Beam focusing characteristic of an elliptical solenoid magnet in the presence of space charge

A solenoid magnet with elliptical pole face aperture creates unequal focusing forces in the two transverse planes compared to a solenoid with circular aperture which produces equal focusing in both the planes. This asymmetric focusing characteristic of elliptical solenoid can therefore be utilized in making a planer beam as well as transverse matching to a system with unequal beam sizes in the two transverse planes. In this paper we have studied the beam optical properties of an elliptical solenoid magnet in the presence of linear space charge effect and discussed the non-conservation of two transverse projected emittances as the beam passes through the magnet. In addition we have studied the feasibility of using an elliptical solenoid for transverse matching of a space charge dominated beam to the acceptance of a spiral inflector.