Effects of defects and surface roughness on the vortex penetration and vortex dynamics in superconductor-insulator-superconductor multilayer structures exposed to RF magnetic fields: numerical simulations within TDGL theory

The vortex penetration and vortex dynamics are significantly important to superconducting devices, for example the superconducting cavities, since the vortex motions would create substantial dissipation. In experiments, different kinds of defects, as well as different degrees of surface roughness were observed. By considering these in superconductor-insulator-superconductor (SIS) structures, the vortex penetration and vortex dynamics are very complex due to the interactions with defects and the influence of surface roughness, especially for radio-frequency (RF) magnetic field, which are quite different from ideal defect-free SIS multilayer structures. In this paper, within Ginzburg-Landau theory, we perform numerical simulations to study the effects of nanoscale defects, surface roughness, and cracks in the coating layer on the vortex penetration and superheating field in Nb3Sn-I-Nb multilayer structures exposed to a quasi-static magnetic field. The validations of the numerical simulations are verified by good consistency with previous theoretical results in ideal defect-free SIS multilayer and single Nb structures. Furthermore, we explore the vortex dynamics and induced voltages in SIS multilayer structures exposed to RF magnetic fields for both ideal defect-free structures and real situations including surface roughness. Our numerical simulations indicate that, unlike the quasi-static case, the advantage of SIS multilayer structures over a single Nb structure depends on the degrees of surface roughness as well as the frequency and amplitude of the RF magnetic field. The results of this paper provide deep insight to evaluate the actual performance-limiting of next-generation superconducting radio-frequency (SRF) cavities with different proposed candidate materials, which are quite susceptible to nonideal surface.

McKean–Vlasov type stochastic differential equations arising from the random vortex method

We study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic differential equations whose coefficients are defined in terms of singular integral kernels such as the Biot–Savart kernel. These SDEs which involve the distributions of solutions are in general not Lipschitz continuous with respect to the usual distances on the space of distributions such as the Wasserstein distance. Therefore there is an obstacle in adapting the ordinary SDE method for the study of this class of SDEs, and the conventional methods seem not appropriate for dealing with such distributional SDEs which appear in applications such as fluid mechanics.

Vortex evolution in a rotating tank with an off-axis drain

Fluid entering the periphery of a steadily rotating cylindrical tank exits through an off-axis drain hole, located in the tank's base at the half-radius. Experiments show that, though a concentrated vortex forms over the drain, it soon advects around the tank in what is at first a circular path. Though inviscid vortex dynamics predicts continued motion, our experiments show that the vortex moves inwards from the predicted circular path, finally coming to rest at approximately $50^{\circ }$ from the drain. In this final state, the vorticity is concentrated in a thin shear layer bounding an irrotational core, which passes over the drain. The broadening of the vortex structure and eventual steady-state formation are believed to be due to the growing boundary layer on the outer wall.

Vortex Dynamics in the Wake of Planetary Ionospheres

Measurements conducted with spacecraft around Venus and Mars have shown the presence of vortex structures in their plasma wake. Such features extend across distances of the order of a planetary radius and travel along their wake with a few minutes rotation period. At Venus, they are oriented in the counterclockwise sense when viewed from the wake. Vortex structures have also been reported from measurements conducted by the solar wind-Mars ionospheric boundary. Their position in the Venus wake varies during the solar cycle and becomes located closer to Venus with narrower width values during minimum solar cycle conditions. As a whole there is a tendency for the thickness of the vortex structures to become smaller with the downstream distance from Venus in a configuration similar to that of a corkscrew flow in fluid dynamics and that gradually becomes smaller with increasing distance downstream from an obstacle. It is argued that such process derives from the transport of momentum from vortex structures to motion directed along the Venus wake and that it is driven by the thermal expansion of the solar wind. The implications of that momentum transport are examined to stress an enhancement in the kinetic energy of particles that move along the wake after reducing the rotational kinetic energy of particles streaming in a vortex flow. As a result, the kinetic energy of plasma articles along the Venus wake becomes enhanced by the momentum of the vortex flow, which decreases its size in that direction. Particle fluxes with such properties should be measured with increasing distance downstream from Venus. Similar conditions should also be expected in vortex flows subject to pressure forces that drive them behind an obstacle.