Fractal properties of periodic plasma waveguides

Abstract

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/<I for a fixed height of the ripples, and tends to unity at decreasing height. It does not depend on the transverse index of a mode. The present message is concentrating on a physical interpretation of the results obtained previously and on an analysis of their expected consequences for microwave plasma electronics. Plasma modes are not waves in the common sense. They have zero group velocity in any point of their dispersion curves which corresponds to the cut-off frequency or lies infinitely close to the cut-off frequency. Any such point should hence be considered as an eigenfrequency of some cavity. The length of the cavity depends on frequency and can be much less than the period of the structure. The field inside the cavity shows standing waves which can reach very high values. Eigenfrequencies can be located infinitely close to each other. These unusual properties of plasma waves in periodic plasma waveguides can essentially promote to reach an adequate understanding of odd plasma behavior in different applications. In particular, they can be the reason for the appearance of electrons and ions of super-high energy in beam-plasma interaction experiments, of the appearance of stochastic regimes of operation of plasma-filled devices, and so forth. It is quite probable that other types of plasma waves like plasma cyclotron modes and ion-acoustic plasma modes may also show fractal properties.