for acceleration of charged particles and for generation of microwaves. Similar wake fields that appear due to propagation of a relativistic electron bunch in a cylindrical dielectric waveguide are investigated in this paper. The problem is solved in the linear approximation for various sets of parameters