Magnetic Buoyancy Research Articles

Solar Surface Magneto-Convection

We review the properties of solar magneto-convection in the top half of the convection zones scale heights (from 20 Mm below the visible surface to the surface, and then through the photosphere to the temperature minimum). Convection is a highly non-linear and nonlocal process, so it is best studied by numerical simulations. We focus on simulations that include sufficient detailed physics so that their results can be quantitatively compared with observations. The solar surface is covered with magnetic features with spatial sizes ranging from unobservably small to hundreds of megameters. Three orders of magnitude more magnetic flux emerges in the quiet Sun than emerges in active regions. In this review we focus mainly on the properties of the quiet Sun magnetic field. The Sun's magnetic field is produced by dynamo action throughout the convection zone, primarily by stretching and twisting in the turbulent downflows. Diverging convective upflows and magnetic buoyancy carry magnetic flux toward the surface and sweep the field into the surrounding downflow lanes where the field is dragged downward. The result is a hierarchy of undulating magnetic Ω- and U-loops of different sizes. New magnetic flux first appears at the surface in a mixed polarity random pattern and then collects into isolated unipolar regions due to underlying larger scale magnetic structures. Rising magnetic structures are not coherent, but develop a filamentary structure. Emerging magnetic flux alters the convection properties, producing larger, darker granules. Strong field concentrations inhibit transverse plasma motions and, as a result, reduce convective heat transport toward the surface which cools. Being cooler, these magnetic field concentrations have a shorter scale height and become evacuated. The field becomes further compressed and can reach strengths in balance with the surrounding gas pressure. Because of their small internal density, photons escape from deeper in the atmosphere. Narrow evacuated field concentrations get heated from their hot sidewalls and become brighter than their surroundings. Wider magnetic concentrations are not heated so they become darker, forming pores and sunspots.

Magnetic Bénard-Marangoni Convection in an Annular Liquid Layer

The linear stability is studied for the Bénard-Marangoni convection in a diamagnetic liquid layer sustained by surface tension around a cylinder in the absence of gravitational force. A surface of the cylinder is kept at a constant temperature while a liquid surface is heated or cooled. An azimuthal magnetic field generated by an electric current through the central axis of the cylinder is considered. A combined convection takes place owing to the radial magnetic buoyancy force as well as the Marangoni effect acting at the liquid surface. It is shown that the convection of diamagnetic liquid can be enhanced or suppressed by the use of magnetic field.

The short-wavelength instability of magnetically buoyant layer

We revisit the problem introduced by Gilman (1970) and Acheson (1979) of linear stability of a plane layer of compressible fluid permeated by a horizontal magnetic field of magnitude decreasing with height with respect to short-wavelength two-dimensional perturbations varying in the directions perpendicular to the applied field. We show, that in the limit of large horizontal wave numbers the perturbations become strongly localised in the vertical direction. The motiavtion for this study is of astrophysical nature and comes from the common belief, that the magnetic buoyancy effects produce short-wavelength instabilities in the solar tachocline. We analyse the solar tachocline parameter regime to speculate about the strength of the magnetic field at the base of the solar convective zone and the time scales of the field variations induced by the magnetic buoyancy instability on the Sun.

THE RISE OF ACTIVE REGION FLUX TUBES IN THE TURBULENT SOLAR CONVECTIVE ENVELOPE

We use a thin flux tube model in a rotating spherical shell of turbulent convective flows to study how active region scale flux tubes rise buoyantly from the bottom of the convection zone to near the solar surface. We investigate toroidal flux tubes at the base of the convection zone with field strengths ranging from 15 kG to 100 kG at initial latitudes ranging from 1 degree to 40 degrees with a total flux of 10^22 Mx. We find that the dynamic evolution of the flux tube changes from convection dominated to magnetic buoyancy dominated as the initial field strength increases from 15 kG to 100 kG. At 100 kG, the development of Omega-shaped rising loops is mainly controlled by the growth of the magnetic buoyancy instability. However, at low field strengths of 15 kG, the development of rising Omega-shaped loops is largely controlled by convective flows, and properties of the emerging loops are significantly changed compared to previous results in the absence of convection. With convection, rise times are drastically reduced (from years to a few months), loops are able to emerge at low latitudes, and tilt angles of emerging loops are consistent with Joy's Law for initial field strengths of greater than or equal to 40 kG. We also examine other asymmetries that develop between the leading and following legs of the emerging loops. Taking all the results together, we find that mid-range field strengths of approximately 40 - 50 kG produce emerging loops that best match the observed properties of solar active regions.

Magnetic spots on hot massive stars

Hot luminous stars show a variety of phenomena in their photospheres and winds which still lack clear physical explanation. Among these phenomena are photospheric turbulence, line profile variability (LPV), non-thermal emission, non-radial pulsations, discrete absorption components (DACs) and wind clumping. Cantiello et al. (2009) argued that a convection zone close to the stellar surface could be responsible for some of these phenomena. This convective zone is caused by a peak in the opacity associated with iron-group elements and is referred to as the "iron convection zone" (FeCZ). Assuming dynamo action producing magnetic fields at equipartition in the FeCZ, we investigate the occurrence of subsurface magnetism in OB stars. Then we study the surface emergence of these magnetic fields and discuss possible observational signatures of magnetic spots. Simple estimates are made using the subsurface properties of massive stars, as calculated in 1D stellar evolution models. We find that magnetic fields of sufficient amplitude to affect the wind could emerge at the surface via magnetic buoyancy. While at this stage it is difficult to predict the geometry of these features, we show that magnetic spots of size comparable to the local pressure scale height can manifest themselves as hot, bright spots. Localized magnetic fields could be widespread in those early type stars that have subsurface convection. This type of surface magnetism could be responsible for photometric variability and play a role in X-ray emission and wind clumping.

Alpha effect due to buoyancy instability of a magnetic layer

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field.

Dynamo-driven plasmoid ejections above a spherical surface

Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress--and--relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space--time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.

BUOYANT MAGNETIC LOOPS IN A GLOBAL DYNAMO SIMULATION OF A YOUNG SUN

The current dynamo paradigm for the Sun and sun-like stars places the generation site for strong toroidal magnetic structures deep in the solar interior. Sunspots and star-spots on sun-like stars are believed to arise when sections of these magnetic structures become buoyantly unstable and rise from the deep interior to the photosphere. Here we present the first 3-D global magnetohydrodynamic (MHD) simulation in which turbulent convection, stratification, and rotation combine to yield a dynamo that self-consistently generates buoyant magnetic loops. We simulate stellar convection and dynamo action in a spherical shell with solar stratification, but rotating three times faster than the current solar rate. Strong wreaths of toroidal magnetic field are realized by dynamo action in the convection zone. By turning to a dynamic Smagorinsky model for subgrid-scale turbulence, we here attain considerably reduced diffusion in our simulation. This permits the regions of strongest magnetic field in these wreaths to rise toward the top of the convection zone via a combination of magnetic buoyancy instabilities and advection by convective giant cells. Such a global simulation yielding buoyant loops represents a significant step forward in combining numerical models of dynamo action and flux emergence.

Dynamo action and magnetic buoyancy in convection simulations with vertical shear

A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We perform numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location of the shear layer, and the magnetic Reynolds number ($\Rm$). Whenever the toroidal magnetic field reaches amplitudes greater a threshold value which is close to the equipartition value, it becomes buoyant and rises into the convection zone where it expands and forms mushroom shape structures. Some events of emergence, i.e. those with the largest amplitudes of the initial field, are able to reach the very uppermost layers of the domain. These episodes are able to modify the convective pattern forming either broader convection cells or convective eddies elongated in the direction of the field. However, in none of these events the field preserves its initial structure.

Spontaneous chiral symmetry breaking by hydromagnetic buoyancy

Evidence for the parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the nonhelical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of this magnetohydrodynamic instability appears to be the first of its kind and has properties similar to those in chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are discussed.

Rossby waves and polar spots in rapidly rotating stars: implications for stellar wind evolution

Rapidly rotating stars show short-period oscillations in magnetic activity and polar appearance of starspots. The aim of this paper is to study large-scale shallow water waves in the tachoclines of rapidly rotating stars and their connection to the periodicity and the formation of starspots at high latitudes. Shallow-water magnetohydrodynamic equations were used to study the dynamics of large-scale waves at the rapidly rotating stellar tachoclines in the presence of toroidal magnetic field. Dispersion relations and latitudinal distribution of wave modes were derived. We found that low-frequency magnetic Rossby waves tend to be located at poles, but high-frequency magnetic Poincare waves are concentrated near the equator in rapidly rotating stars. These results have important implications for the evolution of the stellar wind in young Sun-like stars. Unstable magnetic Rossby waves may lead to the local enhancement of magnetic flux at high latitudes of tachoclines in rapidly rotating stars. The enhanced magnetic flux may rise upwards owing to the magnetic buoyancy in the form of tubes and appear as starspots at polar regions. Magnetic Rossby waves may also cause observed short-term periodicity in the stellar magnetic activity.

NUMERICAL EXPERIMENTS ON THE TWO-STEP EMERGENCE OF TWISTED MAGNETIC FLUX TUBES IN THE SUN

We present the new results of the two-dimensional numerical experiments on the cross-sectional evolution of a twisted magnetic flux tube rising from the deeper solar convection zone (-20,000 km) to the corona through the surface. The initial depth is ten times deeper than most of previous calculations focusing on the flux emergence from the uppermost convection zone. We find that the evolution is illustrated by the two-step process described below: the initial tube rises due to its buoyancy, subject to aerodynamic drag due to the external flow. Because of the azimuthal component of the magnetic field, the tube maintains its coherency and does not deform to become a vortex roll pair. When the flux tube approaches the photosphere and expands sufficiently, the plasma on the rising tube accumulates to suppress the tube's emergence. Therefore, the flux decelerates and extends horizontally beneath the surface. This new finding owes to our large scale simulation calculating simultaneously the dynamics within the interior as well as above the surface. As the magnetic pressure gradient increases around the surface, magnetic buoyancy instability is triggered locally and, as a result, the flux rises further into the solar corona. We also find that the deceleration occurs at a higher altitude than in our previous experiment using magnetic flux sheets (Toriumi and Yokoyama). By conducting parametric studies, we investigate the conditions for the two-step emergence of the rising flux tube: field strength > 1.5x10^4 G and the twist > 5.0x10^-4 km^-1 at -20,000 km depth.

Focusing microparticles in a microfluidic channel with ferrofluids

We report a novel on-chip microparticles focusing technique using stable magnetic nanoparticles suspension (i.e., ferrofluids). The principle of focusing is based on magnetic buoyancy forces exerted on non-magnetic particles within ferrofluids under non-uniform magnetic field. The design, modeling, fabrication, and characterization of the focusing scheme are presented. Focusing of 4.8, 5.8, and 7.3 μm microparticles at various flow rates are demonstrated in a microfluidic channel. Our scheme is simple, low-cost, and label-free compared to other existing techniques.

DISSIPATION AND VERTICAL ENERGY TRANSPORT IN RADIATION-DOMINATED ACCRETION DISKS

Standard models of radiation supported accretion disks generally assume that diffusive radiation flux is solely responsible for vertical heat transport. This requires that heat must be generated at a critical rate per unit volume if the disk is to be in hydrostatic and thermal equilibrium. This raises the question of how heat is generated and how energy is transported in MHD turbulence. By analysis of a number of radiation/MHD stratified shearing-box simulations, we show that the divergence of the diffusive radiation flux is indeed capped at the critical rate, but deep inside the disk, substantial vertical energy flux is also carried by advection of radiation. Work done by radiation pressure is a significant part of the energy budget, and much of this work is dissipated later through damping by radiative diffusion. We show how this damping can be measured in the simulations, and identify its physical origins. Radiative damping accounts for as much as tens of percent of the total dissipation, and is the only realistic physical mechanism for dissipation of turbulence that can actually be resolved in numerical simulations of accretion disks. Buoyancy associated with dynamo-driven, highly magnetized, nearly-isobaric nonlinear slow magnetosonic fluctuations is responsible for the radiation advection flux, and also explains the persistent periodic magnetic upwelling seen at all values of the radiation to gas pressure ratio. The intimate connection between radiation advection and magnetic buoyancy is the first example we know of in astrophysics in which a dynamo has direct impact on the global energetics of a system.

Dependence of the Magnetic Energy of Solar Active Regions on the Twist Intensity of the Initial Flux Tubes

Abstract We present a series of numerical experiments that model the evolution of magnetic flux tubes with a different amount of initial twist. As a result of calculations, tightly twisted tubes reveal a rapid two-step emergence to the atmosphere with a slight slowdown at the surface, while weakly twisted tubes show a slow two-step emergence waiting longer the secondary instability to be triggered. This picture of the two-step emergence is highly consistent with recent observations. These tubes show multiple magnetic domes above the surface, indicating that the secondary emergence is caused by an interchange mode of magnetic buoyancy instability. In the case of the weakest twist, the tube exhibits an elongated photospheric structure, and never rises into the corona. The formation of the photospheric structure is due to an inward magnetic tension force of the azimuthal field component of the rising flux tube (i.e., tube's twist). When the twist is weak, the azimuthal field cannot hold the tube's coherency, and the tube extends laterally at the subadiabatic surface. In addition, we newly found that the total magnetic energy measured above the surface depends on the initial twist. Strong twist tubes follow the initial relation between the twist and the magnetic energy, while weak twist tubes deviate from this relation, because these tubes store their magnetic energy in the photospheric structure.

Magnetic flux generation and transport in cool stars

The Sun and other cool stars harbouring outer convection zones manifest magnetic activity in their atmospheres. The connection between this activity and the properties of a deep-seated dynamo generating the magnetic flux is not well understood. By employing physical models, we study the spatial and temporal characteristics of the observable surface field for various stellar parameters. We combine models for magnetic flux generation, buoyancy instability, and transport, which encompass the entire convection zone. The model components are: (1) a thin-layer alpha-Omega dynamo at the base of the convection zone; (2) buoyancy instabilities and the rise of flux tubes through the convection zone in 3D, which provides a physically consistent determination of emergence latitudes and tilt angles; and (3) horizontal flux transport at the surface. For solar-type stars and rotation periods longer than about 10 days, the latitudinal dynamo waves generated by the deep-seated alpha-Omega dynamo are faithfully reflected by the surface distribution of magnetic flux. For rotation periods of the order of two days, however, Coriolis acceleration of rising flux loops leads to surface flux emergence at much higher latitudes than the dynamo waves at the bottom of the convection zone reach. A similar result is found for a K0V star with a rotation period of two days. In the case of a rapidly rotating K1 subgiant, overlapping dynamo waves lead to noisy activity cycles and mixed-polarity fields at high latitudes.

Testing PPE for Arc-Hazard Protection IEC 61482-1 Test-Rig Evaluation Including Proposed Changes

The International Electrotechnical Commission Standard 61482-1 describes procedures for measuring the thermal performance of fabrics and garments intended for use in clothing for workers exposed to electric arcs. This paper demonstrates that the tests in this Standard fail to produce controlled laboratory conditions. The dominant magnetic and thermal buoyancy forces have been minimized leaving two undefined and uncontrolled forces to randomly dominate arc motion, plasma flow, and thermal stress. The tests also produce hazards significantly different from those faced by victims in real situations. The velocity of the plasma impinging on a victim is incorrect. The color of the radiation is incorrect. The molten metal droplets impinging on the victim are incorrect. The tests only consider clothing stretched over a surface, whereas loose and unbacked cloth suffers considerably more stress. In order to emulate real arcing faults, it will be necessary to use parallel copper and aluminum electrodes. In addition, for personnel working on high-voltage, a “pop-out” test needs to be developed because a fault current that starts by entering and exiting the body becomes an arc inside the clothing.

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied “wall effect” on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.

THE MEAN ELECTROMOTIVE FORCE RESULTING FROM MAGNETIC BUOYANCY INSTABILITY

Motivated both by considerations of the generation of large-scale astrophysical magnetic fields and by potential problems with mean magnetic field generation by turbulent convection, we investigate the mean electromotive force (emf) resulting from the magnetic buoyancy instability of a rotating layer of stratified magnetic field, considering both unidirectional and sheared fields. We discuss why the traditional decomposition into $\alpha$ and $\beta$ effects is inappropriate in this case, and that it is only consideration of the entire mean emf that is meaningful. By considering a weighted average of the unstable linear eigenmodes, and averaging over the horizontal plane, we obtain depth-dependent emfs. For the simplified case of isothermal, ideal MHD we are able to obtain an analytic expression for the emf; more generally the emf has to be determined numerically. We calculate how the emf depends on the various parameters of the problem, particularly the rotation rate and the latitude of the magnetic layer.

Formation of accretion disks in close-binary systems with magnetic fields

We have developed a three-dimensional numerical model and applied it to simulate plasma flows in semi-detached binary systems whose accretor possesses a strong intrinsic magnetic field. The model is based on the assumption that the plasma dynamics are determined by the slow mean flow, which forms a backdrop for the rapid propagation of MHD waves. The equations describing the slow motion of matter were obtained by averaging over rapidly propagating pulsations. The numerical model includes the diffusion of magnetic field by current dissipation in turbulent vortices, magnetic buoyancy, and wave MHD turbulence. A modified three-dimensional, parallel, numerical code was used to simulate the flow structure in close binary systems with various accretor magnetic fields, from $10^5$ to $10^8$ G. The conditions for the formation of the accretion disk and the criteria distinguishing the two types of flow corresponding to intermediate polars and polars are discussed.