Fractal properties of trivelpiece-gould waves in periodic plasma-filled waveguides

It is shown that dispersion curves describing a spectrum of Trivelpiece-Gould (TG) waves in periodic plasma-filled waveguides have a fractal nature. They are not solid lines as for other types of waves in periodic waveguides but suffer from discontinuities of the first kind at any k(z) = (P/Q) (2m+1)pi/d, where P and Q are integers, d is the period of the corrugation, and m is the transverse index of a mode. The gaps correspond to forbidden bands. The evaluation of the Hausdorf dimension of the dispersion curves is presented. Finally, qualitative consequences of the fractal nature of TG waves for plasma microwave electronics are discussed.