We investigated the effect of alloying on the upper critical field H-c2 for 12 MgB2 films, in which disorder was introduced by growth, carbon doping or He-ion irradiation, finding a significant H-c2 enhancement in C-alloyed films, and an anomalous upward curvature of H-c2(T). Record high values of H-c2(perpendicular to)(4.2)approximate to35 T and H-c2(parallel to)(4.2)approximate to51 T were observed perpendicular and parallel to the ab plane, respectively. The temperature dependence of H-c2(T) is described well by a theory of dirty two-gap superconductivity. Extrapolation of the experimental data to T=0 suggests that H-c2(parallel to)(0) may approach the paramagnetic limit of similar to70 T.
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