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The question is how much each kind of imperfection lowers the limit.","posed_since":"","precise":"For a type-II superconductor with surface topography of rms height $h$ and lateral scale $l$, and with local suppression of the order parameter over a region of size comparable to the coherence length $\\xi$, compute the reduction of the vortex penetration field relative to $H_{\\mathrm{sh}}$ of a flat surface. An answer is a formula or computed map $H_p(h/\\xi, l/\\xi, \\kappa)$ usable to set surface specifications.","problem_ref":null,"references":"","settled_by":"Ginzburg-Landau simulations of realistic measured surfaces whose predicted $H_p$ matches cavity quench fields.","status_note":"Ginzburg-Landau simulations of idealized defects and roughness exist (2015 to 2020); predictions from measured cavity surfaces that match quench fields are lacking.","title":"How surface roughness and defects reduce the vortex-entry 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