Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics

We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed.     

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability

Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability is studied. The flow is modeled by the reduced MHD equations with constant resistivity and viscosity. For super-Alfvénic flow, localized transient reconnection is observed on the Kelvin-Helmholtz time scale (this is not new). We study this transient reconnection and consider the peak reconnection rate which occurs with the initial vortex formation. Over the range of resistivities considered, it is shown that this peak reconnection rate is not a function of resistivity, and is a function of the initial flow shear. Additionally, it is demonstrated that there is a fundamental difference between the evolution of a problem at S = 200 and S = 10,000.     

Magnetic zero-modes,vortices and Cartan geometry

We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on \(\mathbb {R}^3\) which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.     

Magnetic vortices in small ferromagnetic particles with the strong dipolar interaction

The ground state of cylindrical magnetic samples of different sizes at nonzero applied magnetic field is studied theoretically taking into account the exchange and dipole-dipole interactions at an arbitrary ratio of coupling constants. In addition to the weakly inhomogeneous and standard vortex states well known for the case of the weak dipole-dipole interaction, the vortex states with the complicated structure of the vortex core have been found. The state diagram for these particles has been constructed and analyzed in terms of scaling consideration.     

Magnetic fields boosted by gluon vortices in color superconductivity

We investigate the effects of an external magnetic field in the gluon dynamics of a color superconductor with three massless quark flavors. In the framework of gluon mean-field theory at asymptotic densities, we show that the long-range component H[over ] of the external magnetic field that penetrates the color-flavor locked phase produces an instability when its strength becomes larger than the Meissner mass of the charged gluons. As a consequence, the magnetic field causes the formation of a vortex state characterized by the condensation of charged gluons and the creation of magnetic flux tubes. Inside the flux tubes, the magnetic field is stronger than the applied one. This antiscreening effect is connected to the anomalous magnetic moment of the gluon field. We suggest how this same mechanism could serve to remove the chromomagnetic instabilities existing in gapless color superconductivity.     

Magnetic interference patterns and vortices in diffusive SNS junctions

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonic decay when the width of the normal wire is smaller than the magnetic length xi(H)=square root Phi(0)/H, where H is the magnetic field and Phi(0) the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how this structure is manifested in the local density of states.     

Magnetic vortices and thermoelectric effect in a hollow superconducting cylinder

The question of a surface barrier which determines the behavior of a vortex in a hollow superconducting cylinder of finite thickness in an external magnetic field is discussed, taking into account magnetic flux quantization in the cavity. The behavior of magnetic vortices in a hollow superconductor in the presence of a thermoelectric current is also considered. Pairs of magnetic vortices with opposite magnetic field orientations (vortex-antivortex pairs) are generated by this current near T _c. The thermoelectric current drives the antivortex (the vortex with oppositely directed field) out of the cylinder, whereas the vortex is ejected into the cavity and remains on the inside cylinder surface as a current. The number of magnetic flux quanta trapped inside the cylinder increases by one. The relation of this mechanism to the “giant” thermoelectric effect in hollow superconductors is discussed. Zh. éksp. Teor. Fiz. 111, 2175–2193 (June 1997)     

二维不可压流体Kelvin-Helmholtz不稳定性的弱非线性研究

通过将扰动速度势展至三阶,提出了Kelvin-Helmholtz（KH）不稳定性的弱非线性理论.在模耦合过程中观察到一个重要的共振现象,共振使得模耦合过程变得相当复杂,单模扰动很快进入非线性区,产生大量高次谐波,共振加强了非线性作用.分析了单模扰动中二次和三次谐波产生效应,以及对基模指数增长的非线性校正.模拟结果支持了解析理论.利用该理论,分析了KH不稳定的非线性阈值问题. 关键词： Kelvin-Helmholtz不稳定性 弱非线性理论 非线性阈值     

双界面耦合作用对KH不稳定的影响（英）

研究了含有中间层的流体系统的双界面KH不稳定性。计算发现:由于耦合作用,界面KH不稳定性呈现出不同的增长模式。主要研究了对增长率影响最大的夹层厚度对增长模式的影响,发现厚度小于半个扰动波长时,耦合作用必须考虑。另外发现在特定厚度下,界面不稳定性将出现简并的增长模式。     

On the Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed on the basis of the first experimental observation of such an instability at the interface between superfluid ³He-A and superfluid ³He-B (R. Blaauwgeers, V. B. Eltsov, G. Eska et al., cond-mat/0111343). We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free-energy consideration all give different values for the instability threshold.     

Nonlinear asymptotic calculation of the Kelvin-Helmholtz instability

The problem of periodic capillary-gravitational wave motion on the uniformly charged interface between two ideal immiscible incompressible liquids is solved in the third order of smallness. The lower liquid is assumed to be ideally conducting, while the upper one is a dielectric executing translational motion parallel to the interface with a constant velocity. A nonlinear frequency correction in the resonance form is found. It is shown that the positions of internal nonlinear resonances depend on the sum of the field and Weber parameters, the density ratio of the liquids, and the wave number. When the upper liquid is denser than the lower one, resonances are absent.     

Kelvin-Helmholtz instability of miscible ferrofluids

We study the stability of an interface between two inviscid magnetic fluids of different densities flowing parallel to each other in an oscillatory manner. The system is pervaded by a uniform oblique magnetic field distribution. The analysis allows for mass and heat transfer across the interface. A general eigenvalue relation is derived and discussed analytically. The classical stability criterion is found to be substantially modified due to the effect of the oblique magnetic field with mass and heat transfer. Some previous studies are reported for appropriate data choices. The longitudinal magnetic field has a strong stabilizing influence on all wavelengths, which can be used to suppress the destabilizing influence of the mass and heat transfer. We conclude with a discussion of the stability of unsteady shear layers on the basis of the results. The parametric excitation of the surface waves is analyzed by means of the multiple-time-scales method. The transition curves are obtained analytically.     

双界面耦合作用对KH不稳定的影响（英）

研究了含有中间层的流体系统的双界面KH不稳定性。计算发现：由于耦合作用,界面KH不稳定性呈现出不同的增长模式。主要研究了对增长率影响最大的夹层厚度对增长模式的影响,发现厚度小于半个扰动波长时,耦合作用必须考虑。另外发现在特定厚度下,界面不稳定性将出现简并的增长模式。     

Magnetic flux trapping and broken Abrikosov vortices in yttrium HTSC ceramic samples

Direct evidence of the existence of broken Abrikosov vortices is obtained from measurements of the distribution and values of residual magnetic fields in ceramic yttrium HTSC samples after the switching off of a transport current. In this case, the intergrain magnetic induction averaged over the sample volume has the same direction as the field that was in the sample before the current was switched off.     

Jamming and diode effects for vortices in nanostructured superconductors

We examine jamming and ratchet effects for vortex matter in superconductors with asymmetric funnel geometries. We show that the vortex–vortex interactions can induce a clogging or jamming effect where it becomes increasingly difficult for the vortices to move through the system. We also find that commensurability effects can arise when certain vortex configurations form highly symmetrical structures in the funnel plaquettes. Due to the asymmetry, the critical currents are different for driving in different directions, leading to a diode effect. We also discuss other possible geometries and approaches that could be used to explore jamming in vortex matter, such as an analog to a granular hopper and a single driven vortex probe moving through an array of other vortices.