= Parallel critical field of a thin London slab
{title2=$B_{\parallel C}/B_C\simeq\sqrt3\lambda/a$}
For a slab of thickness $2a$ with parallel applied field, the local London equation gives $B(x)=B_a\cosh(x/\lambda)/\cosh(a/\lambda)$. Averaging gives $M=-B_a[1-\tanh(a/\lambda)/(a/\lambda)]/\mu_0$. Integrating $-M\,dB_a$ and comparing with the bulk condensation energy yields the displayed thin-slab enhancement. It assumes field-independent condensate density and can be limited by pair breaking or nonlocal electrodynamics.
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