Dynamics of point Josephson junctions in a microstrip line

TL;DR

This paper models the dynamics of point Josephson junctions in a microstrip line, identifying different operational modes and analyzing their effects on wave behavior, IV curves, and the influence of external magnetic fields.

Contribution

It introduces a wave equation model with delta nonlinearities for Josephson junctions, classifies limiting behaviors, and extends analysis to multiple junctions and magnetic field effects.

Findings

Identified ohmic and junction modes in single junction systems.

Bounded IV curves based on mode classification.

Analyzed behavior of multiple junctions and external magnetic field effects.

Abstract

We model the dynamics of point Josephson junctions in a 1D microstrip line using a wave equation with delta distributed sine nonlinearities. The model is suitable for both low T$_c$ and high T$_c$ systems (0 and $\pi$ 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 IV curves of the system. Two junctions in a strip give generally ohmic modes and combined junction/ohmic modes and yield information about the behavior with an array with many junctions. Finally we use this analysis to understand the many junction case for 0 and $\pi$ junctions and the effect of an external magnetic field.