Josephson transmission line revisited

TL;DR

This paper analyzes the dynamics of Josephson transmission lines, including shock velocities and wave behaviors, using various approximations to understand their wave propagation and shock formation in both lossless and lossy cases.

Contribution

It provides a comprehensive analysis of wave solutions, shock velocities, and approximations for the Josephson transmission line, including new simple wave approximation methods.

Findings

Compact waves are kinks and solitons with calculable velocities.

Shock formation in lossy JTL can be effectively modeled.

Continuum and quasi-continuum approximations are validated for different cases.

Abstract

We consider the series-connected Josephson transmission line (JTL), constructed from Josephson junctions, capacitors and (possibly) resistors. We calculate the velocity of shocks in the discrete lossy JTL. We study thoroughly the continuum and the quasi-continuum approximations to the discrete JTL, both lossless and lossy. In the framework of these approximations we show that the compact travelling waves in the lossless JTL are the kinks and the solitons, and calculate their velocities. On top of each of the above mentioned approximations, we propose the simple wave approximation, which decouples the JTL equations into two separate equations for the right- and left-going waves. The approximation, in particular, allows to easily consider the formation of shocks in the lossy JTL.