We consider the full three‐dimensional Ginzburg–Landau model of superconductivity with applied magnetic field, in the regime where the intensity of the applied field is close to the ‘first critical field’ at which vortex filaments appear, and in the asymptotics of a small inverse Ginzburg–Landau parameter . This onset of vorticity is directly related to an ‘isoflux problem’ on curves (finding a curve that maximizes the ratio of a magnetic flux by its length), whose study was initiated in [22] and which we continue here. By assuming a nondegeneracy condition for this isoflux problem, which we show holds at least for instance in the case of a ball, we prove that if the intensity of the applied field remains below , the total vorticity remains bounded independently of , with vortex lines concentrating near the maximizer of the isoflux problem, thus extending to the three‐dimensional setting a two‐dimensional result of [28]. We finish by showing an improved estimate on the value of in some specific simple geometries.
Inviscid damping of an elliptical vortex subject to an external strain flow
Inviscid spatial Landau damping is studied experimentally for the case of oscillatory motion of a twodimensional vortex about its elliptical equilibrium in the presence of an applied strain flow. The experiments are performed using electron plasmas in a Penning–Malmberg trap. They exploit the isomorphism between the twodimensional Euler equations for an ideal fluid and the driftPoisson equations for the plasma, where plasma density is the analog of vorticity. Perturbed elliptical vortex states are created using [Formula: see text] strain flows, which are generated by applying voltages to electrodes surrounding the plasma. Measurements of spatial Landau damping (also called criticallayer damping) are in agreement with previous studies in the absence of an applied strain, where the damping is due to a resonance between the local fluid motion and the vortex oscillations. Interestingly, the damping rate does not change significantly over a wide range of applied strain rates. This can be accurately predicted from the initial vorticity profile, even though the resonant frequency is reduced substantially due to the applied strain. For higher amplitude perturbations, nonlinear trapping oscillations also exhibit behavior similar to the strainfree case. In principle, higherorder effects of the applied strain, such as separatrix crossing of peripheral vorticity and interactions with harmonics of the fundamental resonance, are expected to change the damping rate. However, this occurs only for conditions that are not realized in the experiments described here. Vortexincell simulations are used to investigate the possible roles of these effects.
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 Award ID(s):
 2106332
 NSFPAR ID:
 10334018
 Date Published:
 Journal Name:
 Physics of Plasmas
 Volume:
 29
 Issue:
 5
 ISSN:
 1070664X
 Page Range / eLocation ID:
 052107
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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