Vlasov equilibria for a warm finite radius rotating relativistic electron beam in a magnetized plasma

A Vlasov equilibrium model is developed which can describe a broad class of beam-plasma systems in an applied field, B0z. The model treats arbitrary density profiles and azimuthal self-magnetic fields as well as a thermal spread in the momentum of the beam. It is assumed that the electron gyroradius is small but not negligible compared with the beam radius, and that the beam is completely charge neutralized but only fractionally current neutralized. The electron orbit equations are solved and are used to simplify the form of the distribution function and the calculation of its velocity moments. The rotation frequency of the beam and the diamagnetic or paramagnetic properties of such warm beam-plasma systems are also studied.