In the Bean model, as we start applying a magnetic field $H$ in the plane of a slab, the $B$-field inside the superconductor decreases linearly from each side, and at a sufficiently high field $H^{*}$ there is no longer anywhere in the superconductor where $B=0$. What happens to the $B$-field when $H>H^{*}$? Diagrams that I've seen (such as the one in this answer) implies that the $B$-field continues to increase as if the superconductor were now transparent to any additional field, but I'm confused. Shouldn't field that passes through a superconductor be quantized as vortices, and if so, shouldn't this increase the amount of trapped flux? Is my understanding that the superconductor in the Bean model doesn't react to any increased flux correct, and if so, is this an unphysical assumption that the Bean model makes?

Also, does the Bean model assume that an applied field has no effect on suppressing the superconductivity, so that $H_{c2}$ is meaningless in this model?


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