Conservation of space-charge-dominated beam emittance in a strong nonlinear focusing field

Beam dynamics in a nonlinear uniform focusing channel is studied from the viewpoint of keeping emittance of a high current beam. Conservation of beam emittance is treated as a problem of proper matching of the beam with the uniform focusing channel. To obtain matching conditions for a beam with an arbitrary distribution function, it is necessary to accept that the potential of the external focusing field contains higher-order terms than quadratic. The solution for the external potential is obtained from the stationary Vlasov's equation for the beam distribution function and Poisson's equation for the electrostatic beam potential. An analytical approach is illustrated by results of a particle-in-cell simulation. {} 1996 The American Physical Society.