Interaction and pinning of plane vortices in a three-dimensional Josephsonmedium and possible distances between two isolated vortices

Within a continuous vortex model, exact expressions are obtained for the Jo sephson and magnetic energies of plane (laminar) vortices, as well as for t he energy and force of pinning by cells in a three-dimensional Josephson me dium. If the porosity of the medium is taken into account, the Josephson an d magnetic energies of the vortex differ from those for the continuum case. The contributions to the pinning energy from the Josephson and magnetic en ergies have opposite signs. An algorithm for numerically solving a system o f difference equations is proposed in order to find the shape and the energ y of the vortex in its stable and unstable states. The continuous vortex mo del is shown to fail in predicting correct values of the Josephson and magn etic energy of the vortex, as well as of the pinning energy components. Exp ressions for the least possible distances between two isolated vortices are obtained for a small pinning parameter. Analytical results are in close ag reement with computer simulation. An algorithm for numerically solving a sy stem of difference equations is proposed in order to find the least possibl e distances between two isolated vortices when the pinning parameter I is n ot small. The minimal value of I at which the center-to-center distance N o f the vortices equals three cells is 1.428; for N = 2, I-min = 1.947. At I > 2.907, the vortices can be centered in adjacent cells. (C) 2001 MAIK "Nau ka/Interperiodica".