Electrodynamics of dual superconducting chiral medium

We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

Context. Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. Aims. The magnetic helicity spectrum provides important information about the α effect. Here we demonstrate a formalism in spherical geometry to infer magnetic helicity spectra directly from observations of the magnetic field, taking into account the sign change of magnetic helicity across the Sun’s equator. Methods. Using an angular correlation function of the magnetic field, we develop a method to infer spectra for magnetic energy and helicity. The retrieval of the latter relies on a fundamental definition of helicity in terms of linkage of magnetic flux. We apply the two-scale approach, previously used in Cartesian geometry, to spherical geometry for systems where a sign reversal of helicity is expected across the equator on both small and large scales. Results. We test the method by applying it to an analytical model of a fully helical field, and to magneto-hydrodynamic simulations of a turbulent dynamo. The helicity spectra computed from the vector potential available in the models are in excellent agreement with the spectra computed solely from the magnetic field using our method. In a next test, we use our method to obtain the helicity spectrum from a synoptic magnetic field map corresponding to a Carrington rotation. We observe clear signs of a bihelical spectrum of magnetic helicity, which is in complete accordance to the previously reported spectra in literature from the same map. Conclusions. Our formalism makes it possible to infer magnetic helicity in spherical geometry, without the necessity of computing the magnetic vector potential. It has many applications in solar and stellar observations, but can also be used to analyse global magnetoconvection models of stars and to compare them with observations.

Magnetic free energy powers solar flares and coronal mass ejections, and the buildup of magnetic helicity might play a role in the development of unstable structures that subsequently erupt. To better understand the roles of energy and helicity in large flares and eruptions, we have characterized the evolution of magnetic energy and helicity associated with 21 X-class flares from 2010 to 2017. Our sample includes both confined and eruptive events, with 6 and 15 in each category, respectively. Using the Helioseismic and Magnetic Imager vector magnetic field observations from several hours before to several hours after each event, we employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms to determine the photospheric fluxes of energy and helicity, and (b) nonlinear force-free field extrapolations to estimate the coronal content of energy and helicity in source-region fields. Using superposed epoch analysis, we find, on average, the following: (1) decreases in both magnetic energy and helicity, in both photospheric fluxes and coronal content, that persist for a few hours after eruptions, but no clear changes, notably in relative helicity, for confined events; (2) significant increases in the twist of photospheric fields in eruptive events, with twist uncertainties too large in confined events to constrain twist changes (and lower overall twist in confined events); and (3) on longer timescales (event time +12 hr), replenishment of free magnetic energy and helicity content to near preevent levels for eruptive events. For eruptive events, magnetic helicity and free energy in coronal models clearly decrease after flares, with the amounts of decrease proportional to each region’s pre-flare content.

Two spectral regimes of magnetic field amplification in magnetohydrodynamic (MHD) flows can be distinguished by the scale on which fields are amplified relative to the primary forcing scale of the turbulence. For field amplification at or below the forcing scale, the amplification can be called a “small-scale dynamo.” For amplification at and above the forcing scale the process can be called a “large-scale dynamo.” Non - local (in wave number) effects play a key role in both the growth of the small-scale field in non-helical turbulence and the growth of large and smallscale fields in helical turbulence. Mean field dynamo (MFD) theory represents a simple semi-analytic way to get a handle on large-scale field amplification in MHD turbulence. Helicity has long been known to be important for large scale, flux generating, externally forced MFDs. The extent to which such MFDs operate “slow” or “fast” (dependent or independent on magnetic Reynolds number) has been controversial, but there has been recent progress. Simulations of α2 dynamos in a periodic box dynamo and their quenching can now be largely understood within a simplified dynamical non-linear paradigm in which the MFD growth equation is supplemented by the total magnetic helicity evolution equation. For α2 dynamos, the large-scale field growth is directly related to the large-scale magnetic helicity growth. Magnetic helicity conservation then implies that growth of the large-scale magnetic helicity induces growth of small-scale magnetic (and current) helicity of the opposite sign, which eventually suppresses the α effect driving the MFD growth. Although the α2 MFD then becomes slow in the long time limit, substantial large-scale field growth proceeds in a kinematic, “fast” phase before non-linear asymptotic quenching of the “slow” phase applies. Ultimately, the MFD emerges as a process that transfers magnetic helicity between small and large scales. How these concepts apply to more general dynamos with shear, and open boundary dynamos is a topic of ongoing research. Some unresolved issues are identified. Overall, the following summarizes the most recent progress in mean-field dynamo theory: For a closed turbulent flow, the non-linear mean field dynamo, is first fast and kinematic, then slow and dynamic, and magnetic helicity transfer makes it so.KeywordsMagnetic EnergyMagnetic HelicityMagnetic Reynolds NumberDynamo TheoryForce ScaleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Context. For a better understanding of the dynamics of the solar corona, it is important to analyse the evolution of the helicity of the magnetic field. Since the helicity cannot be directly determined by observations, we have recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field, which however required the flux to be balanced separately on all the sides of the considered volume. Aims. We developed a scheme to obtain the vector potential in a volume without the above restriction at the boundary. We studied the dissipation and escape of relative magnetic helicity from an active region. Methods. In order to allow finite magnetic fluxes through the boundaries, a Coulomb gauge was constructed that allows for global magnetic flux balance. The property of sinusoidal function was used to obtain the vector potentials at the 12 edges of the considered rectangular volume extending above an active region. We tested and verified our method in a theoretical fore-free magnetic field model. Results. We applied the new method to the former calculation data and found a difference of less than 1.2%. We also applied our method to the magnetic field above active region NOAA 11429 obtained by a new photospheric-data-driven magnetohydrodynamics (MHD) model code GOEMHD3. We analysed the magnetic helicity evolution in the solar corona using our new method. We find that the normalized magnetic helicity (H∕Φ2) is equal to −0.038 when fast magnetic reconnection is triggered. This value is comparable to the previous value (−0.029) in the MHD simulations when magnetic reconnection happened and the observed normalized magnetic helicity (−0.036) from the eruption of newly emerging active regions. We find that only 8% of the accumulated magnetic helicity is dissipated after it is injected through the bottom boundary. This is in accordance with the Woltjer conjecture. Only 2% of the magnetic helicity injected from the bottom boundary escapes through the corona. This is consistent with the observation of magnetic clouds, which could take magnetic helicity into the interplanetary space. In the case considered here, several halo coronal mass ejections (CMEs) and two X-class solar flares originate from this active region.

view Abstract Citations (9) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Effect of a Vertical Magnetic Field on the Propagation of Gravity Waves Along the Plane Surface of a Semi-Infinite Viscous, Electrically Conducting Fluid. Roberts, P. H. ; Boardman, A. D. Abstract The basic equations and boundary conditions governing the effect of vertical magnetic and gravitational fields on small-amplitude perturbations of the free equilibrium surface of a viscous, electrically conducting fluid are presented Normal modes are examined. A dispersion relationship is derived which relates the complex "frequency" n of the normal mode to the Allven velocity, V, the viscosity, , the magnetic diffusivity, X, and the horizontal wave number, k. This dispersion relationship is solved in nine extreme cases In six of these, the magnetic field is too weak to modify substantially the familiar gravity- wave solution holding in the absence of a magnetic field. The influence of the field is so strong in the remaining three cases that they have no parallel in the zero-field case One of these holds for any k if the magnetic field is sufficiently strong In this case n = gV-l(X/ l/2 i e, the effect of the magnetic field is so great that the disturbance is attenuated aperiodically as the Aliven waves radiate energy away from the free surface. Another interesting feature demonstrated is the existence (if V is sufficiently large) of a band of wave numbers k for which no normal-mode solution exists It is nevertheless demonstrated that the associated initial-value problem can be solved for such values of k. In addition to the nine extreme cases mentioned above, three special cases are solved for all k for particular values of V, namely, p = p = 0, and X = 0. Publication: The Astrophysical Journal Pub Date: March 1962 DOI: 10.1086/147291 Bibcode: 1962ApJ...135..552R full text sources ADS |

We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30–60 Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.

Experimental and theoretical researches performed by the author (period: 1969-present) showed that magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and immediate sources of all magnetic fields and magnetic manifestations in Nature. Magnetic charges, that constitute together with electrical charges atomic shells got of title: magnetons and antimagnetons (respectively with charges g− and g+ under fundamental condition: g = e). Furthermore, in addition to participating in structures of atomic shells, the magnetic charges exist in potential and even in real zones conduction of solids. The magnetic and electric spinor particles in atoms and substance exist in form such of the spinor associations as the magnetic and electric bispinors. Under influence of external magnetic field in conductor being implemented polarization of magnetic bispinors with formation of magnetic dipoles. Internal fields magnetic dipoles is directed against an external magnetic field and is a simple explanation of such a physical manifestation as diamagnetism. During the rotation of these dipoles in the conductor are formed of the vortex magnetic dipole fields, which and create an electromotive force, i.e. are responsible for the electromagnetic induction. Author proposed new magneto-electric technology called the magnetoelectric induction, as the result of which the permanent current of magnetic charges is created. However, such currents may be implemented solely in the superconductors. In the article presented the main reasons which more hundred year old hinder recognition and technical use of the real magnetic charges and their currents what considerably slow down the global scientific and technological progress.

Introduction. When heating with high-frequency currents (HFCs) at high speeds, more significant strengthening effects can be observed compared to using machine generators. Therefore, hardening at high frequencies is more efficient. However, the increase in the generator frequency results in a decrease in the depth of penetration of eddy currents and an increased unevenness of heating across the cross-section. The application of a constant external magnetic field during HFC hardening can increase the depth of eddy current penetration and create more uniform heating. Unfortunately, there is not enough information available on the effect of the external magnetic field on HFC heating processes and phase transformations in steel. Currently, there are no quantitative estimates for the impact of an external magnetic field on changes in the kinetics of electric heating and the penetration depth of eddy currents. In connection with the above, the aim of this paper is to investigate changes in the kinetics of high-frequency heating of iron-carbon alloys when an external constant magnetic field is applied and, and, based on this, to consider the potential for technological applications. Materials and Methods. Theoretical assessment of the influence of an external magnetic field on the change in the kinetics of electric heating and the penetration depth of eddy currents is based on the general theory of induction heating kinetics. An experimental study of the influence of a magnetic field on the kinetics of high-frequency current heating was performed on samples of 45 steel, pearlitic gray (SCh30), and ferritic malleable cast iron (KCh30-6). The temperature distribution over the cross-section of ferromagnetic materials during induction heating with an external magnetic field has been studied using special samples of iron, 45 steel, and SCh30 gray pearlitic cast iron. Electric tempering processes have been investigated on samples of U8A steel using a vacuum tube generator (heating temperature — 450℃, heating rate — 750℃/s). Changes in austenite grain size after high-speed heating with external magnetization have been examined on samples of reduced-hardenability 55PP steel. To study the processes of thermal treatment in a magnetic field during experiments involving heating samples using high-frequency currents, a specially designed electromagnet was created to apply an external constant magnetic field. Results. Theoretical curves were constructed for heating conditions with and without an external constant magnetic field. Experimental data on the effect of an external constant magnetic field on induction heating in the surface layer of various materials were summarized in kinetic diagrams. Evidence that the observed changes were due to increased depth of penetration of eddy currents came from experiments on cylindrical samples of 45 steel with different wall thicknesses. Kinetic curves were provided for estimating the temperature field (at 6 points at different depths) during high-frequency current heating with and without external magnetization. The paper presents experimental data on the micro-hardness distribution across the cross-section of a U8 steel sample after quenching, quenching and electric tempering, quenching and electric tempering with external magnetization, and quenching and bulk tempering. It also includes the results of the study of the austenite grain size of 55PP steel after high-speed heating with external magnetization and conventional (slow) deep heating. Discussion. The application of a high-intensity external constant magnetic field during the first quasi-stationary process resulted in a decrease in the rate of induction heating of the ferromagnetic material and an increase in the depth of its uniform heating. However, above the Curie point, the effect of the magnetic field was negligible due to the low magnetic susceptibility of the material, and the heating rate remained unchanged as if there was no field present. In addition, due to the insignificant difference in the values of magnetic permeability below and above the Curie point during heating in the field, the thermal curve did not exhibit the characteristic inflection typical of kinetic curves observed during the transition of the surface layer to a paramagnetic state. Experiments with electric tempering have demonstrated that by applying an external field, it was possible to temper a material to the desired depth and it could be done on a single high-frequency current setup. The size of the austenite grains after high-speed heating with magnetization was reduced compared to conventional deep heating of steel with low hardenability, eliminating the issue of induction heating for low-hardenability steel. Conclusion. The results of the study demonstrated that the use of an external magnetic field enabled the achievement of strengthening effects during heating at higher frequencies, thereby eliminating the drawbacks of such heating methods.

Recent theoretical and observational developments in magnetic helicity studies

The influence of the magnetic field on the convective heat transfer characteristics of Fe3O4/water nanofluids

An irreversible electrochemical reaction from material interaction with the environment and causing degradation is known as corrosion. The electrolyte changes significantly affect the corrosion's reaction kinetics. Unknown factors and various notable factors influence the corrosion rate of a particular material in the environmental system. Significant interest in magnetic fields and their effects on electrochemical reactions have recently been gained. This paper studies the effect of an external magnetic field on the electrochemical oxidation of Aluminum (Al) in a 3,5% NaCl solution. The magnetic field 0; 0,8; 1,4; and 2,1 Tesla were used to expose the samples during corrosion testing. We found that the effect of a magnetic field on electrochemical oxidation shifts the oxidation potential to higher or lower than the oxidation potential without a magnetic field. Moreover, the oxidation potential's value depends on the magnetic field's intensity.

We present theoretical and computational results in magnetohydrodynamic turbulence that we feel are essential to understanding the geodynamo. These results are based on a mathematical model that focuses on magnetohydrodynamic (MHD) turbulence, but ignores compressibility and thermal effects, as well as imposing model-dependent boundary conditions. A principal finding is that when a turbulent magnetofluid is in quasi-equilibrium, the magnetic energy in the internal dipole component is equal to the magnetic helicity multiplied by the dipole wavenumber. In the case of the Earth, measurement of the exterior magnetic field gives us, through boundary conditions, the internal poloidal magnetic field. The connection between magnetic helicity and dipole field in the liquid core then gives us the toroidal part of the internal dipole field and a model value of 3 mT for the average core dipole magnetic field. Here, we present the theoretical analysis and numerical simulations that lead to these conclusions. We also test an earlier assertion that differential oblateness may be related to dipole alignment, and while there is an effect, rotation appears to be far more important. In addition, the relationship between dipole quasi-stationarity, broken ergodicity and broken symmetry is clarified. Lastly, we discuss how inertial waves in a rotating magnetofluid can affect dipole alignment.

It is demonstrated that the two-point correlation function of the magnetic helicity in the case of zero mean magnetic field has anomalous scalings for both compressible and incompressible turbulent helical fluid flow. The magnetic helicity in the limit of very high electrical conductivity is conserved. This implies that the two-point correlation function of the conserved property does not necessarily have normal scaling. The reason for the anomalous scalings of the magnetic helicity correlation function is that the magnetic field in the equation for the two-point correlation function of the magnetic helicity plays a role of a pumping with anomalous scalings. It is shown also that when magnetic fluctuations with zero mean magnetic field are generated the magnetic helicity is very small even if the hydrodynamic helicity is large.

The effect of magnetic field on nitric oxide (NO) production of cultured human umbilical vein endothelial cells (HUVECs) was investigated. Static magnetic fields (30 mT, 300 mT) and an oscillating magnetic field (30 mT, 20 Hz) were applied to HUVECs for 0.5, 1 and 6 hours and intracellular NO was observed using a fluorescent indicator. There was no effect of the static magnetic field on the NO production of the HUVECs. In contrast, the NO production increased with applying the oscillating magnetic field for 0.5 hour. However, such an increase of NO production was not observed for 1 and 6 hours. We performed a separate experiment to clarify the mechanism of NO synthesis by using an inhibitor of calcium-independent activation of NO synthase. The inhibitor suppressed the increase of NO production caused by the oscillating magnetic field. It can be concluded that oscillating magnetic field may activate calcium-independent pathway of activation for NO synthase.