Microscopic theory of superconductivity in MgB2-type systems in a magnetic field:: A neighborhood of Hc2

We calculate the upper critical magnetic field H (c2) in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface with the cavity topology typical of the compound MgB2 taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic z axis. We obtain analytic formulas in the low-temperature range (T/T-c << 1) and also near the critical temperature ((T-T-c)/T-c << 1). We compare the temperature dependence of H-c2 for a two-band anisotropic system with that of H-c2(0) corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of the band-structure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important role of the ratio v(1)/v(2) of the velocities on the Fermi surface in determining H-c2. We also obtain the values of the parameters Delta(1) and Delta(2) along the line of the critical magnetic field.