FORMALISM FOR ROTATING ELECTRON-BEAMS FROM CUSP AND COMPRESSION FIELDS

The dynamics of a relativistic electron beam is analyzed for an arbitr ary magnetic field in an axisymmetric system, including a magnetic cus p. The analysis is based on a model utilizing stratified magnetic fiel ds and yields simple algebraic equations for the electron beam paramet ers. The equations are then applied to a magnetic field profile approp riate for the cusptron or the peniotron microwave tubes which include magnetic compression in the downstream region. By virtue of the strati fied model, any experimentally realizable magnetic field can easily be incorporated into the analysis. The analysis also clarifies non-adiab atic phenomena which may occur in these devices as streaming electrons are turned into an axis-rotating electron beam by a magnetic cusp or as the beam is compressed in a relatively short distance. Emphasis is given to the extent of this nonadiabaticity, which contributes to off- centering of the guiding center in the downstream region of the device s.