Inhomogeneous parallel arrays of Josephson junctions

We model new inhomogeneous parallel arrays of small Josephson junctions by taking into account the time and space variations of the field in the cavity and the capacity miss-match at the junctions. The model consists in a wave equation with Dirac delta function sine nonlinearities. We introduce an adapted spectral problem whose spectrum gives the resonances in the current–voltage characteristic curve of any array. It is shown that at the resonances the solution is described by two simple ordinary differential equations. The resonances obtained by this approach are in good agreement with the characteristic curve of a real five junction array. This flexible approach is a first step towards building a device tailored for given purposes.

► New long wave model of an inhomogeneous parallel array of Josephson junctions.
► Adapted spectral problem giving resonances in the current-voltage characteristic.
► At resonances solution is described by two ordinary differential equations.
► Good agreement with the characteristic curve of a real five junction array.