Wakefield and wave propagation at non-linear dispersion

Synchronous wakefield excitation and wave propagation along a dispersive slow-wave structure is considered. An explicit form for wakefields is obtained for a single bunch in the second and third approximations of dispersion while taking into account the effect of substantial group velocity with respect to charge velocity. Generalized differential equations describing diffused fields induced by a beam current or generated by an external source are derived. Field excitation and propagation near the cut-off is considered including trapped modes in the stopband. This theory can be applied to the fields induced by single bunch and bunch train in Standing Wave and Traveling Wave devices operating near π-mode, self-consistent beam break-up simulations, RF-generation, pulse propagation, and breakdown study in waveguides as well as some of new methods of acceleration in a dispersive medium.