Group velocity effect on resonant, long-range wake-fields in slow wave structures

Synchronous wake-fields in a dispersive waveguide are derived in a general explicit form on the basis of a rigorous electro-dynamical approach using Fourier transformations. The fundamental role of group velocity in wake-field propagation, calculation of attenuation, amplitudes, form-factors and loss-factors is analyzed for single bunch radiation. Adiabatic tapering of the waveguide and bunch density variation is taken into account analytically for the time-domain fields. Effects of field “compression/expansion” and group delays are demonstrated. The role of these effects is discussed for single bunch wake-fields, transient beam loading, BBU and HOMs. A novel waveguide structure with central rf coupling and both positive and negative velocities is proposed. It can be used effectively in both high-energy accelerators and single-section linacs.