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We have studied the effect of damage induced by 2 MeV alpha particles on the critical temperature, T c , and resistivity, , of MgB 2 thin films. This technique allows defects to be controllably introduced into MgB 2 in small successive steps. T c decreases linearly as the intragrain resistivity at 40 K increases, while the intergrain connectivity is not changed. T c is ultimately reduced to less than 7 K and we see no evidence for a saturation of T c at about 20 K, contrary to the predictions of the T c of MgB 2 in the dirty limit of interband scattering.

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