Stability of plane electron beams in space-limited plasma

Peculiarities of development of beam-plasma instability in a narrow channel are considered. The transversal dimensions of a beam in plasma coincide with or are comparable to the wavelength of excited oscillations. The increments of the Langmuir and surface waves in a limited system of plasma-beam in a multimode regime are successively calculated. The results are compared with the maximum increment obtained for an unlimited plasma-beam system, and also with the increment obtained for a limited system with provision for development of one instable mode of oscillations. On the basis of numerical calculations of increments estimated are the wavelengths of channels which provide electron beam transport practically without losses