The Transverse Oscillation of Coaxial Multiple Beams Propagating along a Magnetic Field in a Vacuum Tube

A fluid Maxwell theory has been derived to study a system of multibeams propagating parallel to an applied axial magnetic field in an evacuated conducting drift tube. The stability analysis is performed for a rigid-rotor and cold-laminar flow equilibria. It is assumed that the particle beams are tenuous and the guiding field is very strong. As a result, the perturbation theory is derived under the condition that the plasma frequency is much smaller than the cyclotron frequency for each beam particle. A dispersion relation is obtained for a special case of sharp-boundary density profiles. The stability properties of infinitely long beams are illustrated in detail for different geometries and various beam parameters. The results agree with those obtained by Uhm [8] in a special case where a solid electron beam propagates through an annular electron beam. The finite geometry effect of the accelerator is discussed briefly. It might have a substantial influence on the behavior of a real device.