Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.

Universal dynamo paradigm for solar activity, Higgs fields and disasters

There is still a problem of a correct and accurate description of the dynamo and its uses in various fields of physics. To solve this problem, a special and universal representation of dynamo is proposed. The magnetic induction equation of dynamo is presented in the form of a Lienard relaxation oscillator with cubic nonlinear restoring force corresponding to the Mexican hat or champagne bottle potential which is used to determine the Higgs fields which are considered here in its general sense. Universal dynamo paradigm in field theory which can be used to describe disasters is proposed. Using solar activity as an example, it is shown how a dynamo induces a magnetic analogue of the Higgs fields with a broken symmetry of the magnetic field. Various dynamo modes are considered and different dynamo numbers are estimated. The dynamo effect can be used in field theory as an alternative to spontaneous symmetry breaking. Opportunities for the promotion of the new dynamo paradigm are discussed.

Inverse energy transfer in decaying, three dimensional, nonhelical magnetic turbulence due to magnetic reconnection

It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3-dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and the 3D cases, i.e., the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection timescale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse onto one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed.

Entangled dynamos and Joule heating in the Earth's ionosphere

The Earth's neutral atmosphere is the driver of the well-known solar quiet (Sq) and other magnetic variations observed for more than 100 years. Yet the understanding of how the neutral wind can accomplish a dynamo effect has been incomplete. A new viable model is presented where a dynamo effect is obtained only in the case of winds perpendicular to the magnetic field B that do not map along B. Winds where u×B is constant have no effect. We identify Sq as being driven by wind differences at magnetically conjugate points and not by a neutral wind per se. The view of two different but entangled dynamos is favoured, with some conceptual analogy to quantum mechanical states. Because of the large preponderance of the neutral gas mass over the ionized component in the Earth's ionosphere, the dominant effect of the plasma adjusting to the winds is Joule heating. The amount of global Joule heating power from Sq is estimated, with uncertainties, to be much lower than Joule heating from ionosphere–magnetosphere coupling at high latitudes in periods of strong geomagnetic activity. However, on average both contributions could be relatively comparable. The global contribution of heating by ionizing solar radiation in the same height range should be 2–3 orders of magnitude larger.

Dynamo theories

These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids and plasmas, blended with a review of current research in the field. The primary focus is on the physical and mathematical concepts underlying different (turbulent) branches of dynamo theory, with some astrophysical, geophysical and experimental contexts disseminated throughout the document. The text begins with an introduction to the rationale, observational and historical roots of the subject, and to the basic concepts of magnetohydrodynamics relevant to dynamo theory. The next two sections discuss the fundamental phenomenological and mathematical aspects of (linear and nonlinear) small- and large-scale magnetohydrodynamic (MHD) dynamos. These sections are complemented by an overview of a selection of current active research topics in the field, including the numerical modelling of the geo- and solar dynamos, shear dynamos driven by turbulence with zero net helicity and MHD-instability-driven dynamos such as the magnetorotational dynamo. The difficult problem of a unified, self-consistent statistical treatment of small- and large-scale dynamos at large magnetic Reynolds numbers is also discussed throughout the text. Finally, an excursion is made into the relatively new but increasingly popular realm of magnetic-field generation in weakly collisional plasmas. A short discussion of the outlook and challenges for the future of the field concludes the presentation.

Entangled Dynamos and Joule Heating in the Earth’s Ionosphere

The Earth's neutral atmosphere is the driver of the well-known Solar quiet (Sq) and other magnetic variations, observed since more than 100 years. Yet the understanding of how the neutral wind can accomplish a dynamo effect has been incomplete. A new viable model is presented, where a dynamo effect is obtained only in case of winds perpendicular to the magnetic field B that spatially vary along B. Uniform winds have no effect. We identify Sq as being driven by wind differences at magnetically conjugate points, and not by a neutral wind per se. The view of two different but entangled dynamos is favoured, with some conceptual analogy to quantum mechanical states. Because of the large preponderance of the neutral gas mass over the ionized component in the Earth's ionosphere the dominant effect of the plasma adjusting to the winds is Joule heating. The amount of global Joule heating power from Sq is estimated, with uncertainties, to be much lower than Joule heating from ionosphere-magnetosphere coupling at high latitudes in periods of strong geomagnetic activity. However, on average both contributions could be relatively evenly matched. The global contribution of heating by ionizing solar radiation in the same height range should be 2–3 orders of magnitude larger.

Latitudinal differential rotation in the solar analogues 16 Cygni A and B

Context. Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Aims. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. Methods. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. Results. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is 320 ± 269 nHz and 440−383+363 nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are 535 ± 75 nHz and 565−129+150 nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. Conclusions. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.