Self-consistent simulation of the space charge dominated beams in an elliptical solenoid magnet

The behaviour of a space charge dominated beam has been studied through an elliptical solenoid which is used for making a planar beam as well as for matching an axisymmetric beam to a system needing unequal beam sizes in the two transverse planes. We have first developed an envelope model based on the canonical description of the motion and derived ten independent first order differential equations for the beam sigma matrix elements by assuming canonically transformed Kapchinskij-Vladimirskij (KV) like distribution of the beam. In order to investigate the nonlinear space charge effect a 2D particle-in-cell method has been used. Five types of phase space distributions for the initial beam have been utilized to study the evolutions of envelope and emittance as a function of beam current for different initial beam conditions as the beam passes through the elliptical solenoid. It is shown that the evolution of beam sizes depends weakly on the form of initial distributions whereas the projected emittances in the two transverse planes strongly depend on the initial beam conditions and type of distributions