AN ANALYTICAL APPROACH TO OPTICAL-PROPERTIES OF PLASMA LENSES WITH A NONLINEAR MAGNETIC-FIELD PROFILE

The problem of evaluating the charged particle beam dynamics in plasma lenses with non-linear magnetic field profiles is considered. An anal ytical solution is given in terms of Jacobi functions for a proper cla ss of field profiles. Such a solution is successfully compared with re sults obtained from a tracking code. From the analysis of the properti es of the single-particle trajectory equation, deeper insight is gaine d about the focusing process. In particular, the phase space beam cont our dynamic is evaluated. By analysing the beam envelope, it is demons trated that for large emittance beams and in the case of a concave-typ e field profile the spot reduction ratio is larger than that obtained in the linear case and a considerable improvement in the focusing powe r is obtained.