Abstract
A solenoid magnetic field model is presented that describes the on axis field by a parameter of its hard edginess and axial half-width at half-maximum field, which universally define its spherical aberration without solving the ray equation. The model shows an increase in spherical aberration from real soft edge fields to hard edge models, as used in beam tracking. It compares well with existing field models. It simply and accurately finds the spherical aberration in many types of solenoids.
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