COLLECTIVE MODE AND THE C-AXIS CRITICAL-CURRENT OF A JOSEPHSON-COUPLED SUPERCONDUCTOR AT HIGH PARALLEL MAGNETIC-FIELDS

Using Maxwell and time-dependent Ginzburg-Landau equations in the fram ework of a Lawrence-Doniach model we derive dynamical equations for th e order parameter phase difference in Josephson-coupled layered superc onductors. These equations allow the description of nonstationary Jose phson effects in magnetic fields parallel to the layers. We obtain the dispersion relation and relaxation rate of collective modes in the ab sence of a magnetic field and in a strong parallel magnetic field. The dispersion with respect to the momentum in the ab plane in high field s is much stronger that in a single Josephson junction due to the mult ilayer structure. This leads to a very weak c-axis critical current in high magnetic fields. The relaxation rate of collective modes is foun d to be weak in comparison with its frequency. We discuss experimental data for the c-axis plasma resonance and critical current in parallel magnetic fields.