  Axial-symmetric magnetic field is often used in focusing of particle beams.
Most existing ion Low Energy Beam Transport lines are based on solenoid
focusing. Modern accelerator projects utilize superconducting solenoids in
combination with superconducting accelerating cavities for acceleration of
high-intensity particle beams. Present paper discusses conditions for matched
beam in axial-symmetric magnetic field. Analysis allows us to minimize power
consumption of solenoids and beam emittance growth due to nonlinear space
charge, lens aberrations, and maximize acceptance of the channel. Expressions
for maximum beam current in focusing structure, beam emittance growth due to
spherical aberrations and non-linear space charge forces are derived.
