Radiation linewidth of a long Josephson junction in the flux-flow regime

Theoretical model for the radiation linewidth in a multi-fluxon state of a long Josephson junction is presented. Starting from the perturbed sine-Gordon model with the temperature dependent noise term, we develop a collective coordinate approach which allows to calculate the finite radiation linewidth due to excitation of the internal degrees of freedom in the moving fluxon chain. At low fluxon density, the radiation linewidth is expected to be substantially larger than that of a lumped Josephson oscillator. With increasing the fluxon density, a crossover to a much smaller linewidth corresponding to the lumped oscillator limit is predicted.Comment: 11 pages LaTeX, to appear in Phys Rev

Measurements of critical current diffraction patterns in annular Josephson junctions

We report systematic measurements of the critical current versus magnetic field patterns of annular Josephson junctions in a wide magnetic field range. A modulation of the envelope of the pattern, which depends on the junction width, is observed. The data are compared with theory and good agreement is found.Comment: 4 pages, 5 figure

Long Josephson junctions with spatially inhomogeneous driving

The phase dynamics of a long Josephson junction with spatially inhomogeneously distributed bias current is considered for the case of a dense soliton chain (regime of the Flux Flow oscillator). To derive the analytical solution of the corresponding sine-Gordon equation the Poincare method has been used. In the range of the validity of the theory good coincidence between analytically derived and numerically computed current-voltage characteristics have been demonstrated for the simplest example of unitstep function distribution of bias current (unbiased tail). It is shown, that for the considered example of bias current distribution, there is an optimal length of unbiased tail that maximizes the amplitude of the main harmonic and minimizes the dynamical resistance (thus leading to reduction of a linewidth).Comment: 7 pages, 5 figure

Kinks in the Presence of Rapidly Varying Perturbations

Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to derive, in a rigorous way, an effective nonlinear equation for the slowly varying field component in any order of the asymptotic procedure as expansions in the small parameter $\omega^{-1}$, $\omega$ being the frequency of the rapidly varying ac driving force. Three physically important examples of such a dynamics, {\em i.e.}, kinks driven by a direct or parametric ac force, and kinks on rotating and oscillating background, are analysed in detail. It is shown that in the main order of the asymptotic procedure the effective equation for the slowly varying field component is {\em a renormalized sine-Gordon equation} in the case of the direct driving force or rotating (but phase-locked to an external ac force) background, and it is {\em the double sine-Gordon equation} for the parametric driving force. The properties of the kinks described by the renormalized nonlinear equations are analysed, and it is demonstrated analytically and numerically which kinds of physical phenomena may be expected in dealing with the renormalized, rather than the unrenormalized, nonlinear dynamics. In particular, we predict several qualitatively new effects which include, {\em e.g.}, the perturbation-inducedComment: New copy of the paper of the above title to replace the previous one, lost in the midst of the bulletin board. RevTeX 3.

The shape of a moving fluxon in stacked Josephson junctions

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.Comment: 12 pages, 12 figure

Quadratic solitons as nonlocal solitons

We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for novel analytical solutions and the prediction of novel bound states of quadratic solitons.Comment: 4 pages, 3 figure

Review article: MHD wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfven speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfven wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfven-speed profile. In a $\beta=0$ plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfven wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfven wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfven wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.Comment: 34 pages, 5 figures, invited review in Space Science Reviews => Note this is a 2011 paper, not a 2010 pape

Soliton ratchets induced by ac forces with harmonic mixing

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this {\it internal mode} mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.Comment: 9 pages, 13 figure

In-plane fluxon in layered superconductors with arbitrary number of layers

I derive an approximate analytic solution for the in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) with arbitrary number of layers. The validity of the solution is verified by numerical simulation. It is shown that in SJJ's with large number of thin layers, phase/current and magnetic field of the fluxon are decoupled from each other. The variation of phase/current is confined within the Josephson penetration depth, $\lambda_J$, along the layers, while magnetic field decays at the effective London penetration depth, $\lambda_c \gg \lambda_J$. For comparison with real high-$T_c$ superconducting samples, large scale numerical simulations with up to 600 SJJ's and with in-plane length up to 4000 $\lambda_J$%, are presented. It is shown, that the most striking feature of the fluxon is a Josephson core, manifesting itself as a sharp peak in magnetic induction at the fluxon center.Comment: 4 pages, 4 figures. Was presented in part at the First Euroconference on Vortex Matter in Superconductors (Crete, September 1999