The Instability of an Annular Electron Beam Propagating along a Guided Magnetic Field

The instabilities of an infinitely long and azimuthally symmetric annular electron beam propagating along an external applied magnetic field are investigated using the fluid-Maxwell theory. Unlike the treatment in the conventional diocotron instability, full electromagnetic perturbations have been emphasized and no approximation has been made such as k¿~ 0 and ¿ ~ckß in the macroscopic cold fluid description. There have been found two distinct and different instabilities depending on the value of doppler-shifted eigenfrequency ¿-ckß. The diocotron instability dominates in the low frequency region while cyclotron resonance perturbation plays a major role in the high frequency domain. In the case of a sharp boundary density profile, the growth rates versus different wavenumber k are shown for both instabilities in the beam parameters of out interest.