Spectrum of eigenfrequencies of plane superconducting cable

The matrix method is applied for the study on the attenuation of the current in the plane superconducting cable. The discrete spectrum of eigenfrequency of the superconducting cable is obtained. Each eigenfrequency defines the rate of the exponential attenuation of the corresponding eigencurrent. Although the number of eigenfrequencies grows as the cable dimensions increase, their spectrum is finite because maximum and minimum frequencies tend to finite limits. The analysis of eigencurrents is carried out for limit frequencies. It is shown that the eigencurrents are the long-living current loops in the range of minimum eigenfrequencies. The spectrum of eigencurrents in the cable is sinusoidal in the range of high frequencies