Nonlinear Theory of the Plasma Wave Excitation in a Bounded Beam-Plasma System

The excitation of symmetric and antisymmetric plasma waves by a beam layer that moves within a homogeneous plasma enclosed by a metallic wall was dealt with theoretically. Investigations were carried out for the magnetic field free case and for a magnetized electron beam. In the latter case, the beam electrons are assumed to be unable to move in the perpendicular direction. The theoretical model bases upon an extension of the well known single wave theory to a two-dimensional beam-plasma system. Special emphasis should be paid to the fact that the perpendicular wave profile of the excited waves was determined self-consistently. Energy and momentum balance equations are derived for this system. The theoretical method outlined in this paper which is based on a Green's-function technique can be extended easily to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed. Several interesting effects were found in the magnetic field free case: (i) numerical solutions describe an increasing steepening of the wave amplitudes in perpendicular direction near the center of the system for the symmetric potential wave; (ii) for the antisymmetric wave, a smoothing tendency was found in the development of the perpendicular wave potential profile; (iii) spatial separation of the slow and fast beam electrons was observed; (iv) it is shown for the antisymmetric potential wave type that, under certain conditions, a very efficient beam particle retardation mechanism occurs which is connected with a strong reduction of the formation of a fast particle group; (v) generally it was shown that the conversion of the kinetic energy of the beam electrons into the plasma wave energy may be more effective as compared with the case of the magnetized beam.