A novel representation for the static space-charge fields in waveguide excitation theory

In the present technical note, we obtain representations for static electric and magnetic fields induced by charged-particle current in a regular simply connected ideally conducting waveguide in the form of solutions to excitation equations of the Kisunko–Vainshtein waveguide excitation theory. Using generic expressions for evanescent (and propagating) waveguide modes, an equivalence of the developed expressions with Green׳s function representations of these fields is demonstrated as well as a correspondence between equations of excitation for non-static part of the potential electric field in the standard and Sovetov׳s variants of the Kisunko–Vainshtein theory and the present approach is established.