Filamentation Instability of a Relativistic Hollow Electron Beam

摘要

The filamentation instability properties of a relativistic hollow electron beam confined in axial flow by a uniform magnetic field in a pipe are investigated via the Vlasov-Maxwell equations. The instability is found to have two side-bands, one with a spectrum of positive wavenumbers k and the other with a spectrum of negative wavenumbers. The spectral point k=0, associated with the diokotron instability, is excluded from the filamentation instability's two unstable sidebands. Only in the limit of zero axial beam flow, the diokotron instability becomes asymptotically part of the filamentation instability spectrum. In this limit the filamentation instability's two sidebands merge asymptotically and symmetrically toward the diokotron instability spectral point, k=0, in agreement with the basic driving physical mechanisms and geometry configurations for these two distinct and different instabilities.