Thermalization of an intense, space-charge-dominated electron beam in a long focusing channel

A continuous electron beam with a correlated emittance will eventually ther malize. Initially, the beam emittance for an intense, high-brightness, spac e-charge-dominated beam will oscillate, but after a sufficiently long time, it will reach an equilibrium value. The emittance oscillations are due to coherent transverse plasma oscillations in the beam and are a manifestation of periodic energy exchange between potential and kinetic energies. The be am eventually attains an equilibrium emittance, as the beam equipartitions the kinetic and potential energies. This equipartioning is reached as the b eam thermalizes due to a form of Landau damping of the radial oscillations at different radial positions within the beam. Slight differences in the tr ansverse plasma oscillation frequency for different radial positions lead t o incoherence in the oscillations. In this paper, we calculate the equilibr ium time scales required for equipartioning. We show that the equilibrium e mittance scalings and magnitude can be predicted by conservation of energy considerations. In addition, we show that, in the space-charge dominated re gime,there is a correspondence between the energy-conservation approach and the kinematic approach. [S1063-651X(99)10608-1].