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It is shown that a multilayer comprised of alternating thin superconducting and insulating layers on a thick substrate can fully screen the applied magnetic field exceeding the superheating fields of both the superconducting layers and the substrate, the maximum Meissner field is achieved at an optimum multilayer thickness. For instance, a dirty layer of thickness ∼0.1 m at the Nbsurface could increase ≃ 240 mT of a clean Nb up to ≃ 290 mT. Optimized multilayers of NbSn, NbN, some of the iron pnictides, or alloyed Nb deposited onto the surface of the Nb resonator cavities could potentially double the rf breakdown field, pushing the peak accelerating electric fields above 100 MV/m while protecting the cavity from dendritic thermomagnetic avalanches caused by local penetration of vortices.


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