Equilibrium states of planar vortices in a three-dimensional josephson medium and meaning of the pinning-energy concept

Various ways of specifying the pinning-energy concept for planar vortices in a three-dimensional cellular Josephson medium are analyzed. It is shown that, for values of the pinning parameter I that are not small, a universal characteristic of vortex interaction with the lattice cannot be found, since the displacement of a vortex distorts its shape. At small values of I, the maximum pinning force can be chosen for such a characteristic. Two equilibrium states of a vortex are analyzed for stability. It is revealed that the state of higher energy is not inevitably unstable. A correct analysis of stability must be based on exploring a quadratic form that describes the energy of a current configuration. Such an investigation is performed for the equilibrium state of a vortex. At small values of the pinning parameter, the vortex state of higher energy is quasistable.