We explore the analogy between quark confinement and the Meissner effect in superconductors. We measure the response of color-magnetic "supercurrents" from Dirac magnetic monopoles to the presence of a static quark-antiquark pair in fourdimensional U(1) lattice gauge theory. Our results indicate that in the confined phase these currents screen the color-electric flux due to the quarks in an electric analogy of the Meissner effect. We show that U(1) lattice gauge theory obeys both a dual London equation and an electric fluxoid quantization condition.12.38. Aw, 11.15.Ha, 74.30.ci, 74.60.Ec Typeset Using REVTEX 1

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We report detailed calculations of the profiles of energy and action densities in the quarkantiquark string in SU(2) lattice gauge theory. We conclude that at B q-q separation R sz 1.0 fm we are beginning to see the asymptotic flux tube. By employing the Michael sum rules we further conclude that the peak energy density approaches a constant in R.

We calculate the electric flux and magnetic monopole current distribution in the presence of a static quark-antiquark pair for SU(2) lattice gauge theory in the maximal Abelian gauge. The current distribution confines the flux in a dual Abrikosov vortex whose core size is comparable to the flux penetration depth. The observed structure is described by a dual Ginzburg-Landau model.