Effects of Cold Plasma on the Negative Mass Instability of a Relativistic Electron Layer

The stability of a cylindrical layer of gyrating relativistic electrons (E layer), both in vacuum and in a cold plasma, is examined. The beam model assumes concentric particle orbits and allows for a finite thickness of the E layer. It is shown that the background plasma can stabilize the lower azimuthal modes (modes with their frequency less than the cold cyclotron frequency, or azimuthal wavenumber l less than the relativistic mass factor γ). The mechanism of stabilization can be interpreted in terms of an inductive impedance at the beam edge due to the cold plasma. The interaction of the beam with the plasma at the upper hybrid frequency is discussed briefly.