Magnetic induction waves in relaxing vortex matter

When vortices reach the wide plane defect which is clearly observed optically inside BSCCO, they reflect from this plane changing the slope of a magnetic field to the opposite to the regular Bean slope. Moreover, the front of the magnetic flux, which separated the unstable vortex state from the stable one, starts to oscillate forming the "flux waves". The theoretical description of this interesting effect is based on an analysis of two simultaneous nonlinear equations : the Landau-Ginzburg equation for the order parameter and the diffusion equation for the magnetic induction. Linear stability analysis shows an appearance of the oscillatory instabilities. The simple expressions for the period of oscillations is obtained under the simplified experimentally verified assumption of the magnetic induction which is slightly varying along a sample and close in magnitude to that on the phase transition critical line. Both the order of magnitude and the temperature dependence of the period of oscillations show a good agreement between theory and experiment.