Josephson coupling and plasma resonance in a vortex crystal

We investigate the magnetic field dependence of the plasma resonance freque ncy in the vortex crystal state. We find that low magnetic fields induce a small correction to the plasma frequency proportional to the field. The slo pe of this linear field dependence is directly related to the average dista nce between the pancake vortices in the neighboring layers, the wandering l ength. This length is determined by both Josephson and magnetic couplings b etween layers. At higher fields the plasma frequency is suppressed collecti vely and is determined by the elastic energy of the vortex lattice. Analyzi ng experimental data, we find that (i) the wandering length becomes compara ble with the London penetration depth near T-c, (ii) at small melting field s (< 20 G) the wandering length does not change noticeably at the melting t ransition, demonstrating the existence of the line liquid phase in this fie ld range, and (iii) the self consistent theory of pancake fluctuations desc ribes very well the field dependence of the Josephson plasma resonance freq uency up to the melting point.