Dynamics of point Josephson junctions in a microstrip line

We model the dynamics of point Josephson junctions in a 1D microstrip line using a wave equation with delta distributed sine non-linearities. The model is suitable for both low Tc and high-Tc systems (0 and π junctions). For a single junction in the line, we found two limiting behaviors: the ohmic mode where the junction acts as a pure resistor which stops waves and separates the cavity and the junction mode where the wave is homogeneous throughout the strip. This classification allows to bound the I-V curves of the system. Two junctions in a strip give generally ohmic modes and combined junction/ohmic modes and yield information about the behavior of an array with many junctions. Finally, we use this analysis to understand the many junction case for 0 and π junctions and the effect of an external magnetic field.