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We investigate the zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. We obtain the uniform regularity of solutions with respect to the kinematic viscosity coefficient and the magnetic diffusivity coefficient. These solutions are uniformly bounded in a conormal Sobolev space and $W^{1,\infty}(\Omega)$ which allow us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence., Comment: 40 pages

Magnetic fields play such essential roles in star formation as transporting angular momentum and driving outflows from a star-forming cloud, thereby controlling the formation efficiency of a circumstellar disc and also multiple stellar systems. The coupling of magnetic fields to the gas depends on its ionization degree. We calculate the temperature evolution and ionization degree of a cloud for various metallicities of Z/Zsun = 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, and 1. We update the chemical network by reversing all the gas-phase processes and by considering grain-surface chemistry, including grain evaporation, thermal ionization of alkali metals, and thermionic emission from grains. The ionization degree at nH ~ 1e15-1e19 /cm^3 becomes up to eight orders of magnitude higher than that obtained in the previous model, owing to the thermionic emission and thermal ionization of K and Na, which have been neglected so far. Although magnetic fields dissipate owing to ambipolar diffusion or Ohmic loss at nH < 1e15 /cm^3, the fields recover strong coupling to the gas at nH ~ 1e15 /cm^3, which is lower by a few orders of magnitude compared to the previous work. We develop a reduced chemical network by choosing processes relevant to major coolants and charged species. The reduced network consists of 104 (161) reactions among 28 (38) species in the absence (presence, respectively) of ionization sources. The reduced model includes H2 and HD formation on grain surfaces as well as the depletion of O, C, OH, CO, and H2O on grain surfaces., 23 pages, 12 figures, 3 tables, accepted for publication in MNRAS

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

A pendulum with an attached permanent magnet swinging in the vicinity of a conductor is a typical experiment for the demonstration of electromagnetic braking and Lenz’ law of induction. When the conductor itself moves, it can transfer energy to the pendulum. An exact analytical model of such an electromagnetic interaction is possible for a flat conducting plate. The eddy currents induced in the plate by a moving magnetic dipole and the resulting force and torque are known analytically in the quasistatic limit, i.e., when the magnetic diffusivity is sufficiently high to ensure an equilibrium of magnetic field advection and diffusion. This allows us to study a simple pendulum with a magnetic dipole moment in the presence of a horizontal plate oscillating in vertical direction. Equilibrium of the pendulum in the vertical position can be realized in three cases considered, i.e., when the magnetic moment is parallel to the rotation axis, or otherwise, its projection onto the plane of motion is either horizontal or vertical. The stability problem is described by a differential equation of Mathieu type with a damping term. Instability is only possible when the vibration amplitude and the distance between plate and magnet satisfy certain constraints related to the simultaneous excitation and damping effects of the plate. The nonlinear motion is studied numerically for the case when the magnetic moment and rotation axis are parallel. Chaotic behavior is found when the eigenfrequency is sufficiently small compared to the excitation frequency. The plate oscillation typically has a stabilizing effect on the inverted pendulum.

In this paper we give upper bounds on the number of determining Fourier modes, determining nodes, and determining volume elements for a 3D MHD-$ \alpha $ model. Here the bounds are estimated explicitly in terms of flow parameters, such as viscosity, magnetic diffusivity, smoothing length, forcing and domain size.

This paper is concerned with the analysis on a numerical recovery of the magnetic diffusivity in a three dimensional (3D) spherical dynamo equation. We shall transform the ill-posed problem into an output least squares nonlinear minimization by an appropriately selected Tikhonov regularization, whose regularizing effects and mathematical properties are justified. The nonlinear optimization problem is approximated by a fully discrete finite element method and its convergence shall be rigorously established.

The magnetohydrodynamic (MHD) turbulence appears in engineering laboratory flows and is a common phenomenon in natural systems, e.g. stellar and planetary interiors and atmospheres and the interstellar medium. The applications in engineering are particularly interesting due to the recent advancement of tokamak devices, reaching very high plasma temperatures, thus giving hope for the production of thermonuclear fusion power. In the case of astrophysical applications, perhaps the main feature of the MHD turbulence is its ability to generate and sustain large-scale and small-scale magnetic fields. However, a crucial effect of the MHD turbulence is also the enhancement of large-scale diffusion via interactions of small-scale pulsations, i.e. the generation of the so-called turbulent viscosity and turbulent magnetic diffusivity, which typically exceed by orders of magnitude their molecular counterparts. The enhanced resistivity plays an important role in the turbulent dynamo process. Estimates of the turbulent electromotive force (EMF), including the so-called $\alpha$ -effect responsible for amplification of the magnetic energy and the turbulent magnetic diffusion are desired. Here, we apply the renormalization group technique to extract the final expression for the turbulent EMF from the fully nonlinear dynamical equations (Navier–Stokes, induction equation). The simplified renormalized set of dynamical equations, including the equations for the means and fluctuations, is derived and the effective turbulent coefficients such as the viscosity, resistivity, the $\alpha$ -coefficient and the Lorentz-force coefficients are explicitly calculated. The results are also used to demonstrate the influence of magnetic fields on energy and helicity spectra of strongly turbulent flows, in particular the magnetic energy spectrum.

This paper verifies the incompressible limit of the non-isentropic compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a three-dimensional bounded C 4 -domain. The uniform estimates in both the Mach number ϵ and the Peclet number κ for the local strong solutions, which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary, are established in a short time interval independent of ϵ and κ ( κ ≤ O ( ϵ β ) , 0 β ≤ 4 3 ), provided that the “well-prepared” initial condition for the solution and the non-slip boundary condition for the velocity are imposed.

In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27] , we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.

Superconductors are well known for their ability to screen out magnetic fields. In type-II superconductors, as the magnetic field pressure is progressively increased, magnetic flux accumulates at the periphery of the sample, very much like charges accumulate in a capacitor when voltage is increased. As for capacitors, exceeding certain threshold field causes the blocked magnetic flux to abruptly penetrate into the sample. This phenomenon, triggered by a thermomagnetic instability, is somewhat analogous to the dielectric breakdown of the capacitor and leaves behind a similar Lichtenberg imprinting. Even though electrical breakdown threshold has been extensively studied in dielectrics, little information is known about the statistical distribution of the thermomagnetic breakdown in superconductors. In this work, we address this problem by performing magneto-optical imaging experiments on a Nb film where nanometric heating elements are used to rapidly erase the magnetic history of the sample. We demonstrate that the size and shape distributions of avalanches permits to unambiguously identify the transition between two regimes where either thermal diffusivity or magnetic diffusivity dominates. Clear criteria for discriminating athermal dynamic avalanches from thermally driven avalanches are introduced. This allows us to provide the first precise determination of the threshold field of the thermomagnetic breakdown and unveil the details of the transition from finger-like magnetic burst to dendritic branching morphology. These findings open a new avenue in the interdisciplinary exploration of catastrophic avalanches through non destructive repeatable experiments.

Turbulence in the Earth's outer core not only increases all diffusive coefficients, but it can lead to their anisotropic properties. Therefore, the model of rotating magnetoconvection in horizontal plane layer rotating about vertical axis and permeated by homogeneous horizontal magnetic field, influenced by anisotropic diffusivities, viscosity and thermal diffusivity, is advanced by considering the magnetic diffusivity as anisotropic too. The case of full anisotropy, i.e. all coefficients anisotropic, is compared with both the case possessing isotropic diffusion coefficients and the case of partial anisotropy, i.e. mixed case with isotropic and anisotropic diffusive coefficients (viscosity and thermal diffusivity anisotropic and magnetic diffusivity isotropic). The existence and preference of instabilities is sensitive to all non-dimensional parameters, as well as on anisotropic parameter, the ratio of horizontal and vertical diffusivities. Two types of anisotropy, BM (introduced by Braginsky and ...

The zeroth law is one of the oldest conjecture in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a new dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscous dissipation rate in the limit of small viscosity, proving the conjecture of the zeroth law of turbulence and the existence of an anomalous dissipation. As an illustration, we evaluate the shock heating produced by discontinuities detected by Voyager in the solar wind around 5 AU. We deduce a heating rate of $\sim 10^{-18}$J m$^{-3}$ s$^{-1}$, which is significantly higher than the value obtained from the turbulent fluctuations. This suggests that collisionless shocks can be a dominant source of heating in the outer solar wind., 8 pages, 4 figures

Les Jupiters chaudes sont des exoplanètes possédant des caractéristiques uniques. En raison de leur proximité avec leur étoile hôte elles présentent une non-symétrie remarquable. Cette proximité provoquant la rotation synchrone force un côté de la planète à toujours faire face à l'étoile et l'autre à être plongé dans une nuit perpétuelle. Cette géométrie donne lieu à une différence d'allant de 200 K jusqu'à 2000 K entre les deux côtés de la planète, engendrant des écoulements zonaux pouvant atteindre des vitesses de l'ordre du km/s afin de redistribuer la chaleur. Le point chaud, le point le plus chaud de la planète, est un témoin de ces vents intenses. Les observations et les simulations hydrodynamiques montrent que les écoulements zonaux se font d'ouest en est. Cependant, les observations de deux planètes ne se conforment pas aux prédictions. En effet, CoRoT-2 b et HAT-P-7 b montrent des points chauds à l'ouest. L'explication la plus répandue est que le champ magnétique de ces planètes, en interaction avec leur atmosphère partiellement ionisée, peut renverser la direction des écoulements zonaux, si ce champ est assez puissant. Une diffusivité magnétique variable dans l'espace peut générer localement des champs magnétiques lorsque son gradient s'aligne correctement avec le courant électrique. Nous présentons ici un modèle magnétohydrodynamique en une dimension possédant une diffusivité magnétique dépendante de la température dans le plan équatorial dans le contexte de Jupiters chaudes. Les résultats des simulations présentent des oscillations torsionnelles de type alfvéniques reflétant les effets non linéaires dus au couplage des équations aux dérivées partielles de la magnétohydrodynamique et de la température avec la diffusivité magnétique dépendante de la température. Nous explorons un espace des paramètres afin d'établir l'influence de ceux-ci sur les oscillations. Nous avons aussi développé un modèle local afin de dériver des équations analytiques nous permettant de mieux comprendre les résultats observés en plus de comparer les résultats du modèle en une dimension avec ceux du modèle local. Nous finissons par établir que les oscillations générées par notre modèle en une dimension possèdent des périodes équivalentes allant de 225 à 473 jours et des déplacements longitudinaux équivalant à quelques degrés jusqu'à environ 40° pour une planète de la taille de Jupiter. Ces intervalles de périodes et de déplacements sont encourageants, puisque cela signifie que les oscillations pourraient être observées., Hot Jupiters are exoplanets with unique features. Due to their proximity to their host stars, they show remarkable non-symmetry. This proximity with the star causes tidal locking, meaning one side of the planet is always exposed to intense radiation from its host and the other side is immersed in a perpetual night. This geometry means there is a difference of temperature ranging from 200 K up to 2000 K between the day and night side. This gradient in temperature induces zonal winds that can reach the order of 1 km/s to redistribute heat to the night side. The hot spot is the hottest spot of the planet and is a telltale of these strong winds. Observations and hydrodynamic numerical simulations show that zonal winds on these planets go eastward. However, two recent observations are showing westward winds. These planets are CoRoT-2 b and HAT-P-7 b. The most common explanation to this contradiction is that the magnetic field, which is interacting with the partially ionized atmosphere, can reverse these winds. It was previously shown that a magnetic diffusivity varying in space can locally generate magnetic fields when its gradient aligns correctly with the electric current density. We present here a one-dimensional magnetohydrodynamic model with a temperature-dependent magnetic diffusivity in the equatorial plane in the context of hot Jupiters. The simulations develop growing torsional alfvénic oscillations due to the non-linear coupling of the magnetohydrodynamics and the temperature partial differential equations and the temperature-dependent magnetic diffusivity. We explore the parameter space and study their influence on the oscillations. We have also developed a local model in order to derive analytical equations characterizing these waves and compare its results with the results of the one-dimensional model. We end by calculating the corresponding periods and longitudinal displacement of the one-dimension model oscillations for a Jupiter-sized planet. The periods correspond to an interval from 225 to 473 days and the displacements range from a few degrees up to 40°. This means that the oscillations could be observed with a few orbits.

We present simulations of thin accretion disks around black holes investigating a mean-field disk dynamo in our resistive GRMHD code (Vourellis et al. 2019) that is able to produce a large scale magnetic flux. We consider a weak seed field in an initially thin disk, a background (turbulent) magnetic diffusivity and the dynamo action. A standard quenching mechanism is applied to mitigate the otherwise exponential increase of the magnetic field. Comparison simulations of an initial Fishbone-Moncrief torus suggest that reconnection may provide another quenching mechanism. The dynamo-generated magnetic flux expands from the disk interior into the disk corona, becomes advected by disk accretion, and fills the axial region of the domain. The dynamo leads to an initially rapid increase in magnetic energy and flux, while for later evolutionary stages the growth stabilizes. Accretion towards the black hole depends strongly on the magnetic field structure that develops. The radial field component supports extraction of angular momentum and thus accretion. It also sets the conditions for launching a disk wind, initially from inner disk area. When a strong field has engulfed the disk, strong winds are launched that are predominantly driven by the pressure gradient of the toroidal field. For rotating black holes we identify a Poynting flux-dominated jet, driven by the Blandford-Znajek mechanism. This axial Poynting flux is advected from the disk and therefore accumulates at the expense of the flux carried by the disk wind, that is itself regenerated by the disk dynamo., Comment: 26 pages, 16 Figures, accepted for publication in ApJ

Stars and planets possess magnetic fields that permanently change. Earth, for instance, mysteriously interchanges its north and south magnetic poles, so that the time pattern of the switches forms a Cantor-type set on the time scale (see [AnS]). The mechanism of generation of magnetic fields in astrophysical objects (or in electrically conducting fluids) constitutes the subject of dynamo theory. Kinematic dynamo theory studies what kind of fluid motion can induce exponential growth of a magnetic field for small magnetic diffusivity. Avoiding analytical and numerical results (though crucial for this field), we address below the topological side of the theory.

Context. Ultraviolet (UV) bursts and Ellerman bombs (EBs) are transient brightenings observed in the low solar atmospheres of emerging flux regions. Magnetic reconnection is believed to be the main mechanism leading to formation of the two activities, which are usually formed far apart from each other. However, observations also led to the discovery of co-spatial and co-temporal EBs and UV bursts, and their formation mechanisms are still not clear. The multi-thermal components in these events, which span a large temperature range, challenge our understanding of magnetic reconnection and heating mechanisms in the partially ionized lower solar atmosphere. Aims. We studied magnetic reconnection between the emerging magnetic flux and back ground magnetic fields in the partially ionized and highly stratificated low solar atmosphere. We aim to explain the multi-thermal characteristics of UV bursts, and to find out whether EBs and UV bursts can be generated in the same reconnection process and how they are related with each other. We also aim to unearth the important small-scale physics in these events. Methods. We used the single-fluid magnetohydrodynamic (MHD) code NIRVANA to perform simulations. The background magnetic fields and emerging fields at the solar surface are reasonably strong. The initial plasma parameters are based on the C7 atmosphere model. We simulated cases with different resolutions, and included the effects of ambipolar diffusion, radiative cooling, and heat conduction. We analyzed the current density, plasma density, temperature, and velocity distributions in the main current sheet region, and synthesized the Si IV emission spectrum. Results. After the current sheet with dense photosphere plasma emerges and reaches 0.5 Mm above the solar surface, plasmoid instability appears. The plasmoids collide and coalesce with each other, which causes the plasmas with different densities and temperatures to be mixed up in the turbulent reconnection region. Therefore, the hot plasmas corresponding to the UV emissions and colder plasmas corresponding to the emissions from other wavelengths can move together and occur at about the same height. In the meantime, the hot turbulent structures concentrate above 0.4 Mm, whereas the cool plasmas extend to much lower heights to the bottom of the current sheet. These phenomena are consistent with published observations in which UV bursts have a tendency to be located at greater heights close to corresponding EBs and all the EBs have partial overlap with corresponding UV bursts in space. The synthesized Si IV line profiles are similar to that observed in UV bursts; the enhanced wing of the line profiles can extend to about 100 km s−1. The differences are significant among the numerical results with different resolutions, indicating that the realistic magnetic diffusivity is crucial to revealing the fine structures and realistic plasmas heating in these reconnection events. Our results also show that the reconnection heating contributed by ambipolar diffusion in the low chromosphere around the temperature minimum region is not efficient.

The observations and simulations have revealed that large-scale magnetic field and outflows can exist in the inner regions of an advection-dominated accretion disc where the resistive diffusion may also be important. In the present paper, the roles of large-scale magnetic field and outflows in the structure of resistive advection-dominated accretion discs are explored by assuming that the accretion flow is radially self-similar. In the non-ideal magnetohydrodynamic (MHD) approximation, the results show that the angular velocity is always sub-Keplerian when both the outflow and the large-scale magnetic field are taken into account. A stronger toroidal field component leads to faster rotation, while the disc rotates with faster rate if the vertical field component is weaker. The increase of magnetic diffusivity causes the infall velocity to be close to Keplerian velocity. Although the previous studies in the ideal MHD approximation have shown that the disc temperature decreases due to the vertical field component, we find that the effect of vertical field component on the temperature of a resistive disc depends on the magnetic diffusivity. When the magnetic diffusivity is high, the more efficient mechanism for decreasing the disc temperature can be the outflows, and not the large-scale magnetic field. In such a limit of the magnetic diffusivity, the components of the large-scale magnetic field enhance the gas temperature. The increase of temperature can lead to heating and acceleration of the electrons and help us to explain the origin of phenomena such as the flares in Sgr A*. On the other hand, the infall velocity in such a limit rises as the temperature increases, and therefore the surface density falls to too low values. Any change in the density profile can alter the structure and the emitted spectrum of disc., 13 pages, 4 figures

We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lüst differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lüst equation and derive a comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow.

In this paper, we study the three-dimensional incompressible magnetohydrodynamic equations in a smooth bounded domains, in which the viscosity of the fluid and the magnetic diffusivity are concerned with density. The existence of global strong solutions is established in vacuum cases, provided the assumption that (||∇μ(ρ0)||Lp + ||∇ν(ρ0)||Lq + ||b0||L3 + ||ρ0||L∞) (p, q > 3) is small enough, there is not any smallness condition on the velocity.

The natural simplifying assumptions often put forward in the theoretical investigations of the magnetohydrodynamic turbulence are that the turbulent flow is statistically isotropic, homogeneous and stationary. Of course, the natural turbulence in the planetary interiors, such as the liquid core of the Earth is neither, which has important consequences for the dynamics of the planetary magnetic fields generated via the hydromagnetic dynamo mechanism operating in the interiors of the planets. Here we concentrate on the relaxation of the assumption of statistical stationarity of the turbulent flow and study the effect of turbulent wave fields in the Earth’s core, which induces non-stationarity, on the turbulent resistivity in the non-reflectionally symmetric flow and the geodynamo effect. It is shown that the electromotive force, including the so-called α-effect and the turbulent magnetic diffusivity η¯, induced by non-stationary turbulence, evolves slowly in time. However, the turbulent α¯ coefficient, responsible for the dynamo action and η¯ evolve differently in time, thus creating periods of enhanced and suppressed turbulent diffusion and dynamo action somewhat independently. In particular, periods of enhanced α¯ may coincide with periods of suppressed diffusion, leading to a stable and strong field period. On the other hand, it is shown that when enhanced diffusion occurs simultaneously with suppression of the α-effect, this leads to a sharp drop in the intensity of the large-scale field, corresponding to a geomagnetic excursion.

This paper considers the global regularity to the 3D generalized MHD equations with the fractional dissipation and magnetic diffusion ( − Δ ) α for 0 α 5 ∕ 4 . Let μ , ν , u and b denote the viscosity coefficient, magnetic diffusivity, velocity field and magnetic field, respectively. It is shown that ‖ ( u , b ) ‖ H s ( s > 5 ∕ 2 − α ) is globally bounded as long as | μ − ν | ( μ + ν ) − 1 and H 5 2 − 2 α -norm on ( u 0 − b 0 ) or ( u 0 + b 0 ) sufficiently small, which generalizes the previous result about large solutions in He et al. (2014).

The quantum hydrodynamic model is used to study the linear and nonlinear properties of small amplitude magnetosonic shock waves in dissipative plasma with degenerate inertialess spin-up and spin-down electrons and inertial classical ions. Spin effects are considered via spin pressure and macroscopic spin magnetization current. A linear dispersion relation is derived analytically and plotted numerically for different plasma parameters such as spin density, polarization ratio, plasma beta, quantum diffraction, spin magnetization energy, and magnetic diffusivity. Employing the standard reductive perturbation technique, a Korteweg-de Vries-Burgers-type equation is derived for small amplitude waves and studied numerically. We have observed that an oscillatory and monotonic shock waves are generated depending upon the plasma configurations. The phase portraits of both oscillatory and monotonic shock waves are also presented. Interestingly, different plasma parameters are found to play a significant role in the transition of oscillatory to monotonic shock waves or vice versa. Most importantly it is found that, the magnetosonic excitations obtained with spin-up and spin-down electrons are significantly different from the usual electron ion quantum plasma. The work presented is related to magnetosonic waves in dense astrophysical environments such as a pulsar magnetosphere and neutron stars.

The diurnal tidal forces can excite a normal mode of the Earth's core, the free inner core nutation (FICN), which is characterized by a tilt of the rotation axis of the inner core with respect to the rotation axis of the outer core. The differential rotation between the inner core and the outer core induces fluid motions in the outer core and gives rise to Ohmic dissipation in the presence of the Earth's internal magnetic field. Nutation measurements can reflect such dissipation if it is sufficiently strong and thus can provide insights into the properties and dynamics of the Earth's core. In this study we perform a set of numerical calculations of the linear perturbations in the outer core induced by the FICN at very low Ekman numbers (as small as $10^{-11}$). Our numerical results show that the back-reaction of the magnetic field notably alters the structure and length scale of the perturbations induced by the FICN, and thus influences the Ohmic dissipation resulting from the perturbations. When the Ekman number is sufficiently small, Ohmic dissipation tends to be insensitive to the fluid viscosity and to the magnetic diffusivity, which allows us to estimate the Ohmic dissipation associated with the FICN without relying on an extrapolation. In contrast to the results of Buffett (2010b), the estimated Ohmic dissipation based on our numerical calculations is too weak to account for the observed damping of the FICN mode. This also implies that nutation measurements cannot provide effective constraints on the strength of the magnetic field inside the Earth's outer core., Accepted for publication in EPSL

The choice of free parameters in surface flux transport (SFT) models describing the evolution of the large-scale poloidal magnetic field of the Sun is critical for the correct reproduction of the polar magnetic flux built up during a solar cycle, which in turn is known to be a good predictor of the amplitude of the upcoming cycle. For an informed choice of parameters it is important to understand the effect and interplay of the various parameters and to optimize the models for the polar magnetic field. Here we present the results of a large-scale systematic study of the parameter space in an SFT model where the source term representing the net effect of tilted flux emergence was chosen to represent a typical, average solar cycle as described by observations. Comparing the results with observational constraints on the spatiotemporal variation of the polar magnetic field, as seen in magnetograms for the last four solar cycles, we mark allowed and excluded regions in the 3D parameter space defined by the flow amplitude u0, the magnetic diffusivity eta and the decay time scale tau, for three different assumed meridional flow profiles. Without a significant decay term in the SFT equation (i.e., for tau >10 yr) the global dipole moment reverses too late in the cycle for all flow profiles and parameters, providing independent supporting evidence for the need of a decay term, even in the case of identical cycles. An allowed domain is found to exist for tau values in the 5-10 yr range for all flow profiles considered. Generally higher values of eta (500-800 km^2/s) are preferred though some solutions with lower eta are still allowed., 11 pages, 10 figures; Astronomy and Astrophysics, accepted

This research has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214). Aims . This paper presents 2.5D numerical experiments of Alfvén wave phase mixing and aims to assess the effects of nonlinearities on the wave behaviour and dissipation. In addition, this paper aims to quantify how effective the model presented here is at providing energy to the coronal volume. Methods . The model is presented and explored through the use of several numerical experiments which were carried outusing the Lare2D code (Arber et al. 2001). The experiments study footpoint driven Alfvén waves in the neighbourhood of a two-dimensional x-type null point, with initially uniform density and plasma pressure. A continuous sinusoidal driver with a constant frequency is used. Each experiment uses different driver amplitudes to compare weakly nonlinear experiments with linear experiments. Results . It was found that the wave trains phase-mix due to variations in the length of each field line as well asvariations in the field strength. The nonlinearities reduce the amount of energy entering the domain, as they reduce the effectiveness of the driver, but they have relatively little effect on the damping rate (for the range of amplitudes studied). The nonlinearities produce density structures which change the natural frequencies of the field lines and hence cause the resonant locations to move. The shifting of the resonant location causes the Poynting flux associated with the driver to decrease. Reducing the magnetic diffusivity increased the energy build-up on the resonant field lines, however, it has little effect on the total amount of energy entering the system. From an order of magnitude estimate, it was shown that the Poynting flux in our experiments was comparable to the energy requirements of the Quiet Sun corona, although a (possibly unphysically) large amount of magnetic diffusion was used, and it remains unclear if the model is able to provide enough energy under actual coronal conditions. Postprint

Conservation of magnetic helicity by the Hall drift does not prevent Hall instability of helical fields. This conclusion follows from stability analysis of a force-free spatially-periodic Hall equilibrium. The growth rates of the instability scale as $\sigma \propto B^{3/4}\eta^{1/4}$ with the field strength $B$ and magnetic diffusivity $\eta$ and can be large compared to the rate of resistive decay of the background field. The instability deviates the magnetic field from the force-free configuration. The unstable eigenmodes include a fine spatial structure which evolves into current sheets at the nonlinear stage of the instability. The instability catalyses the resistive release of magnetic energy. The energy is released in a sequence of spikes, every spike emits several percent of the total energy. A numerically defined scaling for the energy released in a single spike permits an extrapolation to astrophysically relevant values of the Hall number. The instability can be relevant to magnetic energy release in a neutron star crust and, possibly, in stellar coronae., Comment: 9 two-column pages, 8 figures, submitted to AN

A dynamo model is presented, based on a previously introduced kinematic model, in which the effect of the magnetic field on the mass flow through the Lorentz force is included. Given the base mass flow corresponding to the case with no magnetic field, and assuming that the modification of this flow through the Lorentz force can be treated as a perturbation, a complete model of the large-scale magnetic field dynamics can be obtained. The input needed consists of the large-scale meridional and zonal flows, the small-scale magnetic diffusivity, and a constant parameter entering the expression of the $\alpha $ -effect. When applied to a Sun-like star, the model shows realistic dynamics of the magnetic field, including cycle duration, consistent field amplitudes with the correct parity, progression of the zonal magnetic field toward the equator, and motion toward the poles of the radial field at high latitudes. In addition, the radial and zonal components show a correct phase relation, and at the surface level, the magnetic helicity is predominantly negative in the northern hemisphere and positive in the southern hemisphere.

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time-dependent. The growing mean field can be modeled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (2015, J. Fluid Mech. 783, 23), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos., Comment: 23 pages, 15 figures, 2 tables, submitted to J. Plasma Phys

Magnetic fields play such roles in star formation as the angular momentum transport in star-forming clouds, thereby controlling circumstellar disc formation and even binary star formation efficiency. The coupling between the magnetic field and gas is determined by the ionization degree in the gas. Here, we calculate the thermal and chemical evolution of the primordial gas by solving chemical reaction network where all the reactions are reversed. We find that at ~ 10^14-10^18 /cm^3, the ionization degree becomes 100-1000 times higher than the previous results due to the lithium ionization by thermal photons trapped in the cloud, which has been omitted so far. We construct the minimal chemical network which can reproduce correctly the ionization degree as well as the thermal evolution by extracting 36 reactions among 13 species. Using the obtained ionization degree, we evaluate the magnetic field diffusivity. We find that the field dissipation can be neglected for global fields coherent over > a tenth of the cloud size as long as the field is not so strong as to prohibit the collapse. With magnetic fields strong enough for ambipolar diffusion heating to be significant, the magnetic pressure effects to slow down the collapse and to reduce the compressional heating become more important, and the temperature actually becomes lower than in the no-field case., 17 pages, 13 figures, 2 tables, submitted to MNRAS

In this paper, we consider the initial-boundary value problem to the planar magnetohydrodynamic (MHD) equations with zero magnetic diffusivity. In the case when the coefficients of viscosity and heat conductivity are positive constants, we establish the global existence and uniqueness of strong solution by the a priori estimates. The results are obtained without any smallness restriction to the initial data and the initial density allows vacuum.

We first prove the uniqueness of weak solutions (ψ,A) to the 3-D Ginzburg–Landau model in superconductivity with zero magnetic diffusivity and the Coulomb gauge if (ψ,A)∈W:=(ψ,A)ψ∈L20,T;L∞∩L20,T;H1,A∈C[0,T];L3, which is a critical space for some positive constant T. We also prove the global existence of solutions when ψ0∈L∞∩W23,32 and A0∈L3. Copyright © 2016 John Wiley & Sons, Ltd.

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos et al. 2014. The turbulent electromotive force operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation's meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. 2011, we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed alpha-tensor shows good agreement with that obtained by Racine et al. 2011, who did not include derivatives of the mean-field in their fit, as well as with the alpha-tensor extracted by Augustson et al. 2015 from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor beta is positive definite and reaches values of 5.0x10^7 m2s-1 in the middle of the convecting fluid layers. The spatial variations of both alpha_phiphi and beta_phiphi component are well reproduced by expressions obtained under the SOCA, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. We find the magnetic quenching of the alpha-effect to be driven primarily by a reduction of the small-scale flow's kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the beta_phiphi component, but indicate a weaker quenching, by a factor of 1.36, than of the alpha effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle., Comment: Accepted in Advances in Space Research

We propose, analyze, and test a new MHD discretization which decouples the system into two Oseen problems at each timestep yet maintains unconditional stability with respect to the time step size, is optimally accurate in space, and behaves like second order in time in practice. The proposed method chooses a parameter $$\theta \in [0,1]$$źź[0,1], dependent on the viscosity $$\nu $$ź and magnetic diffusivity $$\nu _m$$źm, so that the explicit treatment of certain viscous terms does not cause instabilities, and gives temporal accuracy $$O(\Delta t^2 + (1-\theta )|\nu -\nu _m|\Delta t)$$O(Δt2+(1-ź)|ź-źm|Δt). In practice, $$\nu $$ź and $$\nu _m$$źm are small, and so the method behaves like second order. When $$\theta =1$$ź=1, the method reduces to a linearized BDF2 method, but it has been proven by Li and Trenchea that such a method is stable only in the uncommon case of $$\frac{1}{2}< \frac{\nu }{\nu _m} < 2$$12

By means of Fourier frequency localization and Bony’s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate \(\int_0^t {{{\left\| {{\nabla _u}} \right\|}_L}\infty ds} \) which is crucial to get the global existence for the general initial data.

Our main object is to establish a regularity criterion ∇B∈Lpp−10,T;ℳ.qpR2 with p≥q > 1 for the incompressible magnetohydrodynamics equations with zero magnetic diffusivity. Copyright © 2016 John Wiley & Sons, Ltd.

A theoretical and numerical study of convective heat transfer of two different types of immiscible fluids in a vertical channel in the presence of a magnetic field is presented in this paper. The study involves several applications in mechanical energy, blood and synovial fluid flow in human health, micropolar fluids contained suspended fine particles in complex rotating motion, complex microstructure under the influence of several physicochemical characteristics …. To achieve a good understanding of the complexity of this flow type a mathematical model was developed which took into account a magnetic diffusivity term in the energy balance equation and allows the appearance of some dimensionless parameters such as the material parameter (K), the Prandtl number (Pr), the mixed convection parameter (GR), the magnetic parameter (Ha) and the Eckert number (Ec). Therefore, the numerical results obtained from the model were used to assume an apparent effect of the magnetic field on linear and spin velocities within micropolar and viscous fluids. Hence these results are subject to a comparative discussion between the current studied model with a magnetic diffusivity term and other studied without a magnetic diffusivity term.