Horizontal Gradient Of Magnetic Field Research Articles

Nowcasting and Validating Earth's Electric Field Response to Extreme Space Weather Events Using Magnetotelluric Data: Application to the September 2017 Geomagnetic Storm and Comparison to Observed and Modeled Fields in Scotland

AbstractIn the United Kingdom, geomagnetically induced currents (GICs) are calculated from thin‐sheet electrical conductivity models. In the absence of conductivity models, time derivatives of magnetic fields are sometimes used as proxies for GIC‐related electric fields. An alternative approach, favored in the United States, is to calculate storm time electric fields from time‐independent impedance tensors computed from an array of magnetotelluric (MT) sites and storm time magnetic fields recorded at geomagnetic observatories or assumed from line current models. A paucity of direct measurements of storm time electric fields has restricted validation of these different techniques for nowcasting electric fields and GICs. Here, we present unique storm time electric field data from seven MT sites in Scotland that recorded before, during, and after the September 2017 magnetic storm. By Fourier transforming electric field spectra computed using different techniques back to the time domain, we are able to make direct comparisons with these measured storm time electric field time series. This enables us to test the validity of different approaches to nowcasting electric fields. Our preferred technique involves frequency domain multiplication of magnetic field spectra from a regional site with a local impedance tensor that has been corrected for horizontal magnetic field gradients present between the local site and the regional site using perturbation tensors derived from geomagnetic depth sounding (GDS). Scatter plots of scaling factors between measured and nowcasted electric fields demonstrate the importance of coupling between the polarization of the storm time magnetic source field and Earth's direction‐dependent deep electrical conductivity structure.

Solar Flare Prediction Using Magnetic Field Diagnostics above the Photosphere

Abstract In this article, we present the application of the weighted horizontal gradient of magnetic field (WG M ) flare prediction method to three-dimensional (3D) extrapolated magnetic configurations of 13 flaring solar active regions (ARs). The main aim is to identify an optimal height range, if any, in the interface region between the photosphere and lower corona, where the flare onset time prediction capability of WG M is best exploited. The optimal height is where flare prediction, by means of the WG M method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and nonlinear force-free field extrapolations, are constructed to study a vertical range from the photosphere up to the low corona with a 45 km step size. The WG M method is applied as a function of height to all 13 flaring AR cases that are subject to certain selection criteria. We found that applying the WG M method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2–8 hr. Certain caveats and an outlook for future work along these lines are also discussed.

Solar photosphere magnetization

Context.A recent review shows that observations performed with different telescopes, spectral lines, and interpretation methods all agree about a vertical magnetic field gradient in solar active regions on the order of 3 G km−1, when a horizontal magnetic field gradient of only 0.3 G km−1is found. This represents an inexplicable discrepancy with respect to the divB = 0 law.Aims.The objective of this paper is to explain these observations through the lawB = μ0(H+M) in magnetized media.Methods.Magnetization is due to plasma diamagnetism, which results from the spiral motion of free electrons or charges about the magnetic field. Their usual photospheric densities lead to very weak magnetizationM, four orders of magnitude lower thanH. It is then assumed that electrons escape from the solar interior, where their thermal velocity is much higher than the escape velocity, in spite of the effect of protons. They escape from lower layers in a quasi-static spreading, and accumulate in the photosphere. By evaluating the magnetic energy of an elementary atom embedded in the magnetized medium obeying the macroscopic lawB = μ0(H+M), it is shown that the Zeeman Hamiltonian is due to the effect ofH. Thus, what is measured isH.Results.The decrease in density with height is responsible for non-zero divergence ofM, which is compensated for by the divergence ofH, in order to ensure div B = 0. The behavior of the observed quantities is recovered.Conclusions.The problem of the divergence of the observed magnetic field in solar active regions finally reveals evidence of electron accumulation in the solar photosphere. This is not the case of the heavier protons, which remain in lower layers. An electric field would thus be present in the solar interior, but as the total charge remains negligible, no electric field or effect would result outside the star.

Estimating the electric field response to the Halloween 2003 and September 2017 magnetic storms across Scotland using observed geomagnetic fields, magnetotelluric impedances and perturbation tensors

Geomagnetic storms generate heightened magnetovariational activity, which induces electric fields that drive hazardous currents known as geomagnetically induced currents (GICs) through man-made technological conductors including power transmission lines, railway networks and gas pipelines. We multiply magnetotelluric (MT) impedances from 23 sites in Scotland and northern England with measured geomagnetic field spectra from the Halloween 2003 and September 2017 storms to estimate maximum peak-to-peak, electric field magnitudes and directions for these storms, which we present as hazard maps. By sampling these electric fields in the direction of the longest (>50 km), high-voltage (275 and 400 kV) Scottish power transmission lines and integrating along their lengths, we estimate their associated transmission-line voltages. Lateral electrical conductivity variations in the Earth generate horizontal magnetic field gradients. We investigate the effect of these gradients on electric field estimates obtained using remote magnetic fields by applying a correction to the impedance tensor derived from the magnetic perturbation tensor between the local MT site and the remote magnetic field site. For the September 2017 storm, we also compare our estimated electric fields with a unique dataset comprising measured storm-time electric fields from 7 MT sites. We find that peak-to-peak, electric field magnitudes may have reached 13 V/km during the Halloween storm in some areas of the Scottish Highlands, with line-averaged electric fields >5 V/km sustained along a number of long-distance, high-voltage power transmission lines; line-averaged electric fields for the September 2017 storm are 1 V/km or less. Our surface electric fields show significant site-to-site variability that arises due to Earth’s internal 3D electrical conductivity structure, as characterised by the MT impedance tensors.

Investigation of pre-flare dynamics using the weighted horizontal magnetic gradient method: From small to major flare classes

There is a wide range of eruptions in the solar atmosphere which contribute to space weather, including the major explosions of radiation known as flares. To examine pre-event behavior in δ-spot regions, we use here a method based on the weighted horizontal gradient of magnetic field (WGM), defined between opposite polarity umbrae at the polarity inversion line of active regions (ARs) as measured using from the Debrecen Heliophysical Observatory catalogues. In this work, we extend the previous analysis of high-energy flares to include both medium (M) and low-energy (C and B) flares. First, we found a logarithmic relationship between the log value of highest flare class intensity (from B- to X-class) in a δ-spot AR and the maximum value of WGM of the 127 ARs investigated. We confirm a trend in the convergence-divergence phase of the barycenters of opposite polarities in the vicinity of the polarity inversion line. The extended sample, (i) affirms the linear connection between the durations of the convergence-divergence phases of barycenters of opposite polarities in δ-spot regions up to flare occurrence and (ii) provides a geometric constraint for the location of flare emission around the polarity inversion line. The method provides a tool to possibly estimate the likelihood of a subsequent flare of the same or larger energy.

Testing and Improving a Set of Morphological Predictors of Flaring Activity

Efficient prediction of solar flares relies on parameters that quantify the eruptive capability of solar active regions. Several such quantitative predictors have been proposed in the literature, inferred mostly from photospheric magnetograms and/or white-light observations. Two of them are the Ising energy and the sum of the total horizontal magnetic field gradient. The former has been developed from line-of-sight magnetograms, while the latter uses sunspot detections and characteristics, based on continuum images. Aiming to include these parameters in an automated prediction scheme, we test their applicability on regular photospheric magnetic field observations provided by the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). We test their efficiency as predictors of flaring activity on a representative sample of active regions and investigate possible modifications of these quantities. The Ising energy appears to be an efficient predictor, and the efficiency is even improved if it is modified to describe interacting magnetic partitions or sunspot umbrae. The sum of the horizontal magnetic field gradient appears to be slightly more promising than the three variations of the Ising energy we implement in this article. The new predictors are also compared with two very promising predictors: the effective connected magnetic field strength and the total unsigned non-neutralized current. Our analysis shows that the efficiency of morphological predictors depends on projection effects in a nontrivial way. All four new predictors are found useful for inclusion in an automated flare forecasting facility, such as the Flare Likelihood and Region Eruption Forecasting (FLARECAST), but their utility, among others, will ultimately be determined by the validation effort underway in the framework of the FLARECAST project.

On the Evolution of Pre-Flare Patterns of a 3-Dimensional Model of AR 11429

AbstractWe apply a novel pre-flare tracking of sunspot groups towards improving the estimation of flare onset time by focusing on the evolution of the 3D magnetic field construction of AR 11429. The 3D magnetic structure is based on potential field extrapolation encompassing a vertical range from the photosphere through the chromosphere and transition region into the low corona. The basis of our proxy measure of activity prediction is the so-called weighted horizontal gradient of magnetic field (WGM) defined between spots of opposite polarities close to the polarity inversion line of an active region. The temporal variation of the distance of the barycenter of the opposite polarities is also found to possess potentially important diagnostic information about the flare onset time estimation as function of height similar to its counterpart introduced initially in an application at the photosphere only in Korsós et al. (2015). We apply the photospheric pre-flare behavioural patterns of sunspot groups to the evolution of their associated 3D-constructed AR 11429 as function of height. We found that at a certain height in the lower solar atmosphere the onset time may be estimated much earlier than at the photosphere or at any other heights. Therefore, we present a tool and recipe that may potentially identify the optimum height for flare prognostic in the solar atmosphere allowing to improve our flare prediction capability and capacity.

PRE-FLARE DYNAMICS OF SUNSPOT GROUPS

Several papers provide evidences that the most probable sites of flare onset are the regions of high horizontal magnetic field gradients in solar active regions. Besides the localization of flare producing areas the present work intends to reveal the characteristic temporal variations in these regions prior to flares. This study uses sunspot data instead of magnetograms, it follows the behaviour of a suitable defined proxy measure representing the horizontal magnetic field gradient. The source of the data is the SDD (SOHO/MDI-Debrecen Data) sunspot catalogue. The most promising pre-flare signatures are the following properties of the gradient variation: i) steep increase, ii) high maximum, iii) significant fluctuation and iv) a gradual decrease between the maximum and the flare onset which can be related to the "pull mode" of the current layer. These properties may yield a tool for the assessment of flare probability and intensity within the next 8-10 hours.

Properties of Magnetic Neutral Line Gradients and Formation of Filaments

We investigate gradient of magnetic field across neutral lines (NLs), and compare their properties for NLs with and without the chromospheric filaments. Our results show that there is a range of preferred magnetic field gradients where the filament formation is enhanced. On the other hand, a horizontal gradient of magnetic field across a NL alone does not appear to be a single factor that determines if a filament will form (or not) in a given location.

Interface profile evolution between binary immiscible fluids induced by high magnetic field gradients

A mechanical analysis is done to find the evolution of the interface profile between binary immiscible fluids induced by a three-dimensional orthogonal magnetic field gradient. In the experiments, the changes of the interface profile between four groups of binary immiscible fluids are investigated under the same horizontal magnetic field gradients. The binary immiscible fluids are made of benzene and other liquids, like CuSO4, Fecl3, FeSO4 or Cucl2 aqueous solutions. In addition, the interface profile between the benzene and CuSO4 aqueous solution is examined under different horizontal magnetic field gradients. The experimental results are consistent with the theoretical analysis. This study explains the enhanced Moses effect from a mechanics standpoint. Furthermore, a new method for susceptibility measurement is proposed based on this enhanced Moses effect.

On the distribution of magnetic energy storage in solar active regions

A two-dimensional probabilistic Cellular Automaton is used to model the appearance of active regions at the solar surface. We assume that two main competing processes control the magnetic field evolution at the solar surface (1) the magnetic field is locally enhanced by the flux emergence and/or the coalescence of emerged magnetic flux and (2) it is diminished by flux cancellation or diffusion. The flux emergence follows a basic percolation rule; it is more probable at the points were magnetic flux already exists. The magnetic field is also enhanced when magnetic fields of the same polarity collide. The flux cancellation is due either to the gradual diffusion of the magnetic field, when it is isolated, or to the partial release of energy when opposite magnetic field lines collide. The percolation model proposed in this article is capable of reproducing the statistical properties of the evolving active regions. The evolving simulated magnetograms, derived from our model, are used to estimate the 3-D magnetic fields above the photosphere using constant α force-free extrapolation techniques. Based on the above analysis we are able to estimate a variety of observed statistical characteristics, e.g. the size and flux distribution of the magnetic fields at the solar surface, the fractal dimension of the magnetic structures formed at the photosphere, the energy release frequency distribution, the waiting time distribution of the sporadic energy releases and the statistical properties of the steep horizontal magnetic field gradients in the extrapolated coronal magnetic field. Our main conclusion is that the photospheric driver plays a crucial role in the observed flare statistics, and the solar magnetograms, when interpreted properly, carry important statistical information for the solar coronal activity (coronal heating, flares, CME etc.).

Numerical analysis of a hydrogen-oxygen diffusion flame in vertical or horizontal gradient of magnetic field

The magnetic force is essentially in proportion to the mass density and the magnetic susceptibility of paramagnetic chemical species and the gradient of magnetic field. In this study, the effect of magnetic field on OH radical distribution in a hydrogen-oxygen diffusion flame was investigated by numerically solving the equations of reactive gasdynamics and magnetism to explore a possibility of combustion control by magnetic force. Particularly, we attempted the analysis for three kinds of cases with different spatial distributions of the magnetic field: Case 1 is without the magnetic field, Case 2 is under the vertical gradient of magnetic field, and Case 3 is under the horizontal gradient of magnetic field. According to the analysis, because the mass density and the magnetic susceptibility of O 2 are much larger than those of other chemical species in the peripheral region of the flame, O 2 was strongly influenced by the magnetic force in that region. Consequently, this force induced the flow of gas including a large amount of O 2 and indirectly changed the OH distribution in the flame. The horizontal magnetic gradient (Case 3) was about 1.2 times more effective in the OH density change than the vertical gradient (Case 2).

Ray tracing survey of Z mode emissions from source regions in the high‐altitude auroral zone

Three‐dimensional ray tracing of Z mode radiation from sources in the auroral zone has been performed. A plasma model which includes a background ambient plasma, plasmasphere, and an optional region of field‐aligned current is used. In the source region the waves are assumed to be excited by the cyclotron maser mechanism for frequencies f ≲ fg (where fg is the electron gyrofrequency) and for wave normal angles in the range 83° < ψ < 90°; we have also considered cases when the source region was located near the center of a region of field‐aligned current. A number of different altitudes and a range of different field lines are used. In addition, we examine cases unrestricted by the cyclotron maser mechanism. Our results indicate that propagation is primarily perpendicular to the magnetic field line (horizontal propagation) for almost all sources considered, except when the wave source is assumed to be unrestricted by the cyclotron maser mechanism (f/fg < 0.9; and ψ < 80°). While the propagation is initially downward, refraction rapidly increases the wave normal angle, and only propagation at near‐constant altitudes occurs. While smaller wave normal angles (ψ ∼ 84°) produce more downward propagation, the frequency bandwidth estimated from the ray paths is found to be less than that observed by DE 1. Large horizontal magnetic field gradients associated with field‐aligned currents produce downward propagation, but still not sufficient to produce the observed bandwidths. These results indicate that wave growth may be due to mechanisms in addition to cyclotron maser resonance. In order to produce the observed bandwidth (Δf/fg ∼ 0.5), it is necessary that f/fg be as low as 0.7 and ψ be as low as 75°.