Mutual inductance effects in rf driven planar Josephson junctions arrays

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillat ing field. We have included in the model the effects due to mutual inductan ce terms, and we have employed an explicit set of differential equations. W e have found that the discretization parameter beta(L) - i.e. the coupling term due to the inductance of the loops is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequen cy of the rf-bias. The amplitude of the Shapiro steps in the case of zero f rustration as a function of the coupling term shows a remarkable minimum fo r intermediate values when we retain all terms of the full model with mutua l inductances, while the limits for very large and very small values of bet a(L) they are the same of the single Josephson junction. For the case of fr ustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., sm all beta(L)) as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large beta(L)).