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The vortex states in a thin mesoscopic disk are investigated within thephenomenological Ginzburg-Landau theory in the presence of different ''model''magnetic field profiles with zero average field which may result from aferromagnetic disk or circulating currents in a loop near the superconductor.We calculated the dependences of both the ground and metastable states on themagnitude and shape of the magnetic field profile for different values of theorder parameter angular moment, i.e. the vorticity. The regions of existence ofthe multi-vortex state and the giant vortex state are found. We analysed thephase transitions between these states and studied the contribution fromring-shaped vortices. A new transition between different multi-vortexconfigurations as the ground state is found. Furthermore, we found a vortexstate consisting of a central giant vortex surrounded by a collection ofanti-vortices which are located in a ring around this giant vortex. The limitto a disk with an infinite radius, i.e. a film, will also be discussed. We alsoextended our results to ''real'' magnetic field profiles and to the case inwhich an external homogeneous magnetic field is present.Comment: 17 pages, 23 figures. Submitted to PR

Vortex structure of thin mesoscopic disks in the presence of an inhomogeneous magnetic field