Beam-plasma instability spectra of a ribbon electron beam in an unbounded plasma

Treatments of the beam-plasma instability of a bounded electron beam in an unbounded plasma usually study the behavior of the growth rate as a function of the parameters of the problem for one or two oscillation modes which have the largest growth rate. This approach has permitted considerable insight into the important role of transverse transport of the oscillation energy with the group velocity out of the beam region in determining the behavior of the beam-plasma interaction. Here, a detailed investigation is presented of the influence of the finite transverse extent of a ribbon-shaped electron beam on the spectrum of the beam-plasma instability. The beam-plasma instability is studied for a ribbon electron beam is an unbounded magnetized plasma. The discrete and continuous instability spectra are analyzed in the case in which the beam has a large thermal velocity spread. The physical mechanism for the formation of the discrete modes is explained. It is shown that the boundedness of the beam essentially always has an effect on the instability spectrum when the beam width is less than the characteristic length on which noise is excited