Long-wave diocotron instability in high-current relativistic electron beams

The stability of a high-current relativistic sheet electron beam located sy ymmetrically between two plane-parallel conducting screens and confined by the longitudinal magnetic field is invstigated. As the electron energy in the beam is not limited, relative transverse electron velocities in the beam (velocity shear) may be relativistic, which does not permit to neglect the beam proper mag gnetic field and non-potentility of disturbances, as it was done before. These factors are found to decrease the increment and to narrow the long-wave diocotro on instability region