Statics of point Josephson junctions in a micro strip line

TL;DR

This paper models the static behavior of point Josephson junctions in a micro strip line using a 1D differential equation, analyzing maximum current and its dependence on geometry and other factors, with practical implications.

Contribution

It introduces a simplified model for static Josephson junctions in micro strips, including a formula for maximum current and analysis of geometric effects, validated by measurements.

Findings

Maximum current exhibits periodicity with magnetic field.

The magnetic approximation accurately predicts maximum current for small currents.

Model aligns well with experimental measurements.

Abstract

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.