The focusing properties of solenoid lenses

Solenoids show inevitability their spherical aberration, which increases beam effective emittance. In this work the make efforts to improve field quality in different ways. Calculations tell that increasing gap size of pole pieces or taping magnet poles can obviously reduce coefficient of spherical aberration. The equivalent parameters of solenoid lenses are calculated according to axial magnetic field pattern of lenses; they only relate to its geometry, independent of its magnetic field inductivity strength