We have probed the superconducting proximity effect through long high-quality monocrystalline Ag nanowires, by realizing Josephson junctions of different lengths, with different superconducting materials. Thanks to the high number of junctions probed, both the contact resistance and electron diffusion constant could be determined, enabling a comparison of the measured critical current to theoretical expectation, over the entire regime from short to long diffusive junction. Although the length dependence of the critical current is as expected, the amplitude of the $R_{N}I_c$ product is smaller than predicted by theory. We also address the magnetic field dependence of the critical current. The quasi-gaussian decay of the critical current with field expected of a long narrow junction is observed for all superconducting contacts we used except for aluminum. We present the striking non-monotonous effect of field on the critical current of junctions with aluminum contacts, and analyze it in terms of improved quasiparticle thermalization by a magnetic field.
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