Vortex dynamics in a type-II superconducting film and complex linear-response functions

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Abstract
The dynamics of interacting vortices in a type-II superconducting film responding to a distribution of currents parallel to the film is investigated. The nonlocality of vortex interactions is taken into account by use of an expansion in normal modes of the flux-line lattice and a wave-vector-dependent dynamical matrix. The theory is applied to obtain linear response functions including the complex mutual inductance and film impedance. For a particular geometry of driving current and pickup coil, the complex mutual inductance is calculated and it is shown that only longitudinal modes contribute to the measurable change in flux when pinning is absent or when it is represented as a linear restoring force acting the same way on each vortex. The configuration so described provides a sensitive means of studying vortex dynamics.