The network approach to calculation of characteristic time constants of the flat two-layer superconducting cable

The matrix method was used to investigate the process of current decay in the samples of flat two-layer superconducting cables. The discrete spectrum of eigen-frequencies has been obtained. Each of these frequencies determines the rate of decay of the correspondent eigen-current. Despite of the increasing of the number of eigen-frequencies with the enlargement of the sample dimensions the spectrum remains finite, as the maximum and minimum frequencies tend to finite limits. An analysis made for the lowest eigen-frequencies showed the corresponding eigen-currents to be slowly decaying long current loops. Within the range of high frequencies the sinusoidal distribution of eigen-currents in the rows of the cable was observed.     

Nonlinear response of a thin metamaterial film containing Josephson junctions

An interaction of electromagnetic field with metamaterial thin film containing split-ring resonators with Josephson junctions is considered. It is shown that dynamical self-inductance in a split-rings results in reduction of magnetic flux through a ring and this reduction is proportional to a time derivative of split-ring magnetization. Evolution of thin film magnetization taking into account dynamical self-inductance is studied. New mechanism for excitation of waves in one dimensional array of split-ring resonators with Josephson junctions is proposed. Nonlinear magnetic susceptibility of such thin films is obtained in the weak amplitude approximation.     

Low frequency impedance of a round superconducting wire

We calculated the electric field E on the surface of a straight superconducting wire with circular cross-section carrying AC transport current I=I_acosωt. Performing the Fourier analysis of E, we found that both components of the first harmonic have the same form: the critical current I_c in prefactor and the rest depending on the ratio F=I_a/I_c. The in-phase component leads to the classical result of loss calculation, while the out-of-phase component was derived for the first time. Thus the wire can be symbolized by a complex self-inductance L₁(I)=L₁′(I)−jL₁″(I) where L₁′ represents the reactive power while L₁″ the losses. When the lock-in amplifier, used to sort out the components of the first harmonic, is utilized in the wide-band mode, it allows one to determine the magnetic flux penetrated in the wire volume at two significant moments of the AC cycle: at zero current (remanent flux) and at the amplitude value of current.