  We investigate the flux penetration patterns and matching fields of a long
cylindrical wire of circular cross section in the presence of an external
magnetic field. For this study we write the London theory for a long cylinder
both for the mixed and Meissner state, with boundary conditions appropriate for
this geometry. Using the Monte Carlo Simulated Annealing method, the free
energy of the mixed state is minimized with respect to the vortex position and
we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The
free energy of the Meissner and mixed state provides expressions for the
matching fields. We find that, as in the case of samples of different geometry,
the finite size effect provokes a delay on the vortex penetration and a vortex
accumulation in the center of the sample. The vortex patterns obtained are in
good agreement with experimental results.
