Dynamo Action Research Articles

Effect of electromagnetic boundary conditions on the onset of small-scale dynamos driven by convection

We present a high-order numerical study of the dependence of the dynamo onset on different electromagnetic boundary conditions, in convecting Boussinesq flows forced by a temperature gradient. Perfectly conducting boundaries, vacuum, and mixed electromagnetic boundary conditions are considered, using a method that treats fields and boundary conditions with close to spectral accuracy. Having one or two conducting boundaries greatly facilitates dynamo action. For the mixed case it is shown that the critical magnetic Reynolds number becomes independent of the Rayleigh number, Ra, for sufficiently large Ra.

Electrical resistivity of liquid Fe-8wt%S-4.5wt%Si at high pressures with implications for heat flux through the cores of Io and sub-earth exoplanets

Potentially resulting in magnetic dynamo action, the heat flow through the outer cores of small terrestrial planetary bodies depends on the thermal conductivity of liquid Fe alloys at high pressures. The electrical resistivity of liquid Fe-8wt%S-4.5wt%Si was measured at 2–5 GPa and 295–1800 K in a 1000-ton cubic anvil press with a sample volume of a few cubic millimeters. Resistivity values of 220–270 μΩ·cm were measured, and a range of thermal conductivity values of 15–19 W/m/K were calculated using the Wiedemann-Franz law. The adiabatic heat flux at the top of a terrestrial exoplanet's Fe-8wt%S-4.5wt%Si core as a function of radius is calculated. The core of Io, if liquid, could have a convective heat flow density of a few μW/m2 without generating a magnetic dynamo powered by thermal convection.

The connection between the equatorial temperature bias and north–south helicity segregation in numerical simulations of the geodynamo

SUMMARY In recent numerical simulations of the geodynamo the dynamo action is driven, primarily, by the effects of helicity, with differential rotation playing only a secondary role. These dynamos display a number of robust features, such as: (i) thin convective columns outside the tangent cylinder whose azimuthally averaged helicity, $\langle h \rangle = \langle {{{\bf u}} \cdot \nabla \times {{\bf u}}} \rangle $, is left-handed in the north and right-handed in the south, (ii) approximately 2-D motion in the equatorial regions, with negligible axial velocity,$\langle {{u}_z} \rangle \approx 0$, (iii) positive radial current at mid-latitudes and negative radial current in the equatorial regions, (iv) a radial outflow in the equatorial regions and (v) elevated temperatures near the equator. We seek the relationship between all five of these observations. First, we note that $\langle {{u}_z} \rangle \approx 0$ near the equator follows from the skew-symmetric distribution of helicity, while a negative radial current at the equator is a generic feature of helicity-driven dynamos which have positive (negative) helicity in the south (north). Next, we confirm an earlier suggestion that the equatorial outflow is driven by Lorentz forces associated with the negative radial current. Crucially, however, this outflow does not account for the elevated equatorial temperatures. Rather, the high temperature near the equator is primarily a consequence of anisotropic turbulent diffusion, which preferentially carries heat radially outward along the equator, this anisotropy being a consequence of the (approximately) 2-D flow near the equator. In short, we show that the high equatorial temperatures are a direct consequence of the skew-symmetric distribution of helicity. Finally, we recall that the high equatorial temperatures can themselves explain the observed helicity distribution, as buoyant anomalies near the equator trigger inertial waves which carry negative helicity upward and positive helicity downward. Thus, there is a direct, two-way coupling between the high equatorial temperatures and the helicity distribution.

Solar-cycle and Latitude Variations in the Internetwork Magnetism

The importance of the quiet-Sun magnetism is that it is always there to a greater or lesser extent, being a constant provider of energy, independently of the solar cycle phase. The open questions about the quiet-Sun magnetism include those related to its origin. Most people claim that the local dynamo action is the mechanism that causes it. This fact would imply that the quiet-Sun magnetism is nearly the same at any location over the solar surface and at any time. Many works claim that the quiet Sun does not have any variation at all, although a few of them raise doubt on this claim and find mild evidence of a cyclic variation in the the quiet-Sun magnetism. In this work, we detect clear variations in the internetwork magnetism both with latitude and solar cycle. In terms of latitude, we find an increase in the averaged magnetic fields toward the solar poles. We also find long-term variations in the averaged magnetic field at the disk center and solar poles, and both variations are almost anticorrelated. These findings do not support the idea that the local dynamo action is the unique factory of the quiet-Sun magnetism.

Spin-down by dynamo action in simulated radiative stellar layers.

The evolution of a star is influenced by its internal rotation dynamics through transport and mixing mechanisms, which are poorly understood. Magnetic fields can play a role in transporting angular momentum and chemical elements, but the origin of magnetism in radiative stellar layers is unclear. Using global numerical simulations, we identify a subcritical transition from laminar flow to turbulence caused by the generation of a magnetic dynamo. Our results have many properties of the theoretically proposed Tayler-Spruit dynamo mechanism, which strongly enhances transport of angular momentum in radiative zones. The dynamo generates deep toroidal fields that are screened by the stellar outer layers. This mechanism could produce strong magnetic fields inside radiative stars without an observable field on their surface.

Thermal Convection in a Central Force Field Mediated by Sound

Convection in radial force fields is a fundamental process behind weather on Earth and the Sun, as well as magnetic dynamo action in both. Until now, benchtop experiments have been unable to study convection in radial force fields due to the inability to generate radial forces of sufficient strength. Recently, it has been appreciated that sound, when averaged over many cycles, exerts a force on density gradients in the gas it travels through. The acoustic radiation pressure on thermal gradients draws cooler gas to regions with large time-averaged acoustic velocity and can be modeled as an effective acoustic gravity. We have constructed a system which generates a high amplitude, spherically symmetric acoustic wave in a rotating spherical bulb containing weakly ionized sulfur gas. Without sound, the gas stratifies itself into an initial state with the warmest gas near the center of the bulb, and the coolest gas near the bulb surface. When the sound is initiated, the acoustic radiation pressure is not balanced and a convective instability is triggered. With high speed videography, we observe the initial shape and growth rate of the most unstable mode at various acoustic amplitudes. Acoustic and rotational forces both contribute to the detailed mode shape, which changes qualitatively at low amplitudes where acoustic forces no longer surpass rotational ones everywhere in the bulb.

Dynamic mode decomposition of the geomagnetic field over the last two decades

Earth's magnetic field, which is generated in the liquid outer core through the dynamo action, undergoes changes on timescales of a few years to several million years, yet the underlying mechanisms responsible for the field variations remain to be elucidated. In this study, we apply a novel data analysis technique developed in fluid dynamics, namely the dynamic mode decomposition, to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available. The dominant dynamic modes are extracted by solving an eigen-value problem, so one can identify modes with periods longer than the time span of data. Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration, justifying the validity of applying the dynamic mode decomposition method to geomagnetic field. We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years, a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years. These modes are possibly related to magnetohydrodynamic waves in the Earth's outer core.

The effect of nutation angle on the flow inside a precessing cylinder and its dynamo action

The effect of the nutation angle on the flow inside a precessing cylinder is experimentally explored and compared with numerical simulations. The focus is laid on the typical breakdown of the directly forced m = 1 Kelvin mode for increasing precession ratio (Poincaré number) and the accompanying transition between laminar and turbulent flows. Compared to the reference case with a 90° nutation angle, prograde rotation leads to an earlier breakdown, while in the retrograde case, the forced mode continues to exist also for higher Poincaré numbers. Depending largely on the occurrence and intensity of an axisymmetric double-roll mode, a kinematic dynamo study reveals a sensitive dependence of the self-excitation condition on the nutation angle and the Poincaré number. Optimal dynamo conditions are found for 90° angle which, however, might shift to slightly retrograde precession for higher Reynolds numbers.

The “New Core Paradox”: Challenges and Potential Solutions

AbstractThe “new core paradox” suggests that the persistence of the geomagnetic field over nearly all of Earth history is in conflict with the core being highly thermally conductive, which makes convection and dynamo action in the core much harder prior to the nucleation of the inner core. Here we revisit this issue by exploring the influence of six important parameters on core evolution: upper/lower mantle viscosity ratio, core thermal conductivity, core radiogenic heat rate, mantle radiogenic heating rate, central core melting temperature, and initial core‐mantle boundary (CMB) temperature. Each parameter is systematically explored by the model, which couples mantle energy and core energy‐entropy evolution. A model is “successful” if the correct present‐day inner core size is achieved and the dynamo remains alive, as implied by the paleomagnetic record. In agreement with previous studies, we do not find successful thermal evolutions using nominal parameters, which includes a core thermal conductivity of 70 Wm−1K−1, zero core radioactivity, and an initial CMB temperature of 5,000 K. The dynamo can be kept alive by assuming an unrealistically low thermal conductivity of 20 Wm−1K−1 or an unrealistically high core radioactive heat flow of 3 TW at present‐day, which are considered “unsuccessful” models. We identify a third scenario to keep the dynamo alive by assuming a hot initial CMB temperature of ∼6,000 K and a central core liquidus of ∼5,550 K. These temperatures are on the extreme end of typical estimates, but should not be ruled out and deserve further scrutiny.

Fury: an experimental dynamo with anisotropic electrical conductivity

We report measurements of dynamo action in a new experimental set-up, named Fury, based on the use of an anisotropic electrical conductivity. It consists of a copper rotor rotating inside a copper stator, electrically connected with a thin layer of liquid metal, galinstan. Grooves have been cut in the copper so that, everywhere, electrical conductivity can be considered to be that of copper along two directions while it is zero along the third one. The configuration is efficient and dynamo action can be powered by hand. We have also used a motor with better control, enabling us to drive the rotor at specified velocity or torque functions of time. The structure of the axisymmetric magnetic field produced is found to be close to the numerical modelling using FreeFem++. The experimental dynamo behaves very nearly as expected for a kinematic dynamo, so that the threshold dynamo velocity cannot be exceeded, or only briefly. More mechanical power in the rotor rotation leads to an increase in the magnetic field intensity, the magnetic energy being proportional to the extra mechanical power beyond the threshold. In the transient following a step increase of torque, magnetic and angular velocity oscillations have been observed and explained.

A new scenario for magnetar formation: Tayler-Spruit dynamo in a proto-neutron star spun up by fallback

Magnetars are isolated young neutron stars characterised by the most intense magnetic fields known in the Universe, which power a wide variety of high-energy emissions from giant flares to fast radio bursts. The origin of their magnetic field is still a challenging question. In situ magnetic field amplification by dynamo action could potentially generate ultra-strong magnetic fields in fast-rotating progenitors. However, it is unclear whether the fraction of progenitors harbouring fast core rotation is sufficient to explain the entire magnetar population. To address this point, we propose a new scenario for magnetar formation involving a slowly rotating progenitor, in which a slow-rotating proto-neutron star is spun up by the supernova fallback. We argue that this can trigger the development of the Tayler-Spruit dynamo while other dynamo processes are disfavoured. Using the findings of previous studies of this dynamo and simulation results characterising the supernova fallback, we derive equations modelling the coupled evolution of the proto-neutron star rotation and magnetic field. Their time integration for different accreted masses is successfully compared with analytical estimates of the amplification timescales and saturation value of the magnetic field. We find that the magnetic field is amplified within 20 − 40 s after the core bounce, and that the radial magnetic field saturates at intensities between ∼1013 and 1015 G, therefore spanning the full range of a magnetar’s dipolar magnetic fields. The toroidal magnetic field is predicted to be a factor of 10–100 times stronger, lying between ∼1015 and 3 × 1016 G. We also compare the saturation mechanisms proposed respectively by H.C. Spruit and J. Fuller, showing that magnetar-like magnetic fields can be generated for a neutron star spun up to rotation periods of ≲8 ms and ≲28 ms, corresponding to accreted masses of ≳ 4 × 10−2 M⊙ and ≳ 1.1 × 10−2 M⊙, respectively. Therefore, our results suggest that magnetars can be formed from slow-rotating progenitors for accreted masses compatible with recent supernova simulations and leading to plausible initial rotation periods of the proto-neutron star.

Confinement of the Solar Tachocline by Dynamo Action in the Radiative Interior

A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3D, global solar simulation that displays a magnetically confined tachocline. The nonaxisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward, similar to the proposed fast magnetic confinement scenario by the Sun’s cyclic dynamo field. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that seem to arise from a combination of equatorial Rossby waves and shear, magnetic, and buoyancy instabilities. Our work thus supports prior studies proposing dynamo action in the radiative interior, and suggests that horizontal motions could play a key role in driving this deep dynamo.

Effects of kinematic and magnetic boundary conditions on the dynamics of convection-driven plane layer dynamos

Rapidly rotating convection-driven dynamos are investigated under different kinematic and magnetic boundary conditions using direct numerical simulations. At a fixed rotation rate, represented by the Ekman number$Ek=5\times 10^{-7}$, the thermal forcing is varied from$2$to$20$times its value at the onset of convection ($\mathcal {R}=Ra/Ra_c=2\unicode{x2013}20$, where$Ra$is the Rayleigh number), keeping the fluid properties constant ($Pr=Pr_m=1$, where$Pr$and$Pr_m$are the thermal and magnetic Prandtl numbers). The statistical behaviour of the dynamos, including the force balance, energetics, and heat transport, depends on the boundary conditions that dictate both the boundary layer and the interior dynamics. At a fixed thermal forcing ($\mathcal {R}=3$), the structure and strength of the magnetic field produced by the dynamos, especially near the walls, depend on both velocity and magnetic boundary conditions. Though the leading-order force balance in the bulk remains geostrophic, the Lorentz force becomes comparable to the Coriolis force inside the thermal boundary layer with no-slip, perfectly conducting conditions. In this case, a term signifying the work done by the Lorentz force in the turbulent kinetic energy (TKE) equation is found to have some components that extract energy from the velocity field to produce the magnetic field, while some other components extract energy from the magnetic field to produce TKE. However, with no-slip, pseudo-vacuum conditions, all the components of the work done by the Lorentz force perform unidirectional energy transfer to produce magnetic energy from the kinetic energy of the fluid to sustain dynamo action. We find heat transfer enhancement in the rotating dynamo convection, as compared with non-magnetic rotating convection, with the peak enhancement lying in the range$\mathcal {R}=3\unicode{x2013}4$. For free-slip conditions, in the absence of an Ekman layer, the dynamo action may alter the heat transport significantly by suppressing the formation of large-scale vortices. However, the highest heat transfer enhancement is found at$\mathcal {R}=3$with no-slip, perfectly conducting walls, which can be attributed to a local magnetorelaxation of the rotational constraint due to enhanced Lorentz force inside the thermal boundary layer.

Behavior of hydrodynamic and magnetohydrodynamic turbulence in a rotating sphere with precession and dynamo action

The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, both in the incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and its dependence with both rotating and precession frequency was analyzed. For the MHD case no self-sustaining dynamos were found for the prograde precession case, whereas on the other hand a critical retrograde precession frequency was found above which dynamo action is self-sustained. It was also found that these correspond to small-scale dynamos with a developed turbulent regime. Furthermore, it is observed the presence of reversals of the magnetic dipole moment with greater waiting times between reversals for smaller precession frequencies.

The role of slow magnetostrophic waves in the formation of the axial dipole in planetary dynamos

The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast inertial waves slightly modified by the magnetic field and buoyancy are dominant under weak fields. However, the dominance of the slow waves is evident for strong fields satisfying ∣ωM/ωC∣∼ 0.1, where ωM and ωC are the frequencies of the Alfvén and inertial waves respectively. A MAC wave window of azimuthal wavenumbers is identified in which helicity generation by the slow waves strongly correlates with dipole generation. Analysis of the magnetic induction equation suggests a poloidal–poloidal field conversion in the formation of the dipole. Finally, the attenuation of slow waves may result in polarity reversals in a strongly driven Earth's core.

Influence of Centrifugal Buoyancy in Thermal Convection within a Rotating Spherical Shell

The dynamo action, which is of importance in the study of the geomagnetism mechanism, is considered to be caused by the convection structure formed inside a rotating spherical shell. This convection structure elongated in the rotation axis is generated by the action of both heat and rotation on the fluid inside a spherical shell. In this study, we analyzed thermal convection in such a rotating spherical shell and attempted to understand the phenomenon of this convective structure. It is known that each value of the Prandtl number, the Ekman number and the Rayleigh number and their balance are important for the generation of such convective structure. We fixed these three parameters and considered the effect of centrifugal buoyancy as the Froude number additionally. To investigate how the effects of centrifugal buoyancy affect the convective structure, we carried out both three-dimensional numerical simulations and linear stability analyses. In particular, we focused on the transition from axisymmetric flow to non-axisymmetric flow having wavenumbers in the toroidal direction and investigated both growth rate and phase velocity of the disturbance. It was found that axisymmetric flow tends to be maintained as the effect of centrifugal buoyancy increases.

On large-scale dynamos with stable stratification and the application to stellar radiative zones

Abstract Our understanding of large-scale magnetic fields in stellar radiative zones remains fragmented and incomplete. Such magnetic fields, which must be produced by some form of dynamo mechanism, are thought to dominate angular-momentum transport, making them crucial to stellar evolution. A major difficulty is the effect of stable stratification, which generally suppresses dynamo action. We explore the effects of stable stratification on mean-field dynamo theory with a particular focus on a non-helical large-scale dynamo (LSD) mechanism known as the magnetic shear-current effect. We find that the mechanism is robust to increasing stable stratification as long as the original requirements for its operation are met: a source of shear and non-helical magnetic fluctuations (e.g. from a small-scale dynamo). Both are plausibly sourced in the presence of differential rotation. Our idealized direct numerical simulations, supported by mean-field theory, demonstrate the generation of near equipartition large-scale toroidal fields. Additionally, a scan over magnetic Reynolds number shows no change in the growth or saturation of the LSD, providing good numerical evidence of a dynamo mechanism resilient to catastrophic quenching, which has been an issue for helical dynamos. These properties – the absence of catastrophic quenching and robustness to stable stratification – make the mechanism a plausible candidate for generating in situ large-scale magnetic fields in stellar radiative zones.

Starspots, chromospheric emission lines, and flares of zero-age main-sequence stars

Abstract Zero-age main-sequence (ZAMS) stars are considered to have enormous starspots and show strong chromospheric emission lines because of their strong surface magnetic field. We discuss the dynamo activities of ZAMS stars with respect to their periodic light variation caused by a starspot and with respect to the strength of the chromospheric emission lines. The light curves of 33 ZAMS stars in IC 2391 and IC 2602 were obtained from TESS (Transiting Exoplanet Survey Satellite) photometric data. The light curves can be grouped into the following four categories: single frequency, possible shape changer, beater, and complex variability. The amplitudes of the light curves are 0.001–0.145 mag, similar to those of ZAMS stars in Pleiades. The starspot coverages are $0.1\%$–$21\%$. We found that the light variations and Ca ii emission line strength of ZAMS stars in IC 2391, IC 2602, and the Pleiades cluster are as large as those of the most active superflare stars and two orders larger than those of the Sun, and are located on the extensions of the superflare stars. These results suggest that superflare stars link the properties of the Sun to those of the ZAMS stars of ages between 30 and 120 Myr. ZAMS stars with a single frequency or possible shape change in the light curve tend to have both large light variation, indicating large spot coverage, and saturated Ca ii emission line strength. ZAMS stars with beat or complex variability have small spot coverage and a faint Ca ii emission line. We also detected 21 flares in the TESS light curves of 12 ZAMS stars in IC 2391 and IC 2602, where most of these stars have saturated chromospheric Ca ii emission lines. The energies of the flares are estimated to be ∼1033–1035 erg, which is comparable with the energy of a superflare.

Energy Conversion and Partition in Plasma Turbulence Driven by Magnetotail Reconnection

A long-outstanding issue in fundamental plasma physics is how magnetic energy is finally dissipated in kinetic scale in the turbulent plasma. Based on the Magnetospheric Multiscale mission data in the plasma turbulence driven by magnetotail reconnection, we establish the quantitative relation between energy conversion ( J • E ; J is current density and E is electric field) and current density (J). The results show that the magnetic energy is primarily released in the perpendicular directions (up to 90%), in the region with current density less than 2.3 J rms, where J rms is the rms value of the total current density ∣ J ∣. In the relatively weak current region (<1.0 J rms), the ions get most of the released energy while the largely negative energy conversion rate of the electrons means a dynamo action. In the strong currents (>1.0 J rms), the ion energization was negligible and the electrons are significantly energized. Moreover, a linearly increasing relationship was established between ∣ J • E ∣ and . The observations indicate that ions overall dominate energy conversion in turbulence, but the electron dynamics are crucial for energy conversion in intense currents and the turbulence evolution.

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

ABSTRACT Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.