Tayler Instability Research Articles

Rotation rate of the solar core as a key constraint to magnetic angular momentum transport in stellar interiors

Context. The internal rotation of the Sun constitutes a fundamental constraint when modelling angular momentum transport in stellar interiors. In addition to the more external regions of the solar radiative zone probed by pressure modes, measurements of rotational splittings of gravity modes would offer an invaluable constraint on the rotation of the solar core. Aims. We study the constraints that a measurement of the core rotation rate of the Sun could bring on magnetic angular momentum transport in stellar radiative zones. Methods. Solar models accounting for angular momentum transport by hydrodynamic and magnetic instabilities were computed for different initial velocities and disc lifetimes on the pre-main sequence to reproduce the surface rotation velocities observed for solar-type stars in open clusters. The internal rotation of these solar models was then compared to helioseismic measurements. Results. We first show that models computed with angular momentum transport by magnetic instabilities and a recent prescription for the braking of the stellar surface by magnetized winds can reproduce the observations of surface velocities of stars in open clusters. These solar models predict both a flat rotation profile in the external part of the solar radiative zone probed by pressure modes and an increase in the rotation rate in the solar core, where the stabilizing effect of chemical gradients plays a key role. A rapid rotation of the core of the Sun, as suggested by reported detections of gravity modes, is thus found to be compatible with angular momentum transport by magnetic instabilities. Moreover, we show that the efficiency of magnetic angular momentum transport in regions of strong chemical gradients can be calibrated by the solar core rotation rate independently from the unknown rotational history of the Sun. In particular, we find that a recent revised prescription for the transport of angular momentum by the Tayler instability can be easily distinguished from the original Tayler–Spruit dynamo, with a faster rotating solar core supporting the original prescription. Conclusions. By calibrating the efficiency of magnetic angular momentum transport in regions of strong chemical gradients, a determination of the solar core rotation rate through gravity modes is of prime relevance not only for the Sun, but for stars in general, since radial differential rotation precisely develops in these regions during the more advanced stages of evolution.

A Model of a Tidally Synchronized Solar Dynamo

We discuss a solar dynamo model of Tayler-Spruit type whose Omega-effect is conventionally produced by a solar-like differential rotation but whose alpha-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with a 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of alpha, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the alpha oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of alpha, even less of the oscillatory alpha part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

Slowing the spins of stellar cores

ABSTRACT The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler–Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.

On the stability of a general magnetic field topology in stellar radiative zones

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.

The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability

ABSTRACTMagnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.

Fluid Mechanics of Liquid Metal Batteries

The design and performance of liquid metal batteries (LMBs), a new technology for grid-scale energy storage, depend on fluid mechanics because the battery electrodes and electrolytes are entirely liquid. Here, we review prior and current research on the fluid mechanics of LMBs, pointing out opportunities for future studies. Because the technology in its present form is just a few years old, only a small number of publications have so far considered LMBs specifically. We hope to encourage collaboration and conversation by referencing as many of those publications as possible here. Much can also be learned by linking to extensive prior literature considering phenomena observed or expected in LMBs, including thermal convection, magnetoconvection, Marangoni flow, interface instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the LMB designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important.

On the Synchronizability of Tayler–Spruit and Babcock–Leighton Type Dynamos

The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a simple time-delay model of Babcock-Leighton type dynamos and ask whether periodic changes of either the minimal amplitude for rising toroidal flux tubes or the Omega effect could eventually lead to synchronization. In contrast to the easy and robust synchronizability of Tayler-Spruit dynamo models, our answer for those Babcock-Leighton type models is less propitious.

The DRESDYN project: planned experiments and present status

AbstractThe Dresden sodium facility for dynamo and thermohydraulic studies (DRESDYN) is a platform for large‐scale liquid sodium experiments devoted to fundamental geo‐ and astrophysical questions as well as to various applied problems related to the conversion and storage of energy. Its most ambitious part is a precession driven dynamo experiment, comprising 8 tons of liquid sodium supposed to rotate with up to 10 Hz and to precess with up to 1 Hz. Another large‐scale set‐up is a Tayler‐Couette experiment with a gap width of 0.2 m and a height of 2 m, whose inner cylinder rotates with up to 20 Hz. Equipped with a coil system for the generation of an axial field of up to 120 mT and two different axial currents through the center and the liquid sodium, this experiment aims at studying various versions of the magnetorotational instability and their combinations with the Tayler instability. We discuss the physical background of these two experiments and delineate the present status of their technical realization. Other installations, such as a sodium loop and a test stand for In‐Service‐Inspection experiments will also be sketched. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetorotational and Tayler Instabilities in the Pulsar Magnetosphere

The magnetospheres around neutron stars should be very particular because of their strong magnetic field and rapid rotation. A study of the pulsar magnetospheres is of crucial importance since it is the key issue to understand how energy outflow to the exterior is produced. In this paper, we discuss magnetohydrodynamic processes in the pulsar magnetosphere. We consider in detail the properties of magnetohydrodynamic waves that can exist in the magnetosphere and their instabilities. These instabilities lead to formation of magnetic structures and can be responsible for short-term variability of the pulsar emission.

Liquid metal batteries - materials selection and fluid dynamics

Liquid metal batteries are possible candidates for massive and economically feasible large-scale stationary storage and as such could be key components of future energy systems based mainly or exclusively on intermittent renewable electricity sources. The completely liquid interior of liquid metal batteries and the high current densities give rise to a multitude of fluid flow phenomena that will primarily influence the operation of future large cells, but might be important for today’s smaller cells as well. The paper at hand starts with a discussion of the relative merits of using molten salts or ionic liquids as electrolytes for liquid metal cells and touches the choice of electrode materials. This excursus into electrochemistry is followed by an overview of investigations on magnetohydrodynamic instabilities in liquid metal batteries, namely the Tayler instability and electromagnetically excited gravity waves. A section on electro-vortex flows complements the discussion of flow phenomena. Focus of the flow related investigations lies on the integrity of the electrolyte layer and related critical parameters.

Magnetic field dynamos and magnetically triggered flow instabilities

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this survey paper, the main results of these two projects are summarized.

On the possibility of helicity oscillations in the saturation of the Tayler instability

Recent numerical results of current‐driven instabilities at low magnetic Prandtl number and high Hartmann number support the possibility of a saturation state characterized by helicity oscillations. We investigate the underlying mechanism by analyzing this possibility using a higher order Landau–Ginzburg effective Lagrangian for the weakly nonlinear amplitude dynamics, where the magnetic and velocity perturbations are linearly dependent. We find that, if the mirror symmetry between left‐ and right‐handed modes is spontaneously broken, it is impossible to achieve an oscillating helical state. We argue that the result is likely to hold also for adding higher order terms and in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to depend on the interaction of chiral modes.

Elementary model of internal electromagnetic pinch-type instability

We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient features of the instability which otherwise may be obscured by the technical details of more comprehensive numerical models and laboratory experiments. Firstly, we show the instability in liquid metals, which are relatively poor conductors, differs significantly from the astrophysically relevant Tayler instability. In liquid metals, the instability develops on the magnetic response time scale, which depends on the conductivity and is much longer than the Alfvén time scale, on which the Tayler instability develops in well conducting fluids. Secondly, we show that this instability is an edge effect caused by the curvature of the magnetic field, and its growth rate is determined by the linear current density and independent of the system size. Our results suggest that this instability may affect future liquid-metal batteries when their size reaches a few metres.

The Tayler instability at low magnetic Prandtl numbers: chiral symmetry breaking and synchronizable helicity oscillations

The current-driven, kink-type Tayler instability (TI) is a key ingredient of the Tayler-Spruit dynamo model for the generation of stellar magnetic fields, but is also discussed as a mechanism that might hamper the up-scaling of liquid metal batteries. Under some circumstances, the TI involves a helical flow pattern which goes along with some alpha effect. Here we focus on the chiral symmetry breaking and the related impact on the alpha effect that would be needed to close the dynamo loop in the Tayler-Spruit model. For low magnetic Prandtl numbers, we observe intrinsic oscillations of the alpha effect. These oscillations serve then as the basis for a synchronized Tayler-Spruit dynamo model, which could possibly link the periodic tidal forces of planets with the oscillation periods of stellar dynamos.

Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle?

Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha-effect. Finally, in the framework of a reduced, zero-dimensional alpha--Omega dynamo model we recover a 22.14-year cycle of the solar dynamo.

Magnetohydrodynamic effects in liquid metal batteries

Liquid metal batteries (LMBs) consist of two liquid metal electrodes and a molten salt ionic conductor sandwiched between them. The density ratios allow for a stable stratification of the three layers. LMBs were already considered as part of energy conversion systems in the 1960s and have recently received renewed interest for economical large-scale energy storage. In this paper, we concentrate on the magnetohydrodynamic aspects of this cell type with special focus on electro-vortex flows and possible effects of the Tayler instability.

Mixing of a passive scalar by the instability of a differentially rotating axial pinch

The mixing of a passive scalar like lithium, beryllium or temperature fluctuations due to the magnetic Tayler instability of a rotating axial pinch is considered. Our study is carried out within a Taylor-Couette setup for two rotation laws: quasi-Kepler and solid-body rotation. The minimum magnetic Prandtl number used is 0.05 while the molecular Schmidt number Sc of the fluid varies between 0.1 and 2. An effective diffusivity coefficient for the mixing is numerically measured by the decay process of a global concentration peak located between the cylinder walls. We find that only models with Sc>0.1 do provide finite eddy diffusivity values. We also find that for quasi-Kepler rotation at a magnetic Mach number Mm~2 the flow transits from the slow-rotation regime to the fast-rotation regime. For fixed Reynolds number the relation between the normalized eddy diffusivity and the Schmidt number of the fluid is always linear so that also a linear relation between the instability-induced diffusivity and the molecular viscosity results just in the sense proposed by Schatzman (1977). The numerical value of the coefficient in this relation will reach a maximum at Mm~2 and will decrease for Mm>>1 implying that only toroidal magnetic fields of order kG can exist in the solar tachocline.

Subcritical excitation of the current-driven Tayler instability by super-rotation

It is known that in a hydrodynamic Taylor-Couette system, uniform rotation or a rotation law with positive shear (“super-rotation”) is linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindrical pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with dΩ/dR ≥ 0. For magnetic Prandtl number Pm ≠ 1 and for slow rotation, however, rigid rotation and super-rotation support the instability by lowering the critical Hartmann numbers. This double-diffusive instability of super-rotation even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile Bϕ ∝ 1/R included. The sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm ≪ 1 and it corotates for Pm ≫ 1 while for rotation laws with negative shear, the instability pattern migrates in the direction of the basic rotation for all Pm. An axial electric-current of minimal 3.6 kA flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kA if a gallium alloy is used.

EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION

We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD "millenium simulation" of Passos & Charbonneau (2014). This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally-oriented bands of strong magnetic field accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly subadiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of subadiabaticity in the stable fluid layers underlying the convection zone.

The Tayler instability at low magnetic Prandtl numbers: between chiral symmetry breaking and helicity oscillations

The Tayler instability is a kink-type, current driven instability that plays an important role in plasma physics but might also be relevant in liquid metal applications with high electrical currents. In the framework of the Tayler–Spruit dynamo model of stellar magnetic field generation (Spruit 2002 Astron. Astrophys. 381 923–32), the question of spontaneous helical (chiral) symmetry breaking during the saturation of the Tayler instability has received considerable interest (Zahn et al 2007 Astron. Astrophys. 474 145–54; Gellert et al 2011 Mon. Not. R. Astron. Soc. 414 2696–701; Bonanno et al 2012 Phys. Rev. E 86 016313). Focusing on fluids with low magnetic Prandtl numbers, for which the quasistatic approximation can be applied, we utilize an integro-differential equation approach (Weber et al 2013 New J. Phys.15 043034) in order to investigate the saturation mechanism of the Tayler instability. Both the exponential growth phase and the saturated phase are analysed in terms of the action of the α and β effects of mean-field magnetohydrodynamics. In the exponential growth phase we always find a spontaneous chiral symmetry breaking which, however, disappears in the saturated phase. For higher degrees of supercriticality, we observe helicity oscillations in the saturated regime. For Lundquist numbers in the order of one we also obtain chiral symmetry breaking of the saturated magnetic field.