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Electric Flux Tube in Magnetic Plasma

In this paper we study a methodical problem related to the magnetic scenario recently suggested and initiated by the authors \cite{Liao_ES_mono} to understand the strongly coupled quark-gluon plasma (sQGP): the electric flux tube in monopole plasma. A macroscopic approach, interpolating between Bose condensed (dual superconductor) and classical gas medium is developed first. Then we work out a microscopic approach based on detailed quantum mechanical calculation of the monopole scattering on electric flux tube, evaluating induced currents for all partial waves. As expected, the flux tube looses its stability when particles can penetrate it: we make this condition precise by calculating the critical value for the product of the flux tube size times the particle momentum, above which the flux tube dissolves. Lattice static potentials indicate that flux tubes seem to dissolve at $T>T_{dissolution} \approx 1.3 T_c$. Using our criterion one gets an estimate of the magnetic density $n\approx 4.4 \sim 6.6 fm^{-3}$ at this temperature.