Statics of point Josephson junctions in a micro strip line

We model the static behavior of point Josephson junctions in a micro strip line using a 1D linear differential equation with delta distributed sine non-linearities. We analyze the maximum current $\gamma_{max}$ crossing the micro strip for a given magnetic field $H$. In particular we establish its periodicity and analyze how it is affected by the geometry, length, type of current feed, position and area of the junctions. For small currents, which is the rule in practice, we show that $\gamma_{max}$ can be obtained by a simple formula, the magnetic approximation. This model is in excellent agreement with measurements obtained for real devices.