Vertical Current Density Research Articles

Surface measurement system for the atmospheric electrical vertical conduction current density, with displacement current density correction

Global thunderstorm and shower cloud activity generate the global electric potential difference between the Earth's surface and the lower ionosphere. The finite conductivity of atmospheric air, which arises from cosmic ray and natural radioactive ionisation, permits a vertical conduction current density (∼1 pA m −2) between the lower ionosphere and the surface during fair-weather conditions; this current provides a physical link between the upper and lower atmospheres. A new instrument system is described to measure the conduction current density at the surface (the “air–Earth current”), which operates on a novel principle using two collecting electrodes of different geometry. Simultaneous measurements from two independent co-located systems using the geometrical principle show close agreement (correlation of 0.96 during 2.5 h of 5 min measurements). The sensor design described is durable and successful measurements in fair and disturbed weather have been obtained in air temperatures between −6 and 35 °C, relative humidity between 44% and 100%, fog, rain and snowfall. The uncertainty in conduction current density determinations is 0.20 pA m −2.

Multi-station synthesis of early twentieth century surface atmospheric electricity measurements for upper tropospheric properties

Abstract. The vertical columnar current density in the global atmospheric electrical circuit depends on the local columnar resistance. A simple model for the columnar resistance is suggested, which separates the local boundary layer component from the upper troposphere cosmic ray component, and calculates the boundary layer component from a surface measurement of air conductivity. This theory is shown to provide reasonable agreement with observations. One application of the simple columnar model theory is to provide a basis for the synthesis of surface atmospheric electrical measurements made simultaneously at several European sites. Assuming the ionospheric potential to be common above all the sites, the theoretical air-earth current density present in the absence of a boundary layer columnar resistance can be found by extrapolation. This is denoted the free troposphere limit air-earth current density, J0. Using early surface data from 1909 when no ionospheric potential data are available for corroboration, J0 is found to be ~6 pA m−2, although this is subject to uncertainties in the data and limitations in the theory. Later (1966–1971) European balloon and surface data give J0=2.4 pA m−2.

Rapid fluctuations of stratospheric electric field following a solar energetic particle event

[1] During January, 2005, there were several large X-class solar flares and associated solar energetic particle (SEP) events. Coincidentally, the MINIS balloon campaign had multiple payloads aloft in the stratosphere above Antarctica measuring dc electric fields, conductivity and x-ray flux. One-to-one increases in the electrical conductivity and decreases to near zero of both the vertical and horizontal electric field components were observed in conjunction with an increase in particle flux at SEP onset. Combined with an atmospheric electric field mapping model, these data are consistent with a shorting out of the global electric circuit and point toward substantial ionospheric convection modifications. Additionally, two subsequent, rapid changes were detected in the vertical electric field component several hours after SEP onset. These changes result in similar fluctuations in the calculated vertical current density. We will describe how rigidity cut-off dynamics may be crucial in understanding these sudden jumps in the vertical electric field.

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.

An Overview of Existing Algorithms for Resolving the 180° Ambiguity in Vector Magnetic Fields: Quantitative Tests with Synthetic Data

We report here on the present state-of-the-art in algorithms used for resolving the 180° ambiguity in solar vector magnetic field measurements. With present observations and techniques, some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.

Vertical current densities and magnetic gradients in sunspots

Aims. The vertical component of electric current densities and the height dependence of the vertical component of the magnetic field in sunspots were determined. Methods. Full-Stokes magnetograms of eight sunspots obtained from infrared spectro-polarimetric measurements were investigated. The magnetic field strength and the magnetic inclination and azimuth were obtained from an inversion code. Vertical current densities and the vertical derivative of the vertical component of the magnetic field strength resulted from Maxwell equations. Results. It is found that electric current densities and magnetic gradients depend on the finestructure of the sunspots. Typical values for current densities vary in the range ±40 mA m -2 , but their errors are of the same order. Disturbances in the radial structure of the penumbra are related to enhanced current densities up to 149 mA m -2 , and a maximum value of 166 mA m -2 was found in a light bridge. There are indications that the radial structure of the penumbra is related to current densities, but no correlation to the local intensity fluctuations was found in the outer penumbra. The vertical component of the magnetic field decreases by 0.5-1.5 G km -1 in the umbra. Mean values in the inner penumbra are somewhat smaller than in the umbra, and locally dark structures exhibit a faster decrease with height than bright ones. In the outer penumbra the vertical magnetic component increases, independent of the local intensity distribution. Conclusions. Electric current densities could be a diagnostic tool for understanding the penumbral finestructure, although the presently available spatial resolution is probably not good enough to avoid artifacts. Magnetic extrapolations might depend crucially on this problem.

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.

On the variability of the stratospheric column resistance in the global electric circuit

There is a discrepancy between the observed amplitudes of vertical current density ( J z ) and electric field ( E z ) in the global circuit responding to inputs modulated by solar activity, as compared to modeled amplitudes. These responses to estimated changes in ionization production are larger than modeled and increase with increasing content of stratospheric aerosol. The discrepancies could be resolved if the column resistance of the stratosphere and upper troposphere is greater than previously calculated due to two effects. The first is the presence of very thin cirrus, subvisible clouds, aerosol and polar stratospheric clouds near the tropopause level and in the lower stratosphere. They raise the resistivity there so that the changes in the lower energy galactic cosmic ray flux, at those altitudes and at middle to high latitudes where the changes are larger than elsewhere, can increase the sensitivity of the global circuit to the solar modulation of the GCR energy spectrum. The second effect is postulated to be most important at times of high stratospheric aerosol loading and is attributed to the presence of a layer of ultrafine H 2SO 4/H 2O aerosol particles that is only present in the descending part of the stratospheric diabatic circulation at middle and high latitudes. With average levels of precipitating relativistic electron flux at those latitudes, the layer has little effect on the ionosphere–Earth column resistance, but for very low flux levels, such as following solar wind heliospheric current sheet crossings, the reduced ionization production allows the column resistance of the layer to rise to become a non-negligible fraction of the total ionosphere–Earth column resistance. This variation in column resistance modulates J z at those latitudes, consistent with the variations that have been inferred from the sparse observations of J z that are available and from observations of other phenomena thought to be causes and effects of the J z variations.

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.

Vertical Lorentz Force and Cross‐Field Currents in the Photospheric Magnetic Fields of Solar Active Regions

We demonstrate that the vertical Lorentz force and a corresponding lower limit of the cross-field electric current density can be calculated from vector magnetograms of solar active regions obtained at a single height in the solar atmosphere, provided that the vertical gradient of the magnetic field strength is known at this height. We use a predicted vertical magnetic field gradient derived from a previous analysis. By testing various force-free solutions, we find that the numerical accuracy of our method is satisfactory. Applying the method to active region photospheric vector magnetograms, we find vertical Lorentz forces ranging from several hundredths to a few tenths of the typical photospheric gravitational force, and typical cross-field current densities up to several times 10 mA m-2. The typical vertical current density is found to be 2-3 times smaller, on the order of 10-15 mA m-2. These differences are above the associated uncertainties. The values of the cross-field currents decrease in an averaged vector magnetogram, but the ratio of the cross-field to the vertical current density increases, also above the uncertainties. We conclude that the photospheric active region magnetic fields are not force-free, contrary to the conjectures of some recent studies.

Influence of Magnetic Field on Electromagnetic Instabilities in Semiconductor Superlattices

Electromagnetic instability criteria in semiconductor superlattices (SL) in the region of a negative differential conductivity (NDC) are studied in the presence of a static transverse field. The regimes with vertical constant electric field in a "short" plate of SL and with vertical current density vector in a "long" plate are considered. The effective differential conductivity tensors for both these regimes are derived and the influence of the magnetic field on the NDC threshold and the growth increment is investigated. The frequencies of the excited waves and the dependence of the growth increment on the direction of propagation for the extraordinary waves are determined.

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.

Atmospheric transparency changes associated with solar wind-induced atmospheric electricity variations

Variations in atmospheric transmission of several percent in nominally clear air are found to accompany solar wind events associated with variations on the day-to-day timescale in the flow of vertical current density ( J z ) in the global electric circuit. The effect has been observed only for stations at high latitudes (>55°N). Increases in transmission are present when inferred J z decreases occurred without changes in tropospheric ion production. These events occurred when there was a high loading of stratospheric aerosols. Responses of opposite sign, i.e., decreases in transmission, are present when Forbush decreases of galactic cosmic ray flux occur, but only during periods of low stratospheric aerosol loading. Forbush decreases are associated with both tropospheric ion production decreases and J z decreases. Similar effects are present on the 11-year solar cycle, with climate consequences that have yet to be analyzed. The mechanisms for these phenomena are not understood, but the nature of the observations suggests that explanations should be sought in terms of theories of the effects of electric charge on the formation of aerosols, and/or effects of charged aerosols on the microphysics of vapor–water–ice conversions.

Photospheric Magnetic Field Properties of Flaring versus Flare‐quiet Active Regions. I. Data, General Approach, and Sample Results

Photospheric vector magnetic field data from the University of Hawai'i Imaging Vector Magnetograph, with good spatial and temporal sampling, are used to study the question of identifying a preflare signature unique to flare events in parameters derived from the magnetic vector field, B. In this first of a series of papers, we present the data analysis procedure and sample results focusing only on three active regions (NOAA Active Regions 8636, 8771, and 0030), three flares (two M class and one X class), and (most importantly) a flare-quiet epoch in a comparable flare-producing region. Quantities such as the distribution of the field morphology, horizontal spatial gradients of the field, vertical current, current helicity, "twist" parameter α, and magnetic shear angles are parameterized using their moments and appropriate summations. The time series of the resulting parameterizations are examined one at a time for systematic differences in overall magnitude and evolution between the flare and flare-quiet examples. The variations expected due to atmospheric seeing changes are explicitly included. In this qualitative approach we find (1) no obvious flare-imminent signatures from the plain magnetic field vector and higher moments of its horizontal gradient or from most parameterizations of the vertical current density; (2) counterintuitive but distinct flare-quiet implications from the inclination angle and higher moments of the photospheric excess magnetic energy; (3) flare-specific or flare-productivity signatures, sometimes weak, from the lower moments of the field gradients, kurtosis of the vertical current density, magnetic twist, current helicity density, and magnetic shear angle. The strongest results are, however, that (4) in ensuring a flare-unique signature, numerous candidate parameters (considering both their variation and overall magnitude) are nullified on account of similar behavior in a flare-quiet region, and hence (5) considering parameters one at a time in this qualitative manner is inadequate. To address these limitations, a quantitative statistical approach is presented in Paper II by Leka & Barnes.

Direct observation of lateral current spreading in ridge waveguide lasers using scanning voltage microscopy

We report results of two-dimensional (2D) local voltage measurement of the transverse cross section of operating multiquantum-well ridge-waveguide (RWG) lasers. We observe lateral nonuniformity of local voltage in the n-cladding layers of the laser and attribute the voltage variation to 2D carrier transport effect within the RWG lasers. The quantitative evaluation of this effect indicates the local vertical current density to be ∼40% smaller at the edge of the ridge than at its center. Our results demonstrate the strength and application of scanning voltage microscopy technique in quantitatively delineating 2D current flow in operating optoelectronic devices.

A New Method for Resolving the 180° Ambiguity in Solar Vector Magnetograms

We present a new method to resolve the 180° ambiguity for solar vector magnetogram measurements. The basic assumption is that the magnetic shear angle (Δθ), which is defined as the difference between the azimuth components of observed and potential fields, approximately follows a normal distribution. The new method is composed of three steps. First, we apply the potential field method to determine the azimuthal components of the observed magnetic fields. Second, we resolve the ambiguity with a new criterion: −90°+ΔθmpleΔθle90°+Δθmp, where Δθmp is the most probable value of magnetic shear angle from its number distribution. Finally, to remove some localized field discontinuities, we use the criterion Bt⋅Bmtge0, where Bt and Bmt are an observed transverse field and its mean value for a small surrounding region, respectively. For an illustration, we have applied the new ambiguity removal method (Uniform Shear Method) to a vector magnetogram which covers a highly sheared region near the polarity inversion line of NOAA AR 0039. As a result, we have found that the new ambiguity solution was successful and removed spatial discontinuities in the transverse vector fields produced in the magnetogram by the potential field method. It is also found that our solution to the ambiguity gives nearly the same results, for highly sheared vector magnetograms and vertical current density distributions, of NOAA AR 5747 and AR 6233 as those of other methods. The validity of the basic assumption for an approximate normal distribution is demonstrated by the number distributions of magnetic shear angle for the three active regions under consideration.

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.

Coronal Heating in Active Regions as a Function of Global Magnetic Variables

A comparison of X-ray images of the Sun and full disk magnetograms shows a correlation between the locations of the brightest X-ray emission and the locations of bipolar magnetic active regions. This correspondence has led to the generally accepted idea that magnetic fields play an essential role in heating the solar corona. To quantify the relationship between magnetic fields and coronal heating, the X-ray luminosity of many different active regions is compared with several global (integrated over entire active region) magnetic quantities. The X-ray measurements were made with the SXT Telescope on the Yohkoh spacecraft; magnetic measurements were made with the Haleakala Stokes Polarimeter at the University of Hawaii's Mees Solar Observatory. The combined data set consists of 333 vector magnetograms of active regions taken between 1991 and 1995; X-ray luminosities are derived from time averages of SXT full-frame desaturated (SFD) images of the given active region taken within ±4 hours of each magnetogram. Global magnetic quantities include the total unsigned magnetic flux Φtot ≡ ∫ dA|Bz|, B2z tot ≡ ∫ dAB2z, Jtot ≡ ∫dA|Jz|, and B2⊥,tot ≡ ∫ dAB2⊥, where Jz is the vertical current density and Bz and B⊥ are the vertical and horizontal magnetic field amplitudes, respectively. The X-ray luminosity LX is highly correlated with all of the global magnetic variables, but it is best correlated with the total unsigned magnetic flux Φtot. The correlation observed between LX and the other global magnetic variables can be explained entirely by the observed relationship between those variables and Φtot. In particular, no evidence is found that coronal heating is affected by the current variable Jtot once the observed relationship between LX and Φtot is accounted for. A fit between LX and Φtot yields the relationship LX 1.2 × 1026 ergs s-1(Φtot/1022 Mx)1.19. The observed X-ray luminosities are compared with the behavior predicted by several different coronal heating theories. The Alfven wave heating model predicts a best relationship between LX and Φtot, similar to what is found, but the observed relationship implies a heating rate greater than the model can accommodate. The Nanoflare Model of Parker predicts a best relationship between LX and B2z,tot rather than Φtot, but the level of heating predicted by the model can still be compared to the observed data. The result is that for a widely used choice of the model parameters, the nanoflare model predicts 1.5 orders of magnitude more heating than is observed. The Minimum Current Corona model of Longcope predicts a qualitative variation of LX with Φtot that agrees with what is observed, but the model makes no quantitative prediction that can be tested with the data. A comparison between LX and the magnetic energy Emag in each active region leads to a timescale that is typically 1 month, or about the lifetime of an active region, placing an important observational constraint on coronal heating models. Comparing the behavior of solar active regions with nearby active stars suggests that the relationship observed between LX and Φtot may be a fundamental one that applies over a much wider range of conditions than is seen on the Sun.

Joule heating due to vertical ion currents in the lower thermosphere over the dip equator

The theory of equatorial electrojet predicts the presence of vertical ion currents (Pedersen currents) as a part of the electrojet current system. The vertical ion current density profile over the dip equator, that forms a part of the meridional current system is derived from an electrojet model. The joule heating due to these currents flowing upward during daytime for a local time for 1100 hrs has been estimated. The primary east-west current density of the model is kept at the same value as that measured by means of rocket-borne magnetometer on one occasion. The electrical power dissipated as heat in the narrow belt in the height region of 100–180 km is estimated and found to be significant. The height of maximum power dissipation coincides with the altitude of maximum ion velocity i.e. 122 km. By solving the heat conduction equation we obtain a maximum temperature increase of 8°K around 135 km. The importance of this localized heating in the lower thermosphere around ±2° of the dip equator is discussed.

Stability of interfacial waves in aluminium reduction cells

We investigate the stability of interfacial waves in conducting fluids under the influence of a vertical current density, paying particular attention to aluminium reduction cells in which such instabilities are commonly observed. We develop a wave equation for the interface in which the Lorentz force is expressed explicitly in terms of the fluid motion. Our wave equation differs from previous models, most notably that developed by Urata (1985), in that earlier formulations rested on a more complex, implicit coupling between the fluid motion and the Lorentz force. Our formulation furnishes a number of quite general stability results without the need to resort to Fourier analysis. (The need for Fourier analysis typifies previous studies.) Moreover, our equation supports both travelling and standing waves. We investigate each in turn.We obtain three new results. First, we show that travelling waves may become unstable in the presence of a uniform, vertical magnetic field. (Our travelling waves are quite different to those discovered by previous investigators (Sneyd 1985 and Moreau & Ziegler 1986) which require more complex magnetic fields to become unstable.) Second, in line with previous studies we confirm that standing waves may also become unstable. In this context we derive a simple energy criterion which shows which types of motion may extract energy from the background magnetic field. This indicates that a rotating, tilted interface is particularly prone to instability, and indeed such a motion is often seen in practice. Finally, we use Gershgorin's theorem to produce a sufficient condition for the stability of standing waves in a finite domain. This allows us to place a lower bound on the critical value of the background magnetic field at which an instability first appears, without solving the governing equations of motion.