We construct a complete phase diagram for a type-II superconductor carrying a transport current embedded into ac magnetic field. As it has been first experimentally observed in Ref.[1] and explained theoretically in Ref.[2], depending on the amplitude of the magnetic field, its frequency and value of the transport current, such a superconductor reveals two distinct regimes of magnetic response. In the usual “in-phase” regime the maxima of voltage and, in turn, of the energy dissipation measured as a function of time coincide with the corresponding maxima of the absolute value of the external magnetic field H(t). Contrariwise, in the “out of phase” regime, the maxima in H(t) and V(t) do not coincide and the flux dynamics is mainly determined by the retardation of flux motion at the zero-field lines (also called as annihilation lines) where B=0 (here B denotes the magnetic induction inside superconductor).
In this work, we’ve solved numerically the equation of flux propagation in an infinite slab and found the same two types of vortex dynamics observed experimentally. The agreement between the experimental data and our theoretical analysis is encouraging. In the transition (crossover) area between the in- and out-of-phase regimes of flux motion there appear two maxima in the voltage V(t). We managed to prove by choosing appropriate dimensionless parameters that the “three dimensional” H-I-ω phase diagram can be reduced to a “two dimensional” I ̃-ω ̃ one. The width of the transition region between the two regimes is also calculated. We show that the frequency of the external field is mainly responsible for the transition between in- and out-of-phase regimes: at low ω the in-phase regime is expected whereas as ω increases the out-of-phase state becomes dominant. The transport current I has much less effect and it’s possible to “switch” between the two regimes by changing current only in a small “window” of frequencies.
We also studied the energy dissipation in these two regimes and found out that, quite surprisingly and contrary to intuitive considerations, the energy dissipation in the in- and out-of-phase regimes are quite similar by value. This issue needs further investigation.

[1] G. Lukovsky et al, IEEE Trans. on Appl. Supercond. 17, 3137 (2007).
[2] L. Burlachkov, N. Fuzailov and E. Swartz, submitted to Phys. Rev. B