Track fitting in slightly inhomogeneous magnetic fields

A fitting method to reconstruct the momentum and direction of charged particles in slightly inhomogeneous magnetic fields is presented in detail. For magnetic fields of the order of 1 T and inhomogeneity gradients as large as 1 T/m the typical momentum bias due to the proposed approximations is of the order of few MeV, to be compared with scattering components of the order of 20 MeV or even larger. This method is currently being employed in the reconstruction programs of the AMS experiment.