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This is based on a minimal extension of the Kraichnan-Moffatt model, to include a background linear shear and Galilean-invariant $\\alpha$-statistics. Using the first order smoothing approximation we derive a linear integro-differential equation for the large-scale magnetic field, which is non perturbative in the shearing rate $S\\,$, and the $\\alpha$-correlation time $\\tau_\\alpha\\,$. 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