Nonlinear interactions of azimuthal surface waves in a magnetoactive plasma waveguide

Abstract

Several possible three-wave and four-wave interactions, namely decay and modulational instabilities of a specific type of surface waves-azimuthal sufaces waves (ASW)-in a magnetoactive plasma waveguide are considered. The studied ASW propagate in the azimuthal direction at the cylindrical waveguide wall-plasma interface.Three-and'four-wave interactions in bounded plasma structures are of principal interest as possible nonlinear phenomena available for experimental observation [ 1 -51. The interest of such interactions is growing nowadays with the development of plasma electronics [6]. The solution of a number of applied problems in this area needs a detailed study of the dispersion and nonlinear properties of plasma waveguide structures. The electromagnetic field topography and the dispersion properties of a majority of possible volume-type and surface-type modes as well as several nonlinear wave interactions in plasma waveguide structures have been thoroughly investigated up till now. In a cylindrical plasma waveguide fully filled by a magnetoactive plasma, the existence of a specific type of surface waves-azimuthal surface waves-is possible [7]. The interest of these waves is due to possible application of ASW in plasma gyrotron structures [8]. This type of waves is considerably less studied up till now compared with other propagating modes of plasma waveguide. The ASW propagate in the azimuthal direction (i.e. across the external magnetic field, which is directed along the waveguide axis z ) at the plasma-metal cylinder interface. The dependence of all wave perturbations on the azimuthal angle cp and time t in the ASW field is expressed in the following formwhere m is the azimuthal wavenumber (i.e. the mode number), w is the ASW eigenfrequency, A represents the totality of plasma parameters (electromagnetic fields of ASW, plasma density, hydrodynamic velocities). The existence of these waves in a cold magnetoactive plasma is possible in the frequency ranges ol < o < o, and oll > o > oh, where w, is the electron cyclotron and w , ,~ are the lower hybrid and upper-hybrid frequencies, respectively,In both frequency ranges of existence the character of these waves propagation is nonreciprocal. In the first frequency range the ASW may propagate only with m > 0, and the second one provides ASW propagation only with m < 0. The linear theory of the ASW is developed in papers [7-91, the paper [lo] presents the results associated with the