Low-field magnetic response of multi-junction superconducting quantum interference devices

. The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φ ex . The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φ ex . The stability of these states is qualitatively studied by means of the effective potential notion for the system.