Instability regions of an electron beam in superimposed periodic and uniform magnetic fields

The stability of an electron beam in a superimposed sinusoidal and uniform magnetic field is theoretically and experimentally investigated. The first instability region degenerates to a point within the first well-known passband for a zero uniform field component, whereas the second instability region coincides with the first stopband of the sinusoidal field. These considerations are of practical significance for periodic magnetically-focused electron beams.