Fluxon dynamics in three stacked Josephson junctions (original) (raw)

Fluxons and their interactions in a system of three stacked Josephson junctions

Physical Review B, 2003

Fluxon dynamics in a system of three coupled driven damped sine-Gordon equations is investigated. Bunching of fluxons is observed. It is shown that fluxon-fluxon-fluxon bound states exist in a certain interval of the fluxon velocity. Attraction between fluxons occurs as a result of indirect fluxon-fluxon interaction mediated by Swihart waves. To tackle the problem analytically a piece-wise linear approach is developed. The analytical approximations show good agreement with the results obtained by direct numerical simulations.

Numerical study of fluxon dynamics in a system of two‐stacked Josephson junctions

1995

The dynamics of magnetic fluxons in a system of two vertically stacked long Josephson junctions is investigated numerically. The model is based on the approach by S. Sakai, P Bodin, and N. F. Pedersen [J. Appl. Phys. 73, 2411] and is described by two strongly coupled sine-Gordon equations. In agreement with recent experimental data, we confirm numerically the effect of splitting of the fluxon travelling mode into two separated modes with different characteristic velocities. The simulated current-voltage characteristics indicate stable phase-locked flux-flow resonances of two junctions. These results support a possibility of application of the stacked long Josephson junctions as a system of coherent oscillators for millimeter and sub-millimeter wave bands. 0 -1995 American institute of Physics. %

Shape of a moving fluxon in stacked Josephson junctions

Physical Review B

We study numerically and analytically the shape of a single fluxon moving in a double stacked Josephson junctions (SJJ's) for various junction parameters. We show that the fluxon in a double SJJ's consists of two components, which are characterized by different Swihart velocities and Josephson penetration depths. The weight coefficients of the two components depend on the parameters of the junctions and the velocity of the fluxon. It is shown that the fluxon in SJJ's may have an unusual shape with an inverted magnetic field in the second junction when the velocity of the fluxon is approaching the lower Swihart velocity. Finally, we study the influence of fluxon shape on flux-flow current-voltage characteristics and analyze the spectrum of Cherenkov radiation for fluxon velocity above the lower Swihart velocity. Analytic expression for the wavelength of Cherenkov radiation is derived.

Static and dynamic properties of stacked Josephson junctions: Analytic solution

Physical Review B

Static and dynamic properties of stacked Josephson junctions are studied theoretically. An approximate analytic solution for a stack with arbitrary junction parameters was obtained. The analytic solution is in good agreement with numerical simulations. Characteristic penetration depths, Swihart velocities, the lower critical field, the first integral, and the free energy for a stack of nonidentical junctions were derived and studied for different parameters of the stack. We show that attractive interaction of fluxons in adjacent junctions exists in the dynamic state of the stack, leading to appearance of the ''in-phase'' state with fluxons on top of each other. In a given external magnetic field the Gibbs free energy has a number of local minima corresponding to particular fluxon distributions ͑modes͒ in the stack each representing a quasiequilibrium state. For a stack of N junctions each mode would result in N distinct flux-flow branches in the current-voltage characteristic. Taking into account that different modes with equal total number of fluxons are not identical we conclude that the total possible number of flux-flow branches can be much larger than the number of junctions in the stack.

Two-fluxon dynamics in an annular Josephson junction

Physical Review B, 2004

Two-fluxon state in an annular Josephson junction in the presence of external magnetic field is studied analytically, numerically and experimentally. We obtain an analytical expression for the potential of interaction between the fluxons moving at arbitrary velocities (without the use of the "nonrelativistic" approximation). Treating the fluxons as quasi-particles, we then derive equations of motion for them. Direct simulations of the full extended sine-Gordon equation are in good agreement with results produced by the analytical model, in a relevant parameter region. Experimental data qualitatively agree with the numerical results.

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

Physics Letters A, 2000

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. 74.50.+r, 41.60.Bq, 74.80.Dm

Fluxons in a triangular set of coupled long Josephson junctions

Journal of Mathematical Physics, 2015

We report results of an analysis of the dynamics of magnetic flux solitons in the system of three long Josephson junctions between three bulk superconductors that form a prism. The system is modeled by coupled sine-Gordon equations for the phases of the junctions. The Aharonov-Bohm constraint takes into account the axial magnetic flux enclosed by the prism and reduces the system from three independent phases to two. The equations of motion for the phases include dissipative terms, and a control parameter δ which accounts for the deviation of the enclosed flux from half a quantum. Analyzing the effective potential of the coupled equations, we identify different species of topological and non-topological phase solitons (fluxons) in this system. In particular, subkinks with fractional topological charges ±1/3 and ±2/3, confined inside integer-charge fluxons, may be mapped onto the root diagrams for mesons and baryons in the original quark model of hadrons. Solutions for straight-line kinks and for two types of non-topological solitons are obtained in an explicit analytical form. Numerical tests demonstrate that the former species is unstable against breakup into pairs of separating single-fluxon kinks. The non-topological kinks feature metastability, eventually breaking up into fluxonantifluxon pairs. Free fractional-fluxon kinks, that connect different potential minima and are, accordingly, pulled by the potential difference, are also considered. Using the momentum-balance method, we predict the velocity at which these kinks should move in the presence of the dissipation. Numerical tests demonstrate that the analysis predicts the velocity quite closely. Higher-energy static solutions for all of the stable kink types mentioned above, as well as kinks connecting false vacua, are found by means of the shooting method. Inelastic collisions among the stable fractional and single-fluxon kinks are investigated numerically.