Vertical Current Density Research Articles

Peculiarities of heat transfer at anodic plasma electrolytic treatment of cylindrical pieces

Heat transfer in a three-phase electrochemical system consisting of a metal cylindrical anode (a workpiece), a vapor-gas envelope, and an electrolyte solution is considered. The purpose of the study is to determine the effect of the length of the sample part contacting with the electrolyte on the distribution of the heating characteristics on its surface. It is established that the increase of the length of the part of the anode submerged into the electrolyte causes a decrease in the average current density, reduction in the vertical current density gradient, and a decrease in the density of the heat flux from the envelope to the sample. A model is proposed to calculate the stationary cylindrical anode temperature and the current in the system with the evaluation of the convective heat flux from the anode portion protruding above the electrolyte into the atmosphere. The influence of the electrolyte flow along the sample on its temperature and the average current density in the system is determined and attributed to the variation of the vapor-gas envelope thickness.

Dynamics of Undisturbed Midlatitude Atmospheric Electricity: From Observations to Scaling

Long-term dynamics of the electric field of the midlatitude near-surface atmosphere in a wide range of temporal scales is analyzed according to multiyear observatory and seasonal field observations. It is found that the daily dynamics of the aeroelectric field at mid-latitudes most authentically repeats a diurnal variation for the winter months. It is stated that short-period pulsations of the electric field have a self-similar power-law spectrum. Spatio-temporal scales of the self-similarity interval are estimated and the nature of the generalized diffusive process of the aeroelectric pulsation generation is defined. Characteristics of the turbulent ΔE pulsations are analyzed. Estimates of interrelation between the dynamic (fractal dimensions, intermittency indices) and power (degrees of spectral index and structure function) ΔE characteristics are obtained. Mutual correlations between atmospheric electric field variations, vertical atmospheric electrical current density, space charge density, and atmospheric electrical conductivity are studied. It is shown that variations of the light atmospheric ion number density and space charge density are related with variations of the Radon-222 emanations. Spectral analysis of the space charge density variations is carried out. It is shown that the electrodynamic state of the surface atmosphere depends on the convective state of the atmospheric boundary layer.

Space weather driven changes in lower atmosphere phenomena

During a period of heliospheric disturbance in 2007–9 associated with a co-rotating interaction region (CIR), a characteristic periodic variation becomes apparent in neutron monitor data. This variation is phase-locked to periodic heliospheric current sheet crossings. Phase-locked electrical variations are also seen in the terrestrial lower atmosphere in the southern UK, including an increase in the vertical conduction current density of fair weather atmospheric electricity during increases in galactic cosmic ray-induced neutron monitor count rate at the surface and energetic proton count rates measured by geosynchronous spacecraft. At the same time as the conduction current increases, changes in the cloud microphysical properties lead to an increase in the detected height of the cloud base at Lerwick Observatory, Shetland, with associated changes in surface meteorological quantities. As electrification is expected at the base of layer clouds, which can influence droplet properties, these observations of phase-locked thermodynamic, cloud, atmospheric electricity and solar sector changes are not inconsistent with a heliospheric disturbance driving lower troposphere changes.

Effects of sudden stratospheric warming (SSW) on the lunitidal modulation of the F‐region dynamo

The E‐region dynamo in the equatorial ionosphere changes significantly during Sudden Stratospheric Warming (SSW) events. However, little is known about the modulation of the F‐region dynamo by SSW events. During the SSW event of December 2001 the vertical current density in the daytime equatorial F‐region, as observed by the CHAMP satellite, exhibited oscillations with a 13‐day period. This period reflects the lunar tide in the CHAMP satellite data. Two independent drivers are known to contribute to the F‐region vertical current: thermospheric zonal wind (F‐region dynamo) and vertical electric field (E‐region dynamo). The thermospheric zonal wind as observed by CHAMP was modulated in a similar way as the F‐region vertical current. Vertical electric field in the equatorial F‐region can be estimated from the magnetic and plasma/neutral observations of the CHAMP satellite. The obtained values also show quasi 13‐day modulations. The thermospheric wind and vertical electric field drove the F‐region vertical currents in opposite directions, and the polarity of the net current generally followed the former (F‐region dynamo). From the observed phase delays of the 13‐day oscillations we conclude that the F‐region vertical current during the SSW event was not only modulated by the variation of the thermospheric wind but also by the variations of the E‐region electric field and the F‐region plasma density distribution.

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.

Modeling and Interpreting the Effects of Spatial Resolution on Solar Magnetic Field Maps

Different methods for simulating the effects of spatial resolution on magnetic field maps are compared, including those commonly used for inter-instrument comparisons. The investigation first uses synthetic data, and the results are confirmed with {\it Hinode}/SpectroPolarimeter data. Four methods are examined, one which manipulates the Stokes spectra to simulate spatial-resolution degradation, and three "post-facto" methods where the magnetic field maps are manipulated directly. Throughout, statistical comparisons of the degraded maps with the originals serve to quantify the outcomes. Overall, we find that areas with inferred magnetic fill fractions close to unity may be insensitive to optical spatial resolution; areas of sub-unity fill fractions are very sensitive. Trends with worsening spatial resolution can include increased average field strength, lower total flux, and a field vector oriented closer to the line of sight. Further-derived quantities such as vertical current density show variations even in areas of high average magnetic fill-fraction. In short, unresolved maps fail to represent the distribution of the underlying unresolved fields, and the "post-facto" methods generally do not reproduce the effects of a smaller telescope aperture. It is argued that selecting a method in order to reconcile disparate spatial resolution effects should depend on the goal, as one method may better preserve the field distribution, while another can reproduce spatial resolution degradation. The results presented should help direct future inter-instrument comparisons.

The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare

Solar flares occur due to the sudden release of energy stored in active-region magnetic fields. To date, the pre-cursors to flaring are still not fully understood, although there is evidence that flaring is related to changes in the topology or complexity of an active region's magnetic field. Here, the evolution of the magnetic field in active region NOAA 10953 was examined using Hinode/SOT-SP data, over a period of 12 hours leading up to and after a GOES B1.0 flare. A number of magnetic-field properties and low-order aspects of magnetic-field topology were extracted from two flux regions that exhibited increased Ca II H emission during the flare. Pre-flare increases in vertical field strength, vertical current density, and inclination angle of ~ 8degrees towards the vertical were observed in flux elements surrounding the primary sunspot. The vertical field strength and current density subsequently decreased in the post-flare state, with the inclination becoming more horizontal by ~7degrees. This behaviour of the field vector may provide a physical basis for future flare forecasting efforts.

Fair weather atmospheric electricity

Not long after Franklin's iconic studies, an atmospheric electric field was discovered in "fair weather" regions, well away from thunderstorms. The origin of the fair weather field was sought by Lord Kelvin, through development of electrostatic instrumentation and early data logging techniques, but was ultimately explained through the global circuit model of C.T.R. Wilson. In Wilson's model, charge exchanged by disturbed weather electrifies the ionosphere, and returns via a small vertical current density in fair weather regions. New insights into the relevance of fair weather atmospheric electricity to terrestrial and planetary atmospheres are now emerging. For example, there is a possible role of the global circuit current density in atmospheric processes, such as cloud formation. Beyond natural atmospheric processes, a novel practical application is the use of early atmospheric electrostatic investigations to provide quantitative information on past urban air pollution.

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.

Current carriers near dipolarization fronts in the magnetotail: A THEMIS event study

[1] We study current carriers observed within thin current sheets ahead of and during the passage of earthward moving dipolarization fronts in the near‐Earth plasma sheet using Time History of Events and Macroscale Interactions During Substorms (THEMIS) multipoint measurements. The fronts are embedded within flow bursts at the initial stage of bursty bulk flow events. Simultaneous north‐south and radial separations between probes P3, P4, and P5 and the planar current sheet approximation enable estimation of cross‐tail current density in the current sheet ahead of and within the fronts, respectively. The cross‐tail current density increase ahead of the fronts, a substorm growth phase signature, is predominantly due to the ion diamagnetic current; at times, however, the electron pressure gradient may contribute up to 60% of the total current density. Note that in this paper we refer to the horizontal (vertical) current sheet as the cross‐tail current sheet (current sheet associated with dipolarization fronts). At the dipolarization fronts, the horizontal cross‐tail current sheet (with a current density of several nA/m 2 ) relaxes, and a vertical current sheet (with a current density of several tens of nA/m 2 ), consistent with the thin interface of the front, appears. Thus, the cross‐tail current at longitudes adjacent to the flow burst feeds into the dipolarization front’s current sheet and may be extended to higher latitudes. The vertical current density also decreases after passage of the front. The pressure gradient of 1–10 keV electrons is a dominant contributor to the current in the dipolarization fronts. In the event studied, probes P1 and P2, which were several Earth radii downtail, reveal a tailward expansion of the current reduction process at a propagation velocity ∼50 km/s, even as the bulk flow carrying the magnetic flux remains earthward. This study shows how dipolarization fronts and their current systems are building blocks of the large‐scale substorm current wedge.

VECTOR MAGNETIC FIELDS AND CURRENT HELICITIES IN CORONAL HOLES AND QUIET REGIONS

In the solar photosphere, many properties of coronal holes (CHs) are not known, especially vector magnetic fields. Using observations from \emph{Hinode}, we investigate vector magnetic fields, current densities and current helicities in two CHs and compare them with two normal quiet regions (QRs) for the first time. We find that, in the CHs and QRs, the areas where large current helicities are located are mainly co-spatial with strong vertical and horizontal field elements both in shape and location. In the CHs, horizontal magnetic fields, inclination angles, current densities and current helicities are larger than those in the QRs. The mean vertical current density and current helicity, averaged over all the observed areas including the CHs and QRs, are approximately 0.008 A m$^{-2}$ and 0.005 G$^{2}$ m$^{-1}$, respectively. The mean current density in magnetic flux concentrations where the vertical fields are stronger than 100 G is as large as 0.012 $\pm$ 0.001 A m$^{-2}$, consistent with that in the flare productive active regions. Our results imply that the magnetic fields, especially the strong fields, both in the CHs and QRs are nonpotential.

Self-organized criticality in solar flares: a cellular automata approach

Abstract. We give an overview of a novel lattice-based avalanche model that reproduces well a number of observed statistical properties of solar flares. The anisotropic lattice is defined as a network of vertically-connected nodes subjected to horizontal random displacements mimicking the kinks introduced by random motions of the photospheric footpoints of magnetic fieldlines forming a coronal loop. We focus here on asymmetrical driving displacements, which under our geometrical interpretation of the lattice correspond to a net direction of twist of the magnetic fieldlines about the loop axis. We show that a net vertical electrical current density does build up in our lattice, as one would expect from systematic twisting of a loop-like magnetic structure, and that the presence of this net current has a profound impact on avalanche dynamics. The presence of an additional energy reservoir tends to increase the mean energy released by avalanches, and yield a probability distribution of released energy in better agreement with observational inferences than in its absence. Symmetrical driving displacements are in better conceptual agreement with a random shuffling of photospheric footpoint, and yield a power-law distribution of energy release with exponent larger than 2, as required in Parker's nanoflare model of coronal heating. On the other hand, moderate asymmetrical driving generate energy distribution exponents that are similar to those obtained from SOHO EUV observations.

First results of fair-weather atmospheric electricity measurements in Northeast India

During the month of March 2006, a short campaign was conducted to measure fair-weather atmospheric electricity parameters in Tripura, Northeast India (23.50°N, 91.25°E). The campaign was the first of its kind in this region of the globe. The main objective of the campaign was to characterize the diurnal variation of three parameters namely vertical potential gradient (E), vertical air-earth current density (J z ) and atmospheric electrical conductivity (σ) in fair-weather conditions. The diurnal variation of E and J z over sixteen fair-weather days shows two distinct maxima around 14UT and 20UT and a minimum around 03UT. The average vertical potential gradient is found to be 108V·m−1 and air-earth current density 1.85 pA·m−2. The average bipolar atmospheric electrical conductivity at the ground level is found to be 19.6 fS·m−1. An excellent positive correlation between E and J z is found, with a correlation coefficient of 0.96. A comparative study with Carnegie universal variation shows 70% correlation with observed variation of vertical potential gradient during the period of the campaign. The results are discussed in view of difficulty as well as possibility of getting global signatures in atmospheric electricity measurements made from tropical land stations.

Solar modulation in surface atmospheric electricity

The solar wind modulates the flux of galactic cosmic rays impinging on Earth inversely with solar activity. Cosmic ray ionisation is the major source of air's electrical conductivity over the oceans and well above the continents. Differential solar modulation of the cosmic ray energy spectrum modifies the cosmic ray ionisation at different latitudes, varying the total atmospheric columnar conductance. This redistributes current flow in the global atmospheric electrical circuit, including the local vertical current density and the related surface potential gradient. Surface vertical current density and potential gradient measurements made independently at Lerwick Observatory, Shetland, from 1978 to 1985 are compared with modelled changes in cosmic ray ionisation arising from solar activity changes. Both the lower troposphere atmospheric electricity quantities are significantly increased at cosmic ray maximum (solar minimum), with a proportional change greater than that of the cosmic ray change.

Vertical current flow through extensive layer clouds

The global atmospheric electrical circuit sustains a vertical current density between the ionosphere and the Earth's surface, the existence of which is well-established from measurements made in fair-weather conditions. In overcast, but non-thunderstorm, non-precipitating conditions, the current travels through the cloud present, despite cloud layers having low electrical conductivity. For extensive layer clouds, this leads to space charge at the upper and lower cloud boundaries. Using a combination of atmospheric electricity and solar radiation measurements at three UK sites, vertical current measurements have been categorised into clear, broken, and overcast cloud conditions. This approach shows that the vertical “fair weather” current is maintained despite the presence of cloud. In fully overcast conditions with thick cloud, the vertical current is reduced compared to thin cloud overcast conditions, associated with the cloud's resistance contributions. Contribution of cloud to the columnar resistance depends both on cloud thickness, and the cloud's height.

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 three-dimensional structure of sunspots

Aims. We investigate the height dependence of the magnetic field of a sunspot, which has been until now a controversial issue. Methods. Full-Stokes profiles of a sunspot, derived from infrared spectro-polarimetric measurements, were investigated. The magnetic field strength, inclination and azimuth were obtained using an inversion code. The results from two different spectral lines deliver the height dependence of the magnetic vector field. Vertical current densities and helicities as well as the vertical derivative of the vertical component of the magnetic field strength are calculated using Maxwell’s equations. Results. Inside the spot, the total magnetic field strength decreases with height, even in the outer penumbra, where the opposite trend was reported by other investigators. Outside the spot, the field strength increases with height apart from at a few small locations. This result is interpreted in terms of magnetic canopies. Magnetic field lines are less inclined in higher layers everywhere in the field of view. In the umbra, the vertical component of the magnetic field decreases by values in the range 0.5–2.2 G km −1 , depending on the applied method. Mean values in the inner penumbra are smaller than in the umbra. In the outer penumbra, the vertical magnetic component increases independently of the local intensity distribution. A pore close to the spot exhibits a more rapid decrease with height than the spot itself. The electric current densities and helicities depend on the fine structure of the sunspots. Typical values of the current densities vary in the range ±40 mA m −2 . The mean values are −11 mA m −1 for the umbra and − 2m A m −1 for the penumbra, respectively, but the propagated errors are of the same order as the mean values. There are indications that the radial structure of the penumbra is related to enhanced current densities, but at the present resolution we are unable to establish a correlation with local intensity fluctuations. Conclusions. If the spatial resolution is sufficiently high, electric current densities and helicities could be applied as reliable diagnostic tools for understanding penumbral fine structure.

Enhancement of cloud formation by droplet charging

Charge affects the activation of cloud droplets by reducing the minimum supersaturation at which haze droplets begin to grow. Although the droplet charge required to enhance activation is substantial, we show that sufficient charging occurs at the edges of layer clouds because the fair-weather current in the global atmospheric electrical circuit flows through a discontinuity in conductivity. Our theory predicts that droplet neutralization will cause a transient cooling of cloud base. This hypothesis was tested during a period of extreme solar activity, when we detected transient current bursts at the surface beneath a layer of cloud. We attribute these to bursts of ion production, which would cause transient droplet neutralization in the cloud and an associated increase in droplet critical supersaturation. We observed transient decreases in downward long-wave radiation measurements coincident with the transient current bursts. As the vertical current density passing through stratiform clouds is a global phenomenon, there are many regions in which a charge enhancement effect on cloud formation can potentially occur; we find that the effect of charge-enhanced activation on surface radiation in the present-day climate could be as large as 0.1 W m −2 .