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In the asymptotic limit of a large Ginzburg-Landau parameter, we give a newasymptotic formula for the $L^2$-norm of the Ginzburg-Landau order parameter.The formula is valid in the bulk regime where the intensity of the appliedmagnetic field is of the same order as the Ginzburg-Landau parameter andstrictly below the second critical field. Our formula complements thecelebrated one of Sandier-Serfaty for the $L^4$-norm.

The density of superconductivity in the bulk regime