Particle Distribution Function Forming in Nonlinear Systems

Modern ion-optical systems are used in different fields of beam physics both independent facilities as consisting of large machines. One of these destination is to create beams with a desired distribution of beams particles. Often there is a need to ensure a homogeneous distribution for a terminal beam phase portrait in a transverse configuration space. This is one of problems of nonlinear aberrations management. It is known that nonlinearity properties inhere to any beam lines. Such these nonlinearities have unremovable character, and their influence can be remove using only special nonlinear lattice elements, which are introduced artificially into the beam line. In this paper we suggest a procedure to find necessary nonlinear correcting control elements for purposive forming of beam particle distribution functions.