  In the present work we investigate the behavior of a vortex in a long
superconducting cylinder near to a columnar defect at the center. The
derivations of the local magnetic field distribution and the Gibbs free energy
will be carried out for a cylinder and a cavity of arbitrary sizes. From the
general expressions, it considered two particular limits: one in which the
radius of the cavity is very small but the radius of the superconducting
cylinder is kept finite; and one in which the radius of the superconducting
cylinder is taken very large (infinite) but the radius of the cavity is kept
finite. In both cases the maximum number of vortices which are allowed in the
cavity is determined. In addition, the surface barrier field for flux entrance
into the cavity is calculated.
