Warm-fluid equilibrium theory of an intense charged-particle beam propagating through a Periodic solenoidal focusing channel

A warm-fluid theory of a thermal equilibrium for a rotating charged-particle beam in a periodic solenoidal focusing magnetic field is presented. The warm-fluid equilibrium equations are solved in the paraxial approximation. It is shown that the flow velocity for the thermal equilibrium corresponds to periodic rotation and radial pulsation. The equation of state for the thermal equilibrium is adiabatic. The beam envelope equation and self-consistent Poisson´s equation are derived. The comparison between analytically computed density profiles and the recent experimental results from University of Maryland Electron Ring (UMER) is presented. Temperature effects in the beam equilibria are investigated. The radial confinement of the beam is discussed.