Paraxial optics of charged particles in solenoids

Paraxial optics of charged particles in solenoid magnets with axisymmetric field is considered. Analytic and symplectic transverse maps for charged particle motion through solenoids with 3D magnetic fields have been derived. The formula for transverse maps contains both linear and nonlinear effects caused by entrance and exit fringe fields of the solenoid. The explicit transfer map can be used for applications of accelerator physics that use solenoid magnets.