Vortex Interaction Energy in Planar Josephson Junction Arrays at High Density

We study the vortex-vortex and vortex-antivortex interaction in arrays of Josephson junction particularly addressing the effect of mutual induction in the intermediate screening ranges (beta_a = 0.5). The modifications of the barrier energy for the displacement of a vortex in presence of a second vortex (antivortex), or more vortices (antivortices), are derived in an "adiabatic" approach. To this end, we have developed a fast explicit algorithm, which permits to retrieve the phases and the magnetization of the array in a reasonable time and with little memory occupation for relatively large arrays [e.g. o(100 times 100)]. This new model is able to catch the essential characters of the more complex "fully mutual coupling" model. We provide also some indications on the relation between energy barriers and the observation of vortex quantum tunneling phenomena in Josephson arrays and related systems as high-T_C films.