Magnetic Helicity Flux Research Articles

A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces

This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.

The Relationship between Kinetic and Magnetic Helicity in Solar Active Regions

Using Helioseismic and Magnetic Imager/Solar Dynamics Observatory data, we search for a relationship between kinetic helicity and magnetic helicity in solar active regions (ARs) using a sample of 62 ARs from 2010 May to 2015 May. The sample includes 32 mature ARs and 30 emerging ARs. We calculate kinetic helicity in the interior in the depth range from 0.6 to 11.6 Mm, magnetic helicity in the corona, helicity flux across the photosphere, and the magnetic twist and magnetic writhe of the ARs at the photosphere. From these data, relationships are found between magnetic helicity, helicity flux, and magnetic twist. However, magnetic writhe appears not to be related to the other magnetic quantities. No relationship is found between the kinetic helicity and any magnetic quantity. In particular, no relationship is found between the kinetic helicity and any of the following: magnetic helicity, magnetic helicity flux, magnetic twist, or magnetic writhe. These results suggest that (1) the magnetic helicity in the corona above ARs is mainly derived from the magnetic twist, and (2) the flow dynamics in the region from 0.6 to 11.6 Mm below the photosphere is not the primary source for the generation of magnetic helicity in ARs.

Long-period oscillations in the lower solar atmosphere prior to flare events

Multiple studies have identified a range of oscillation periods in active regions, from 3-5 minutes to long-period oscillations that last from tens of minutes to several hours. Recently, it was also suggested that these periods are connected with eruptive activity in the active regions. Thus, it is essential to understand the relation between oscillations in solar active regions and their solar eruption activity. We investigate the long-period oscillations of NOAA12353 prior to a series of C-class flares and correlate the findings with the 3- to 5-minute oscillations that were previously studied in the same active region. The objective of this work is to elucidate the presence of various oscillations with long periods in the lower solar atmosphere both before and after the flare events. To detect long-period oscillations, we assessed the emergence, shearing, and total magnetic helicity flux components from the photosphere to the top of the chromosphere. To analyze the magnetic helicity flux in the lower solar atmosphere, we used linear force-free field extrapolation to construct a model of the magnetic field structure of the active region. Subsequently, the location of long-period oscillations in the active region was probed by examining the spectral energy density of the measured intensity signal in the 1700\,AA , 1600\,AA , and 304\,AA channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Significant oscillation periods were determined by means of a wavelet analysis. Based on the evolution of the three magnetic helicity flux components, 3- to 8-hour periods were found both before and after the flare events, spanning from the photosphere to the chromosphere. These 3- to 8-hour periods were also evident throughout the active region in the photosphere in the 1700\,AA channel. Observations of AIA 1600\,AA and 304\,AA channels, which cover the chromosphere to the transition region, revealed oscillations of 3-8 hours near the region in which the flare occurred. The spatial distribution of the measured long-period oscillations mirror the previously reported distribution of 3- to 5-minute oscillations in NOAA12353 that were seen both before and after the flares. This case study suggest that the varying oscillation properties in a solar active region could be indicative of future flaring activity.

Data analysis methods and applications of the eddy current diagnostic system in the Keda Torus eXperiment device

Since the establishment of the eddy current diagnostic system within the Keda Torus eXperiment (KTX) device, it has unveiled many applications. Recent developments have introduced innovative data analysis techniques alongside compelling experimental results, underscoring the necessity for a comprehensive summary of the system's data analysis approaches and broad applications. Notable features of the system encompass exceptional precision, the ability to encompass shell currents on the entirety of the closed boundary, vector detection of shell currents, and measurement of diverse physical quantities. In terms of data analysis methodologies, meticulous scrutiny of the null field region is conducted, and we reveal a distinctive characteristic within the complex shell current signals, namely the asymmetry of the amplitudes of ±n Fourier coefficients. Moreover, the Hodge decomposition emerges as a pivotal technique, allowing for the distinctive separation of shell currents into three orthogonal components based on their distinct spatial topological properties. With regard to practical applications, an in-depth examination of the vector potential and magnetic helicity flux densities are presented in detail, further highlighting the far-reaching utility of the system's capabilities.

Conserving Local Magnetic Helicity in Numerical Simulations

Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy, it is not dissipated at small scales. This plays a major role in suppressing the kinematic large-scale dynamo and may also be responsible for driving the large-scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. In these simulations, magnetic helicity is lost either through numerical errors or through the action of an unrealistically large resistivity. Errors in the internal distribution of magnetic helicity are equally important and typically larger. Here, we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations, so that their evolution more closely approximates that of real systems.

ARTop: an open-source tool for measuring active region topology at the solar photosphere

ABSTRACT The importance of measuring topological quantities, such as magnetic helicity, in solar observations has long been recognized. In particular, topological quantities play an important role in both understanding and predicting solar eruptions. In this paper, we present ARTop (Active Region Topology), an open-source and end-to-end software tool that allows researchers to calculate the fluxes of topological quantities based on solar magnetograms. In addition to this, ARTop also allows for the efficient analysis of these quantities in both 2D maps and time series. ARTop calculates the fluxes of magnetic helicity and magnetic winding, together with particular decompositions of these quantities. To perform these calculations, SHARP magnetograms are downloaded and velocity maps are created using the DAVE4VM method. Visualization tools, written in Python, are provided to aid in the selection of appropriate output variables and for the straightforward creation of maps and time series. Additionally, other analysis functions are included to facilitate and aid solar flare investigations. This software offers researchers a powerful tool for investigating the behaviour of active regions and the origins of space weather.

Magnetic Helicity Fluxes from Triple Correlators

Fluxes of the magnetic helicity density play an important role in large-scale turbulent dynamos, allowing the growth of large-scale magnetic fields while overcoming catastrophic quenching. We show here, analytically, how several important types of magnetic helicity fluxes can arise from terms involving triple correlators of fluctuating fields in the helicity density evolution equation. For this, we assume incompressibility and weak inhomogeneity, and use a quasi-normal closure approximation: fourth-order correlators are replaced by products of second-order ones, and the effect of the fourth-order cumulants on the evolution of the third moments is modeled by a strong damping term. First, we show how a diffusive helicity flux, until now only measured in simulations, arises from the triple correlation term. This is accompanied by what we refer to as a random advective flux, which predominantly transports magnetic helicity along the gradients of the random fields. We also find that a new helicity flux contribution, in some aspects similar to that first proposed by Vishniac, can arise from the triple correlator. This contribution depends on the gradients of the random magnetic and kinetic energies along the large-scale vorticity, and thus arises in any rotating, stratified system, even if the turbulence is predominantly non-helical. It can source a large-scale dynamo by itself while spatially transporting magnetic helicity within the system.

Turbulent magnetic helicity fluxes in solar convective zone

ABSTRACT Combined action of helical motions of plasma (the kinetic α effect) and non-uniform (differential) rotation is a key dynamo mechanism of solar and galactic large-scale magnetic fields. Dynamics of magnetic helicity of small-scale fields is a crucial mechanism in a non-linear dynamo saturation where turbulent magnetic helicity fluxes allow to avoid catastrophic quenching of the α effect. The convective zone of the Sun and solar-like stars, as well as galactic discs, are the source for production of turbulent magnetic helicity fluxes. In the framework of the mean-field approach and the spectral τ approximation, we derive turbulent magnetic helicity fluxes using the Coulomb gauge in a density-stratified turbulence. The turbulent magnetic helicity fluxes include non-gradient and gradient contributions. The non-gradient magnetic helicity flux is proportional to a non-linear effective velocity (which vanishes in the absence of the density stratification) multiplied by small-scale magnetic helicity, while the gradient contributions describe turbulent magnetic diffusion of the small-scale magnetic helicity. In addition, the turbulent magnetic helicity fluxes contain source terms proportional to the kinetic α effect or its gradients, and also contributions caused by the large-scale shear (solar differential rotation). We have demonstrated that the turbulent magnetic helicity fluxes due to the kinetic α effect and its radial derivative in combination with the non-linear magnetic diffusion of the small-scale magnetic helicity are dominant in the solar convective zone.

Magnetic Helicity Flux Oscillations in the Atmospheres of Flaring and Nonflaring Active Regions

Analyzing the evolution of magnetic helicity flux at different atmospheric heights is key for identifying its role in the dynamics of active regions (ARs). The three-dimensional (3D) magnetic field of both flaring and nonflaring ARs is constructed using potential field extrapolations, enabling the derivation of emergence, shearing, and total magnetic helicity components at a range of atmospheric heights. An analysis of temporal oscillations of the derived components shows that the largest significant period of the three helicity fluxes are common (within ±2 hr) from the photosphere up to at least 1 Mm for flaring ARs—being consistent with the presence of a coupled oscillatory behavior that is absent in the nonflaring ARs. We suggest that large, energetic solar eruptions may have been produced in ARs when the vertical and horizontal helicity flux components became a coupled oscillatory system in the low solar atmosphere.

Measurement of helicity flux density using the eddy-current diagnostic system in Keda Torus eXperiment device

The flux of magnetic helicity characterizes how the topology of a magnetic field changes and helicity and its transport play essential roles in plasma equilibrium and instabilities in the reversed-field pinch (RFP) device configuration. Used to suppress magnetohydrodynamic instabilities effectively, the stabilizing conducting shell located at the boundary of an RFP device is always characterized by an eddy-current distribution that evolves rapidly with time. After measuring and analyzing the eddy currents on this stabilizing shell during tokamak discharges in the Keda Torus eXperiment device, the distributions of multiple physical quantities on the shell are obtained, including the magnetic fields, eddy currents, and electric fields. An experimental technique for measuring helicity flux density is demonstrated, combined with eddy-current diagnosis and these physical vectors on the boundary. How the magnetic and current helicity flux densities evolve is given by a feasible mathematical analysis, and data suggest that the plasma mediates both the generation and transport of magnetic helicity during the discharge. The experimental results of the distribution of the magnetic helicity flux densities (MHFDs) due to the instability on the boundary are given, and the average of these MHFDs over the whole boundary surface is far less than the maximum value of the MHFDs. In addition, the results of current helicity flux densities on the boundary are also presented.

Comparison of Two Methods for Calculating Magnetic Helicity in the Solar Corona

Duo to the large magnetic Reynolds number, the magnetic helicity originating from the solar interior can be carried away through the photosphere into the corona. However, the relationship between the accumulated magnetic helicity flux through the photosphere and the magnetic helicity in the corona is still unclear. By selecting 36 newly emerging active regions in the 23rd solar cycle, we apply optical flow methods to derive the accumulated magnetic helicity through the photosphere (H m p ) by using the sequential longitudinal magnetograms, we use nonlinear force-free field extrapolation to obtain the 3D coronal magnetic field, and we adopt finite volume methods to calculate the instantaneous relative magnetic helicity in the corona (H m c ) by using vector magnetograms. It is found that the local correlation tracking (LCT)–based H m p is larger than H m c in 1″, and that the Differential Affine Velocity Estimator–based H m p is more consistent with H m c than the LCT-based H m p . H m p is more consistent with H m c in evaluation from 2″ than from 1″. Moreover, systematically shows consistency with the Hemispheric Helicity Rule (over 55%), no matter which resolution and method are used. These estimations suggest that the consistency of H m c and H m p is partly dependent on the resolution of the magnetograms and the calculation methods.

On the Differences in the Periodic Behavior of Magnetic Helicity Flux in Flaring Active Regions with and without X-class Events

Abstract Observational precursors of large solar flares provide a basis for future operational systems for forecasting. Here, we study the evolution of the normalized emergence (EM), shearing (SH), and total (T) magnetic helicity flux components for 14 flaring (with at least one X-class flare) and 14 nonflaring (<M5-class flares) active regions (ARs) using the Space-weather Helioseismic Magnetic Imager Active Region Patches vector magnetic field data. Each of the selected ARs contain a δ-type spot. The three helicity components of these ARs were analyzed using wavelet analysis. Localized peaks of the wavelet power spectrum (WPS) were identified and statistically investigated. We find that (i) the probability density function of the identified WPS peaks for all the EM/SH/T profiles can be fitted with a set of Gaussian functions centered at distinct periods between ∼3 and 20 hr. (ii) There is a noticeable difference in the distribution of periods found in the EM profiles between the flaring and nonflaring ARs, while no significant difference is found in the SH and T profiles. (iii) In flaring ARs, the distributions of the shorter EM/SH/T periods (<10 hr) split up into two groups after flares, while the longer periods (>10 hr) do not change. (iv) When the EM periodicity does not contain harmonics, the ARs do not host a large energetic flare. (v) Finally, significant power at long periods (∼20 hr) in the T and EM components may serve as a precursor for large energetic flares.

Helical turbulent nonlinear dynamo at large magnetic Reynolds numbers

To investigate large-scale magnetic field generation in highly conducting magnetohydrodynamic (MHD) regimes typical of rotating astrophysical systems, we conduct high-resolution MHD simulations in the dynamical regime of large magnetic Reynolds numbers, of turbulence with an inhomogeneous kinetic helicity distribution. We obtain a nonlinear helical dynamo solution, characterized by a weak large-scale magnetic wave slowly propagating over saturated small-scale MHD turbulence, bypassing the catastrophic resistive quenching problem of homogeneous helical dynamos by developing turbulent fluxes of magnetic helicity through the system equator. Hints of fast-reconnection plasmoids are found.

Magnetic Helicity Flux across Solar Active Region Photospheres. II. Association of Hemispheric Sign Preference with Flaring Activity during Solar Cycle 24

Abstract In our earlier study (Paper I) of this series, we examined the hemispheric sign preference (HSP) of magnetic helicity flux dH/dt across photospheric surfaces of 4802 samples of 1105 unique active regions (ARs) observed during solar cycle 24. Here, we investigate any association of the HSP, expressed as a degree of compliance, with flaring activity, analyzing the same set of dH/dt estimates as used in Paper I. The AR samples under investigation are assigned to heliographic regions (HRs) defined in the Carrington longitude–latitude plane with a grid spacing of 45° in longitude and 15° in latitude. For AR samples in each of the defined HRs, we calculate the degree of HSP compliance and the average soft X-ray flare index. The strongest flaring activity is found to be in one distinctive HR with an extremely low-HSP compliance of 41% as compared to the mean and standard deviation of 62% and 7%, respectively, over all HRs. This sole HR shows an anti-HSP (i.e., <50%) and includes the highly flare-productive AR NOAA 12673, however this AR is not uniquely responsible for the HR’s low HSP. We also find that all HRs with the highest flaring activity are located in the southern hemisphere, and they tend to have lower degrees of HSP compliance. These findings point to the presence of localized regions of the convection zone with enhanced turbulence, imparting a greater magnetic complexity and a higher flaring rate to some rising magnetic flux tubes.

Magnetic winding – a key to unlocking topological complexity in flux emergence

Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that encodes information on the topology of magnetic field lines. It has long been appreciated that magnetic topology is an important constraint for the evolution of magnetic fields in MHD. In applications to the solar atmosphere, understanding magnetic topology is crucial for following the evolution and eruption of magnetic fields. At present, magnetic helicity flux can be measured in solar observations but the interpretation of results is difficult due to the combination of confounding factors. We propose that a renormalization of helicity flux, the magnetic winding, can be used to detect more detailed topological features in magnetic fields and thus provide a more reliable signature for predicting the onset of solar eruptions.

Magnetic Helicity Flux across Solar Active Region Photospheres. I. Hemispheric Sign Preference in Solar Cycle 24

Abstract A hemispheric preference in the dominant sign of magnetic helicity has been observed in numerous features in the solar atmosphere, i.e., left-handed/right-handed helicity in the northern/southern hemisphere. The relative importance of different physical processes that may contribute to the observed hemispheric sign preference (HSP) of magnetic helicity is still under debate. Here, we estimate magnetic helicity flux (dH/dt) across the photospheric surface for 4802 samples of 1105 unique active regions (ARs) that appeared over an 8 yr period from 2010 to 2017 during solar cycle 24, using photospheric vector magnetic field observations by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The estimates of dH/dt show that 63% and 65% of the investigated AR samples in the northern and southern hemispheres, respectively, follow the HSP. We also find a trend that the HSP of dH/dt increases from ∼50%–60% up to ∼70%–80% as ARs (1) appear at the earlier inclining phase of the solar cycle or higher latitudes and (2) have larger values of , the total unsigned magnetic flux, and the average plasma-flow speed. These observational findings support the enhancement of the HSP mainly by the Coriolis force acting on a buoyantly rising and expanding flux tube through the turbulent convection zone. In addition, the differential rotation on the solar surface as well as the tachocline α-effect of a flux-transport dynamo may reinforce the HSP for ARs at higher latitudes.

On magnetic helicity generation and transport in a nonlinear dynamo driven by a helical flow

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ( $Rm$ ). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$ .

Magnetic helicity flux for mean magnetic field equations

The mean magnetic field equation describes the process of generating a magnetic field on a large scale as a result the EMF arising on a small scale. We consider the case where the large-scale magnetic field is also random and determine the density function of magnetic helicity. This function is invariant under gauge transformations of the magnetic vector potential. We study the equation for the magnetic helicity flux of a large-scale field and introduce a correction term related to the quadratic magnetic helicity invariant.

The origin and effect of hemispheric helicity imbalance in solar dynamo

In this paper we study the effects of the net magnetic helicity density on the hemispheric symmetry of the dynamo generated large-scale magnetic field. Our study employs the axisymmetric dynamo model which takes into account the nonlinear effect of magnetic helicity conservation. We find that, on the surface, the net magnetic helicity follows the evolution of the parity of the large-scale magnetic field. Random fluctuations of the $\unicode[STIX]{x1D6FC}$ -effect and the helicity fluxes can invert the causal relationship, i.e. the net magnetic helicity or the imbalance of magnetic helicity fluxes can drive the magnetic parity breaking. We also found that evolution of the net magnetic helicity of the small-scale fields follows the evolution of the net magnetic helicity of the large-scale fields with some time lag. We interpret this as an effect of the difference of the magnetic helicity fluxes out of the Sun from the large and small scales.

Interpreting magnetic helicity flux in solar flux emergence

Magnetic helicity flux gives information about the topology of a magnetic field passing through a boundary. In solar physics applications, this boundary is the photosphere and magnetic helicity flux has become an important quantity in analysing magnetic fields emerging into the solar atmosphere. In this work we investigate the evolution of magnetic helicity flux in magnetohydrodynamic (MHD) simulations of solar flux emergence. We consider emerging magnetic fields with different topologies and investigate how the magnetic helicity flux patterns correspond to the dynamics of emergence. To investigate how the helicity input is connected to the emergence process, we consider two forms of the helicity flux. The first is the standard form giving topological information weighted by magnetic flux. The second form represents the net winding and can be interpreted as the standard helicity flux less the magnetic flux. Both quantities provide important and distinct information about the structure of the emerging field and these quantities differ significantly for mixed sign helicity fields. A novel aspect of this study is that we account for the varying morphology of the photosphere due to the motion of the dense plasma lifted into the chromosphere. Our results will prove useful for the interpretation of magnetic helicity flux maps in solar observations.