Influence of Josephson current second harmonic on stability of magnetic flux in long junctions

TL;DR

This paper investigates how the second harmonic of the Josephson current affects the stability and flux distribution in long Josephson junctions, revealing new solutions and stability behaviors through numerical analysis.

Contribution

It introduces a modified LJJ model incorporating the second harmonic and explores its impact on flux stability, uncovering new solutions not present in traditional models.

Findings

Discovery of new static flux solutions due to second harmonic effects

Numerical analysis of flux stability depending on model parameters

Identification of stability changes in flux distributions

Abstract

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The dependence of the static magnetic flux distributions on parameters of the model are investigated numerically. Stability of the static solutions is checked by the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New solutions which do not exist in the traditional model, have been found. Investigation of the influence of second harmonic on the stability of magnetic flux distributions for main solutions is performed.