Fractal properties of periodic plasma waveguides

Summary form only given. Electromagnetic properties of periodic plasma waveguides at frequencies below the plasma frequency remain a mystery for researchers. The traditional approach leads to the divergence of numerical results and appearance of the "dense" spectrum, containing spurious information. A closed form analytical solution was previously obtained for electrostatic oscillations in a planar periodic waveguide filled with strongly magnetized, uniform, cold, collisionless plasma. It enables us to get a wide and deep insight into basic properties of plasma modes in spatially bounded periodic plasma configurations frequently encountered in different technological applications. In particular, it has been shown that the spectrum of plasma (Trivelpiece-Gould) modes in periodic structures has a fractal nature. Dispersion curves of these modes can suffer from an infinite number of breaks in a finite frequency range. Stopbands occur at any wavenumber satisfying the relation k/sub z/ = (P/Q)r/d, where P and Q are integers, and d is the period of the plasma-filled waveguide. The obtained dispersion curves can be characterized by the fractal (Hausdorf) dimension D/sub H/. Calculations of D/sub H/ for sinusoidally rippled plasma-filled waveguides show that D/sub H/