Vertical Electric Current Density Research Articles

On the ratio of the components of the atmospheric vertical electric current density in fair weather

This work presents the results of ground-based and tethered balloon observations of altitude profiles of the components of the atmospheric vertical electric current density. The magnitude of the conduction current density was observed in the range 0.2 - 2 pAm−2. The ratio of the negative to positive component of the conduction current density averaged 1.6 outside the layer, where their dependence on the height was noticeable. In the framework of developed numerical model with reasonable values of the parameters it is found that the ratio of the convection current density to the density of the total vertical atmospheric electric current in the atmospheric boundary layer mainly falls in the range 0.2 - 0.6 and tends to increase under strong convection and low electrical conductivity. An exponential parameterization of the dependence of the electromotive force on the ground-level electrical conductivity is proposed.

Chromospheric plasma ejection above a pore

ABSTRACT We present high spatial resolution observations of short-lived transients, ribbons and jet-like events above a pore in Ca ii H images where fine structure, like umbral dots, light bridges and penumbral microfilaments, is present in the underlying photosphere. We found that current layers are formed at the edges of the convective fine structure, due to the shear between their horizontal field and the ambient vertical field. High vertical electric current density patches are observed in the photosphere around these events, which indicates the formation of a current sheet at the reconnection site. In the framework of past studies, low altitude reconnection could be the mechanism that produces such events. The reconnection is caused by an opposite polarity field produced by the bending of field lines by convective downflows at the edge of pore fine structure.

Turbulent electric current in the marine convective atmospheric boundary layer

The atmospheric boundary layer considered a part of the planetary global electric circuit is known to exhibit a most dramatically changing in space and time atmospheric electrical variables. Extremely low specific electrical conductivity in the lower atmosphere is accompanied by the work of the electric generator associated with turbulent dynamo realizing itself through the space charge transport by boundary layer flows. The electromotive force of this generator acting in fair weather atmospheric regions provides a contribution to the global potential drop between the lower ionosphere and the earth's surface. In this study, the vertical electric current density produced by the turbulent transfer of space charge is investigated in the cases of the buoyancy-dominated and shear-dominated convective boundary layer (CBL) over the oceans based on second-order dissipation-conditioned Lagrangian stochastic model (LSM) applied near air-sea interface and conjugated with first-order LSM in the rest of the CBL. The total electric charge flux is treated in terms of mechanical transfer of atmospheric ions and charged aerosol particles by Lagrangian turbulence together with the drift of small ions in the self-consistent electric field. This approach based on a transported probability density function method offers persuasive advantages for quantitative estimates of local perturbations in the fair-weather electric field created by the atmospheric space charge carried by turbulent flows. It is found that the space charge density vertical profile only slightly depends on turbulence everywhere except for the wavy boundary layer about 10 m thick, a new parameterization of space charge vertical profile is proposed. Based on the simulation results, it can be predicted that in the buoyancy-dominated CBLs the electric field must be greater than in the sheared CBLs with other things being equal. Turbulent electromotive force and changes in total downward atmospheric electric current density are quantified. Simulated vertical profiles of electrical conductivity, space charge, electric field, and turbulent current density reasonably well reproduce previously reported observation results.

Electrical signatures of Nimbostratus and Stratus clouds in ground-level vertical atmospheric electric field and current density at mid-latitude station Swider, Poland

We analyse the occurrences of low-level stratiform clouds such as Nimbostratus and Stratus, in Swider, Poland (51.15 N, 21.23 E) in the years 2005–2015. There have been on average 44 days with Nimbostratus a year between 2005 and 2015 at Swider and 51 days with Stratus over this period. Atmospheric electric field, current density and air conductivity available for the recorded cloud cases from years 2012–2015 have been analysed and their average values obtained for all cases and separately for the cloud cases with their main types of precipitation: rain and snow for Nimbostratus, drizzle and granular snow for Stratus. The analysis of atmospheric electricity parameters confirms previous results indicating differences in the electrical behaviour of raining and snowing clouds. The atmospheric electric field and conduction current is more likely downward under Stratus cloud as is its precipitation-convection current. This type of cloud mostly behaves like a passive element of the global circuit. The electric field under Nimbostratus during rain at the ground is upward and upward precipitation current occurs during heavier rain. Such raining mid-latitude Nimbostratus can potentially be an electric cloud generator which charges the Earth's global atmospheric circuit, the contribution of which needs to be investigated in more detail.

Hard X-ray emitting energetic electrons and photospheric electric currents

The energy released during solar flares is believed to be stored in non-potential magnetic fields associated with electric currents flowing in the corona. While no measurements of coronal electric currents are presently available, maps of photospheric electric currents can now be derived from SDO/HMI observations. Photospheric electric currents have been shown to be the tracers of the coronal electric currents. Particle acceleration can result from electric fields associated with coronal electric currents. We revisit here some aspects of the relationship between particle acceleration in solar flares and electric currents in the active region. We study the relation between the energetic electron interaction sites in the solar atmosphere, and the magnitudes and changes of vertical electric current densities measured at the photospheric level, during the X2.2 flare on February 15 2011 in AR NOAA 11158. X-ray images from RHESSI are overlaid on magnetic field and electric current density maps calculated from the spectropolarimetric measurements of SDO/HMI using the UNNOFIT inversion and Metcalf disambiguation codes. X-ray images are also compared with EUV images from SDO/AIA to complement the flare analysis. Part of the elongated X-ray emissions from both thermal and non-thermal electrons overlay the elongated narrow current ribbons observed at the photospheric level. A new X-ray source at 50-100 keV (produced by non-thermal electrons) is observed in the course of the flare and is cospatial with a region in which new vertical photospheric currents appeared during the same period (increase of 15%). These observational results are discussed in the context of the scenarios in which magnetic reconnection (and subsequent plasma heating and particle acceleration) occurs at current-carrying layers in the corona.

Estimating Electric Current Densities in Solar Active Regions

Electric currents in solar active regions are thought to provide the energy released via magnetic reconnection in solar flares. Vertical electric current densities J z at the photosphere may be estimated from vector magnetogram data, subject to substantial uncertainties. The values provide boundary conditions for nonlinear force-free modelling of active region magnetic fields. A method is presented for estimating values of J z taking into account uncertainties in vector magnetogram field values, and minimising \(J_{z}^{2}\) across the active region. The method is demonstrated using the boundary values of the field for a force-free twisted bipole, with the addition of noise at randomly chosen locations.

Electric current density and related sigmoid in an active region

Using THEMIS vector magnetograms we measured vertical electric current density in the leading sunspot of NOAA 11127 active region during its disk passage. The current structures evolve versus time. MHD modelling allows us to explain the spiral pattern by torsion. We found observational visible counterparts in the SDO/AIA 335 A images. The field lines are visible as loops in the AIA images. When the torsion is increasing, a sigmoid is observed. In the present event observed on November 24th 2010, we find that reconnection is also necessary to explain their sigmoidal shape.

ACHIEVING SELF-CONSISTENT NONLINEAR FORCE-FREE MODELING OF SOLAR ACTIVE REGIONS

A nonlinear force-free solution is constructed for the coronal magnetic field in NOAA solar active region (AR) 10953 based on a photospheric vector magnetogram derived from Hinode satellite observations on 2007 April 30, taking into account uncertainties in the boundary data and using improved methods for merging multiple-instrument data. The solution demonstrates the "self-consistency" procedure of Wheatland & Régnier, for the first time including uncertainties. The self-consistency procedure addresses the problem that photospheric vector magnetogram data are inconsistent with the force-free model, and in particular that the boundary conditions on vertical electric current density are overspecified and permit the construction of two different nonlinear force-free solutions. The procedure modifies the boundary conditions on current density during a sequence of cycles until the two nonlinear force-free solutions agree. It hence constructs an accurate single solution to the force-free model, with boundary values close, but not matched exactly, to the vector magnetogram data. The inclusion of uncertainties preserves the boundary conditions more closely at points with smaller uncertainties. The self-consistent solution obtained for AR 10953 is significantly non-potential, with magnetic energy E/E0 ≈ 1.08, where E0 is the energy of the reference potential (current-free) magnetic field. The self-consistent solution is shown to be robust against changes in the details of the construction of the two force-free models at each cycle. This suggests that reliable nonlinear force-free modeling of ARs is possible if uncertainties in vector magnetogram boundary data are included.

HINODE OBSERVATION OF THE MAGNETIC FIELDS IN A SUNSPOT LIGHT BRIDGE ACCOMPANIED BY LONG-LASTING CHROMOSPHERIC PLASMA EJECTIONS

We present high-resolution magnetic field measurements of a sunspot light bridge (LB) that produced chromospheric plasma ejections intermittently and recurrently for more than 1 day. The observations were carried out with the Hinode Solar Optical Telescope on 2007 April 29 and 30. The spectro-polarimeter reveals obliquely oriented magnetic fields with vertical electric current density higher than 100 mA m–2 along the LB. The observations suggest that current-carrying highly twisted magnetic flux tubes are trapped below a cusp-shaped magnetic structure along the LB. The presence of trapped current-carrying flux tubes is essential for causing long-lasting chromospheric plasma ejections at the interface with pre-existing vertically oriented umbral fields. A bidirectional jet was clearly detected, suggesting magnetic reconnections occurring at very low altitudes, slightly above the height where the vector magnetic fields are measured. Moreover, we found another strong vertical electric current on the interface between the current-carrying flux tube and pre-existing umbral field, which might be a direct detection of the currents flowing in the current sheet formed at the magnetic reconnection sites.

VECTOR MAGNETIC FIELDS AND ELECTRIC CURRENTS FROM THE IMAGING VECTOR MAGNETOGRAPH

First, we describe a general procedure to produce high quality vector magnetograms using the Imaging Vector Magnetograph (IVM) at Mees Solar Observatory. At the spatial resolution 2"x2", the Stokes Q,U,V uncertainty reaches 0.001-0.0005 in time-averaged data over 1-hour in the quiet Sun. When vector magnetic fields are inferred from the time-averaged Stokes spectral images of FeI 6302.5A, the resulting uncertainties are on the order of 10 G for the longitudinal fields, 40 G for the transverse field strength and 9 degree for the magnetic azimuth. The magnetic field inversion used in this work is the "Triplet" code, which was developed and implemented in the IVM software package by the late Barry J. LaBonte. The inversion code is described in detail in the Appendix. Second, we solve for the absolute value of the vertical electric current density, |Jz|, accounting for the above IVM problems, for two different active regions. One is a single sunspot region (NOAA 10001 observed on 20 June 2002) while the other is a more complex, quadrupolar region (NOAA10030 observed on 15 July 2002). We use a calculation that does not require disambiguation of 180 degree in the transverse field directions. The |Jz| uncertainty is on the order of 7.0 mA m^-2. The vertical current density increases with increasing vertical magnetic field. The rate of increase is about 1 -2 times as large in the quadrupolar NOAA 10030 region as in the simple NOAA 10001, and it is more spatially variable over NOAA 10030 than over NOAA 10001.

Electric current density calculation and error analysis of solar active regions

This investigation centers upon calculating the vertical electric current densities from the two transverse components of vector magnetograms. The electric current density calculated by using the differential form of Ampere’s law, j z = 1 μ 0 ( ∇ × B ) z , on the basis of spatially sampled transverse magnetic fields varies widely over an active region. In order to investigate how errors in the vector magnetograph measurements produce errors in the vertical electric current densities, we have numerically simulated the effects of random noise on a standard photospheric magnetic configuration produced by electric currents satisfying the force-free field conditions. We have also compared the results of the densities calculated by three different methods, and analyzed the reason inducing the differences in the results. The three methods are (1) to calculate the density using the differential form of Ampere’s law, j z = 1 μ 0 ( ∇ × B ) z ; (2) to calculate the density using the integral form of Ampere’s law along the square with edges at ( x - Δ x , y - Δ y ), ( x + Δ x , y - Δ y ), ( x + Δ x , y + Δ y ), ( x - Δ x , y + Δ y ) (hereafter small integral path), j z = ( 1 μ 0 ∮ C 1 B t · d l ) / d S ; (3) to calculate the density by using the integral form of Ampere’s law along the square with edges at ( x - 2 Δ x , y - 2 Δ y ), ( x + 2 Δ x , y - 2 Δ y ), ( x + 2 Δ x , y + 2 Δ y ), ( x - 2 Δ x , y + 2 Δ y ) (hereafter big integral path), j z = ( 1 μ 0 ∮ C 2 B t · d l ) / d S . It is found that the uncertainty of the measured electric current density increases along with the decreasing of the spatial pixel size ds . When the spatial pixel size of vector magnetograms is small enough, properly expanding the integral path can help us decrease the effect of random noise and demodulate the “true” electric current density from the measured transverse magnetograms. Close attention should be paid to the fact that some true fine-structure of the electric current density will be lost when the integral path exceeds the linear size of the smallest spatially resolved structure in the studied magnetogram.

The Influence of Faraday Rotation on the Vertical Electric Current Density

In this Letter we analyze the effects of Faraday rotation on the vertical electric current density in solar active regions. On the basis of the numerical solutions of the transfer equations of Stokes parameters for the Fe I 5324.19 Å line at the solar disk center, we derive the variations of the vertical current with wavelengths, which are caused by Faraday rotation. The simulations show that Faraday rotation changes both the sign and the magnitude of the vertical current at line center, but it changes only its magnitude at the far wings of the line. At the selected locations on a simple sunspot, the observed variations of the vertical current with wavelengths are compared with the model. We find that the azimuth rotation is significant when observations are taken near the center of the Fe I 5324.19 Å line: the sign change of the vertical current occurs in about 13.5% of the total selected locations, and in about 26% of those the magnitude increases the vertical current more than 100% of the "real" value. We also make a preliminary attempt to correct a case of the vector magnetic field observations for Faraday rotation. For NOAA AR 10162, in particular, it appears that Faraday rotation has a significant effect on the vertical current.

A New Technique for a Routine Azimuth Disambiguation of Solar Vector Magnetograms

We introduce a nonpotential magnetic field calculation (NPFC) technique to perform azimuth disambiguation in solar vector magnetograms. It is shown that resolving the 180° ambiguity would be a numerically fully determined problem if the vertical electric current density was known a priori. Since this is not the case, we enforce a minimum-magnitude current density solution. The NPFC disambiguation is otherwise assumption-free, with the quality of the results depending on the quality of the measurements. The NPFC method first infers the nonpotential magnetic field component responsible for the assumed vertical currents and then determines the vertical magnetic field whose potential extrapolation, added to the nonpotential field, best reproduces the observationally inferred horizontal magnetic field. The technique is fast, effective, and physically sound, so it may be instrumental in a routine, real-time, disambiguation of future space-borne solar vector magnetograms.

Balloon observations of temporal variation in the global circuit compared to global lightning activity

Vertical electric current density was obtained from direct electric field and conductivity measurements on two stratospheric balloon payloads during the 2nd polar patrol balloon (PPB) campaign from Syowa Station in Antarctica during January 2003. Payloads of these two flights were identical and were launched 8-h apart resulting in separation distances of a few hundred km during the time of overlapping data. The float altitude of each was a little over 30 km. The global circuit return current derived from these measurements is compared to the global lightning activity determined by the world wide lightning location (WWLLN) network. The total number of lightning events detected anywhere in the world are simply summed to form an hourly lightning flash rate for the time of the PPB data. The WWLLN and return current density data are shown to have a strong correlation, often with a strong universal time daily variation, similar to that expected for the global circuit.

Seasonal variations of atmospheric electricity measured at Amundsen‐Scott South Pole Station

Recent studies have shown that the general understanding of the Earth's global circuit is not entirely complete. Electric current originates from thunderstorm cloud tops and travels to the ionosphere, where it then leaks back down to the Earth's surface. Superimposed on this current is the dynamo generated from the interaction of the solar wind with Earth's magnetosphere. This paper investigates seasonal variations of the vertical electric field and current density as measured at the South Pole between 1991 and 1993. After initial data reduction, a model approach was used to decouple the magnetospheric and atmospheric components of the measurements. This approach calculated and subtracted the polar cap ionospheric potential from the measured data to obtain a signal of global tropospheric origin, in principle. The diurnal variations of the resulting data were averaged as a function of UT. These averages were calculated for the data as a whole and for the date sorted and binned by season and by magnetic activity level. The seasonally binned average results are consistent with recent papers indicating that the electric field measurement show global convective electrical activity to be a minimum during the Northern Hemisphere winter, in contradiction to the original 1929 Carnegie data. Because the electric field was a maximum during the Northern Hemisphere summer season, the midlatitude regions must contribute more strongly than the tropics to global atmospheric electricity. This analysis supports the link of electrical activity to global temperature. The magnetic activity binned results suggest that the polar cap potential model used underestimates the cross polar cap potential when there is a high Kp index.

EFFECTS OF 'SEEING' ON VECTOR MAGNETOGRAPH MEASUREMENTS

We present a study of the effects of atmospheric seeing on quantities derived from observations of solar polarized light – specifically, the vector magnetic flux and quantities derived from its magnitude and direction. Data from the Imaging Vector Magnetograph (‘IVM’) at the U. Hawaii/Mees Solar Observatory, are degraded by various degrees by applying a blur function to the ‘incoming light’, simulating a range of seeing conditions. A quantitative study of the resulting effects on derived quantities including total magnetic flux, vertical electric current density and magnetic shear angles, are discussed as a function of the imposed degradation. The generality of the seeing effects is explored by comparing the results from two different active regions; we find that the results are comparable for those quantities directly computed from the magnetic flux vector (e.g., summed, as in total flux) but less so for those quantities involving higher-order calculations (e.g., derivatives, as in vertical currents). We suggest that for temporal series data from any instrument, a method such as that which we outline here, be applied in order to model the uncertainties imposed on the data (in addition to instrumental uncertainties, etc.) due to seeing variations.

Cross-Section Variations of Coronal Magnetic Loops

Axisymmetric nonlinear force-free field models were employed to study the variation of the cross-section of coronal loops. In order to simulate these loops, we placed the point source of the fields under the photosphere and made the symmetric axis parallel to the photospheric surface. Based upon qualitative theoretical analyses and numerical simulations on the dipoles in these models, we compared the simulated magnetic loops with similar arclength and symmetric distributions of magnetic strength, and obtained the following results: The cross-section expansion of the current-free loops is fairly large and nearly isotropic, and that of highly sheared force-free loops is small and anisotropic. The anisotropy of the cross-section expansion, however, tends to vanish in extremely sheared loops. Magnetic loops with constant thickness, as an extreme case in the dipole nonlinear force-free fields, can be reached asymptotically when the magnetic shear increases. They tend to appear in the vicinity of the plane, vertically intersecting the symmetric axis at the point source, and their footpoints are not exactly located in the peak sites of vertical electric current density on the photospheric surface.

Reduction, analysis, and properties of electric current systems in solar active regions

The specific attraction and, in large part, the significance of solar vector magnetograms lie in the fact that they give the most important data on the electric currents and the nonpotentiality of active regions. Using the vector magnetograms from the Marshall Space Flight Center (MSFC), we employ a unique technique in the area of data analysis for resolving the 180 degree ambiguity in order to calculate the spatial structure of the vertical electric current density. The 180 degree ambiguity is resolved by applying concepts from the nonlinear multivariable optimization theory. The technique is shown to be of particular importance in very nonpotential active regions. The characterization of the vertical electric current density for a set of vector magnetograms using this method then gives the spatial scale, locations, and magnitude of these current systems. The method, which employs an intermediate parametric function which covers the magnetogram and which defines the local preferred direction, minimizes a specific functional of the observed transverse magnetic field. The specific functional that is successful is the integral of the square of the vertical current density. We find that the vertical electric current densities have common characteristics for the extended bipolar beta gamma delta-regions studied. The largest current systems have j(sub z)'s which maximizes around 30 mA per square meter and have a linear decreasing distribution to a diameter of 30 Mm.

Improved method for calibrating filter vector magnetographs

We have developed a method to improve present techniques for calibrating linear and circular polarization signals in terms of the vector magnetic field from observations with a filter vector magnetograph. The method substantially reduces inaccuracies in deriving the inclination of the field from theoretical calibrations for inclination angles in the range 30°–60°. We outline the method and demonstrate its improved accuracy in applications to a model magnetic field and to actual magnetograph observations. We also demonstrate how the method affects the calculation of derived parameters using the example of the vertical electric current density.

Evolution of vector magnetic fields and vertical currents and their relationship with solar flares in AR 5747

NOAA 5747 was a flare-productive active region during its transit across the solar disk in October 1989. After the resolution of the 180° ambiguity of the transverse field synthetically, and transformation of vector magnetograms from the image plane to the heliographic frame, we have determined the distribution of the photospheric vertical electric current density in the active region. By analyzing the evolution of vector magnetograms and vertical current over a 6-day period (October 17–22) in the active region, we get the following results: (1) Two magnetic fluxes of opposite polarities emerged synchronously with their separating motion, one of which converged with an old magnetic structure and caused a number of flares. (2) There appeared a new current system, with the emergence of the fluxes. (3) The initial Hβ bright kernels occurred in the vicinity of the neutral line of vertical current (Jz = 0) with a steep gradient, but not just on the sites of vertical current peaks. (4) The flares were probably triggered by the interaction between the new emerging electric current system and old current system.