Invariability of intense beam emittance in nonlinear focusing channel

New approach to keep emittance of a high current beam in a uniform focusing channel is presented. The matching conditions for a beam with arbitrary distribution function in a nonlinear focusing channel are examined. To obtain proper matching, it is necessary to accept that the potential of the external focusing field contains higher order terms than quadratic. The solution for external potential is obtained from the stationary Vlasov´s equation for beam distribution function and Poisson´s equation for electrostatic beam potential. An analytical approach is illustrated by results of a particle-in-cell simulation