Linear ac dynamics of vortices in a periodic pinning array

The vortex-dominated ac response of a superconducting film with a periodic array of pinning centers is studied in the linear regime for vortex densities greater than the saturation number. A simple model is introduced to describe small oscillations of the vortex lattice, which is considered to be composed of two distinct lattices formed by trapped vortices and interstitial vortices. The frequency-dependent complex resistivity is calculated as a function of frequency and magnetic induction for vortex densities between the first and the second matching fields. It is shown that the absorption spectra has two peaks corresponding to two characteristic pinning frequencies: one due to the periodic pinning array and another due to vortex-cage pinning. The range of validity of the model is determined from direct numerical simulations.