Flux Rings Research Articles

Similarity Parameter for Synthetic Jet Vortex Rings Impinging onto Porous Walls

Previous studies have shown that vortex rings impinging onto porous walls will pass through the wall more easily as the vortex ring strength, wall porosity, and pore size increase and the wall thickness decreases. Thus, there should exist a similarity parameter formed from these factors that will allow determination of the dynamics of the vortex rings/porous wall interaction. To find this similarity parameter, the effects of the Reynolds number (309–1238) and pore size (0.07–0.20) on the vortex rings/porous wall interaction are investigated by laser-induced fluorescence and particle image velocimetry (PIV) techniques. By dimensional analysis and quantitative investigation of PIV data, a similarity parameter is proposed to effectively characterize the losses in jet dynamical parameters, such as momentum flux, kinetic energy, and vortex ring circulation, due to impingement onto a porous wall. Physically, reflects the relative importance of the forces due to the momentum relative to the viscous forces, and the drag forces associated with the porous wall geometry. Finally, the results of the flow visualization validate that the near-wall flow structure during the interaction is qualitatively similar at the closest matching .

Vortex line topology during vortex tube reconnection

The evolving topology of vortex lines during reconnection of vortex tubes is addressed. New features of the reconnection process are revealed, such as the generation of many small flux rings, and of vorticity null points. Methods to measure changes in flux connectivity are discussed.

MODELING THE RISE OF FIBRIL MAGNETIC FIELDS IN FULLY CONVECTIVE STARS

ABSTRACT Many fully convective stars exhibit a wide variety of surface magnetism, including starspots and chromospheric activity. The manner by which bundles of magnetic field traverse portions of the convection zone to emerge at the stellar surface is not especially well understood. In the solar context, some insight into this process has been gleaned by regarding the magnetism as consisting partly of idealized thin flux tubes (TFTs). Here we present the results of a large set of TFT simulations in a rotating spherical domain of convective flows representative of a 0.3 M ⊙ main-sequence star. This is the first study to investigate how individual flux tubes in such a star might rise under the combined influence of buoyancy, convection, and differential rotation. A time-dependent hydrodynamic convective flow field, taken from separate 3D simulations calculated with the anelastic equations, impacts the flux tube as it rises. Convective motions modulate the shape of the initially buoyant flux ring, promoting localized rising loops. Flux tubes in fully convective stars have a tendency to rise nearly parallel to the rotation axis. However, the presence of strong differential rotation allows some initially low-latitude flux tubes of moderate strength to develop rising loops that emerge in the near-equatorial region. Magnetic pumping suppresses the global rise of the flux tube most efficiently in the deeper interior and at lower latitudes. The results of these simulations aim to provide a link between dynamo-generated magnetic fields, fluid motions, and observations of starspots for fully convective stars.

Flux cutting in superconductors

This paper describes experiments and theories of flux cutting in superconductors. The useof the flux line picture in free space is discussed. In superconductors cutting can either beby means of flux at an angle to other layers of flux, as in longitudinal current experiments,or due to shearing of the vortex lattice as in grain boundaries in YBCO. Experiments onlongitudinal currents can be interpreted in terms of flux rings penetrating axial lines. Morephysical models of flux cutting are discussed but all predict much larger fluxcutting forces than are observed. Also, cutting is occurring at angles betweenvortices of about one millidegree which is hard to explain. The double criticalstate model and its developments are discussed in relation to experiments oncrossed and rotating fields. A new experiment suggested by Clem gives moredirect information. It shows that an elliptical yield surface of the critical stateworks well, but none of the theoretical proposals for determining the direction ofE are universally applicable. It appears that, as soon as any flux flow takes place, cutting alsooccurs. The conclusion is that new theories are required.

Operation of TCSU with Internal Flux-Conserving Rings

The Translation, Confinement, and Sustainment Upgrade (TCSU) device is a facility to form and sustain a field-reversed configuration (FRC) in quasi-steady state using rotating magnetic fields (RMF). Recent campaigns include Ti gettering, the installation of a set of internal flux rings, and RMF frequency scans. The Ti gettering campaign was successful, reduced impurities, and reduced deuterium recycling from the walls allowing density control and hotter FRCs [J.A. Grossnickle et al., Phys. Plasmas 17, 032506 (2010)]. Internal flux rings have been installed to provide a uniform flux surface and minimize plasma-wall contact. Results from the internal flux ring operation and an additional Ti gettering campaign are reported. RMF frequencies of 123 kHz and 170 kHz have been investigated and initial results are reported.

Influence of Magnetic Helicity in MHD

AbstractObservations have shown that the Sun's magnetic field has helical structures. The helicity content in magnetic field configurations is a crucial constraint on the dynamical evolution of the system. Since helicity is connected with the number of links we investigate configurations with interlocked magnetic flux rings and one with unlinked rings. It turns out that it is not the linking of the tubes which affects the magnetic field decay, but the content of magnetic helicity.

Magnetic-field decay of three interlocked flux rings with zero linking number

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.

MAGNETO-THERMOHALINE MIXING IN RED GIANTS

We revise a magnetic buoyancy model that has recently been proposed as a mechanism for extra mixing in the radiative zones of low-mass red giants. The most important revision is our accounting of the heat exchange between rising magnetic flux rings and their surrounding medium. This increases the buoyant rising time by five orders of magnitude, therefore the number of magnetic flux rings participating in the mixing has to be increased correspondingly. On the other hand, our revised model takes advantage of the fact that the mean molecular weight of the rings formed in the vicinity of the hydrogen burning shell has been reduced by 3He burning. This increases their thermohaline buoyancy (hence, decreases the total ring number) considerably, making it equivalent to the pure magnetic buoyancy produced by a frozen-in toroidal field with B_phi ~ 10 MG. We emphasize that some toroidal field is still needed for the rings to remain cohesive while rising. Besides, this field prevents the horizontal turbulent diffusion from eroding the mu contrast between the rings and their surrounding medium. We propose that the necessary toroidal magnetic field is generated by differential rotation of the radiative zone, that stretches a pre-existing poloidal field around the rotation axis, and that magnetic flux rings are formed as a result of its buoyancy-related instability.

Surface Analytical Observations During Construction and Initial Operation of TCSU

To minimize radiation-loss effects, preparation and in-situ conditioning of plasma-facing surfaces in the Translation Confinement and Sustainment Upgrade experiment (TSCU) was carried out with utmost attention. To assess the condition of the TCSU first walls during the construction and operation, chemical and morphological surface analysis techniques such as X-ray photoelectron spectroscopy (XPS), energy dispersive X-ray spectroscopy (EDS), and scanning electron microscopy (SEM) were utilized. Here we present a summary of the preliminary and ongoing work performed for TCSU wall-conditioning, including preparation of UHV compatible surfaces, glow discharge cleaning (GDC), and siliconization. Effective techniques were developed for cleaning various plasma-facing components, including Al flux rings, stainless steel chambers and components, and quartz surfaces, prior to their installation. Helium-GDC was tested and proved to be useful in reducing the plasma impurities; however, extended periods of GDC resulted in the coating of quartz surfaces due to the sputtering of neighboring stainless steel walls by energetic glow particles. In addition, as a wall conditioning technique, siliconization has been examined in a separate system dedicated for detailed analysis of the process.

Effect of Different Si/C flux Ratios on the Growth of SiC on Si (111) by SSMBE

利用固源分子柬外延（SSMBE）生长技术,在不同的硅碳蒸发速率比（Si/C）条件下,在Si（111）衬底上生长SiC单晶薄膜.利用反射式高能电子衍射（RHEED）、X射线衍射（XRD）、原子力显微镜（AFM）和傅立叶变换红外光谱（FTIR）等实验技术,对生长的样品形貌和结构进行了研究.结果表明,在Si/C比（1.1：1.0）下生长的薄膜样品,XRDω扫描得到半高宽为2.1°;RHEED结果表明薄膜具有微弱的衍射环,有孪晶斑点.在Si/C比（2.3：1.0）下生长的薄膜,XRDω扫描得到的半高宽为1.5°,RHEED显示具有Si的斑点和SiC的孪晶斑点.AFM显示在这两个Si/C比下生长的样品表面都有孔洞或者凹坑,表面比较粗糙.从红外光谱得出薄膜存在着比较大的应力.但在Si/C比（1.5：1.0）下生长的薄膜样品,XRDω扫描得到的半高宽仅为1.1°;RHEED显示出清晰的SiC的衍射条纹,并可看到SiC的3×3表面重构,无孪晶斑点;AFM图像表明,没有明显的空洞,表面比较平整.FTIR谱的位置显示,在此Si/C比下生长的薄膜内应力比较小.因此可以认为,存在着一个优化的Si/C比（1.5：1.0）,在这个Si/C比下,生长的薄膜质量较好.

Chromoelectric knot in QCD

We argue that the Skyrme theory describes the chromomagnetic (not chromoelectric) dynamics of QCD. This shows that the Skyrme theory could more properly be interpreted as an effective theory which is dual to QCD, rather than an effective theory of QCD itself. This leads us to predict the existence of a new type of topological knot, a twisted chromoelectric flux ring, in QCD which is dual to the chromomagnetic Faddeev–Niemi knot in Skyrme theory. Although classically stable, the knot has a quantum instability and can decay to gluon pairs. We estimate the mass and the decay width of the lightest chromoelectric knot to be around 50 GeV and 7 GeV.

Reinterpretation of Faddeev–Niemi knot in Skyrme theory

We identify the Faddeev–Niemi knot in Skyrme theory as a vortex ring made of a helical baby skyrmion (a twisted chromomagnetic vortex which is periodic in z-coordinate) with the periodic ends connected together. This allows us to interpret the knot as two quantized magnetic flux rings linked together, the first one winding the second m times and the second one winding the first n times, whose linking number mn is fixed by the Chern–Simon index of the magnetic potential. This interpretation strongly suggests that the Skyrme theory could also describe a very interesting low energy physics in a completely different environment, which puts the theory in a totally new perspective.

A revised slug model boundary layer correction for starting jet vorticity flux

The flux of vorticity from a piston-cylinder vortex generator is commonly approximated using a model in which the fluid efflux is treated as a uniform slug of fluid with negligible boundary layer thickness. Shusser et al. (2002) introduced a correction to the slug model that accounts for boundary layer growth within the cylinder. We show that their implemented boundary layer solution contains an error, leading to an underestimate of the calculated boundary layer growth. We present a corrected model that agrees more closely with experimental measurements of starting jet vorticity flux and vortex ring core thickness.

Dynamics of magnetic flux tubes in close binary stars

Observations of magnetically active close binaries with orbital periods of a few days reveal the existence of starspots at preferred longitudes (with respect to the direction of the companion star). We numerically investigate the non-linear dynamics and evolution of magnetic flux tubes in the convection zone of a fast-rotating component of a close binary system and explore whether the tidal effects are able to generate non-uniformities in the surface distribution of erupting flux tubes. Assuming a synchronised system with a rotation period of two days and consisting of two solar-type components, both the tidal force and the deviation of the stellar structure from spherical shape are considered in lowest-order perturbation theory. The magnetic field is initially stored in the form of toroidal magnetic flux rings within the stably stratified overshoot region beneath the convection zone. Once the field has grown sufficiently strong, instabilities initiate the formation of rising flux loops, which rise through the convection zone and emerge at the stellar surface. We find that although the magnitude of tidal effects is rather small, they nevertheless lead to the formation of clusters of flux tube eruptions at preferred longitudes on opposite sides of the star, which result from the cumulative and resonant character of the action of tidal effects on rising flux tubes. The longitude distribution of the clusters depends on the initial parameters of flux tubes in the overshoot region like magnetic field strength and latitude, implying that there is no globally unique preferred longitude along a fixed direction.

Magnetic Fields in Massive Stars. II. The Buoyant Rise of Magnetic Flux Tubes through the Radiative Interior

We present results from an investigation of the dynamical behavior of buoyant magnetic flux rings in the radiative interior of a uniformly rotating, early-type star. Our physical model describes a thin, axisymmetric, toroidal flux tube that is released from the outer boundary of the convective core and is acted on by buoyant, centrifugal, Coriolis, magnetic tension, and aerodynamic drag forces. We find that rings emitted in the equatorial plane can attain a stationary equilibrium state that is stable with respect to small displacements in radius, but is unstable when perturbed in the meridional direction. Rings emitted at other latitudes travel toward the surface along trajectories that largely parallel the rotation axis of the star. Over much of the ascent, the instantaneous rise speed is determined by the rate of heating by the absorption of radiation that diffuses into the tube from the external medium. Since the timescale for this heating varies like the square of the tube cross-sectional radius, for the same field strength, thin rings rise more rapidly than do thick rings. For a reasonable range of assumed ring sizes and field strengths, our results suggest that buoyancy is a viable mechanism for bringing magnetic flux from the core to the surface, being capable of accomplishing this transport in a time that is generally much less than the stellar main-sequence lifetime.

Thermal properties of magnetic flux tubes

We consider the consequences of radiative heating for the storage of magnetic flux in the overshoot region at the bottom of the solar convection zone. In the first part of the paper, we study the evolution of axisymmetric flux tubes (flux rings), which are initially in neutrally buoyant mechanical equilibrium. Radiative heating leads to a slow upward drift of the flux ring with a velocity depending on the degree of subadiabaticity of the stratification. Maintaining the flux tubes within the overshoot region for time intervals comparable with the solar cycle period requires a strongly subadiabatic stratification with $\delta=\nabla-\nabla_{\rm{ad}}< -10^{-4}$, which is not predicted by most current overshoot models (e.g., Skaley & Stix 1991; van Ballegooijen 1982; Schmitt et al. 1984). The drag force exerted by equatorward flow due to meridional circulation permits states of mechanical and thermal equilibrium in the overshoot region, but these apply only to very thin magnetic flux tubes containing less than $1\%$ of the flux of a large sunspot. In the second part, we consider the influence of radiative heating (and cooling) on magnetic flux stored in the form of a magnetic layer. In contrast to the case of isolated flux tubes, the suppression of the convective energy transport within the magnetic layer affects the overall stratification of the overshoot region. In the case of a quenching of the convective heat conductivity by a factor of the order 100, the overshoot layer receives a net cooling leading to a stronger subadiabaticity, so that values of $\delta< -10^{-4}$ are reached. The stabilization of the stratification relaxes the conditions for flux storage. Stronger quenching of the heat conductivity leads to larger temperature perturbations (of both signs) and to the destabilization of the upper part of the overshoot layer, with the likely consequence of rapid magnetic flux loss.

Heating of Coronal Loop Footpoints by Slingshot Magnetic Reconnection during Two Loop Interactions Driven by a Moving Solitary Magnetic Kink

Recent Transition Region and Coronal Explorer observations of active loops in the EUV showed that there is a class of EUV loops that consists of near-isothermal loop threads with substantially smaller temperature gradients than are predicted by the uniform loop heating model. These results support coronal heating mechanisms operating in or near the chromosphere and transition region. We propose a new local heating model of loop footpoints in the chromosphere in which there occurs nonuniform heating by slingshot magnetic reconnection during two loops' interaction, driven by the moving solitary magnetic kink, which was recently found by three-dimensional MHD simulation and is characterized as a moving solitary magnetic flux ring with a pair of counterrotating vortex rings. We also show that the loop interaction results in the formation of helical up- and downflows driven by the slingshot magnetic reconnection.

A Model of a Single‐Loop Flare: Disruption of a Magnetic Flux Tube Driven by Collision of Two Moving Solitary Magnetic Kinks

We propose a new model of a single-loop flare based on the fact that a magnetic flux tube with axial current can be explosively disrupted during collision of two moving solitary magnetic kinks (MoSMaKs). The concept of the MoSMaK found by three-dimensional MHD simulation is characterized as a moving solitary magnetic flux ring with a pair of counterrotating vortex rings. We investigate the collision process of two MoSMaKs along a slightly bent magnetic flux tube with axial current. We find that the magnetic flux tube can be explosively disrupted during the collision of two MoSMaKs. It is shown that current sheets appear where high-energy particles can be generated through magnetic reconnection. About 20% of the magnetic field energy can be converted to the kinetic energy of upward plasma motions during the disruption of the magnetic flux tube. We apply the collision process of the MoSMaKs to a single-loop flare.

On the Twist of Emerging Flux Loops in the Solar Convection Zone

We perform numerical simulations of emerging flux loops in the solar convective envelope based on a weakly twisted thin flux tube model recently derived by Longcope and Klapper, generalizing the original formulation for the dynamics of untwisted thin flux tubes by Spruit. The generalized formulation includes the description of torsional Alf ven waves and takes into account the coupling of the writhing motion of the tube axis to the change in the flux tube twist based on the requirement of global helicity conservation of the closed thin flux tube. In this model, the twist of the thin flux tube is described by a quantity q defined as the angular rate of field-line rotation about the tube axis per unit length of the tube. We examine the evolution of twist along Ω-shaped emerging flux loops which are formed as a result of the non-linear growth of the Parker instability of toroidal magnetic flux tubes at the base of the solar convection zone. We find that: (1) In the northern hemisphere, a left-handed twist is generated in the flux tubes as a result of the right-handed tilt or writhe of the emerging loops induced by the Coriolis force. The generated twist increases with the latitude of emergence over the range from 0° to about 38° latitude, but then decreases when the emerging latitude exceeds 38°, because of a change in the preferred eruption pattern. The magnitude of the generated twist q is very small, ≗ 2 × 10-4 rad Mm-1, more than an order of magnitude smaller than the observed amplitude of twist (~ 0.01 rad Mm-1) in solar active regions. (2) For a toroidal flux ring with a uniform initial twist q 0 along the ring, the twist amplitude |q| at the apex of the emerging loop decrease by a factor of about 0.67 because of the stretching of the loop, as it rises from the base of the convection zone to about 20 Mm below the photosphere, at which depth the flux tube can no longer be considered thin. However, because of the more rapid increase of the tube cross-sectional radius a with height, |qa|, which corresponds to the ratio between the azimuthal field to the axial field B θ /B l of the tube, increases by a factor of about 2.5 at the apex of the loop, as it rises over the same distance. (3) Because of the effect of the Coriolis force, the distribution of twist along the emerging loop is asymmetric between the leading (in the direction of rotation) and the following sides of the loop. Both |q| and |qa| are greater at the following side than the leading at any depth. Based on the evolution of twist along emerging flux loops, we discuss possible constraints on the twist q 0 of initial toroidal flux tubes at the base of the convection zone.

Evidence for a Singularity in Ideal Magnetohydrodynamics: Implications for Fast Reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\infty \sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.