Maximum velocity of a fluxon in a stack of coupled Josephson junctions

TL;DR

This paper investigates the maximum velocity of fluxons in coupled Josephson junction stacks, revealing it can differ from plasma wave velocities and providing an analytical formula for its dependence on system parameters.

Contribution

It introduces an analytical formula for fluxon maximum velocity considering coupling and critical current distribution, supported by numerical simulations.

Findings

Fluxon maximum velocity can differ from plasma wave velocities.

Nonzero dissipation stabilizes fluxons.

Analytical formula accurately predicts maximum velocity in low dissipation limit.

Abstract

Dynamics of a fluxon in a stack of inductively coupled long Josephson junctions is studied analytically and numerically. We demonstrate that the fluxon has a maximum velocity, which does not necessarily coincide with any of the characteristic Josephson plasma wave velocities. The maximum fluxon velocity is found by means of numerical simulations of the quasi-infinite system. Using the variational approximation, we propose a simple analytical formula for the dependence of the fluxon's maximum velocity on the coupling constant and on the distribution of critical currents in different layers. This analysis yields rather precise results in the limit of small dissipation. The simulations also show that nonzero dissipation additionally stabilizes the fluxon.