The pioneering work of about the open nature of the magnetosphere and the role of magnetic reconnection processes between the interplanetary magnetic field (IMF) and the geomagnetic main field paved the way for the understanding of the large-scale structure and dynamics of the Earth's spatial environment. It provided the theoretical framework for subsequent successful investigations to understand the solar-wind–magnetosphere–ionosphere–thermosphere coupling processes over several decades .

The reconnection processes on the dayside give rise to open magnetic flux areas, the polar caps, and together with the nightside reconnections, they are driving a large-scale internal magnetospheric plasma convection and current systems that connect magnetospheric and ionospheric domains. Due to the large variability of the solar wind and IMF conditions, the whole system is very dynamic and the amount of open flux in the polar cap changes continuously. The theoretical understanding of the polar cap formation and its time evolution was advanced to the fully time-dependent “expanding-contracting polar cap” (ECPC) paradigm by the work of . A comprehensive review of all the aspects of the magnetosphere–ionosphere–thermosphere interaction processes under the solar wind driver was provided recently by .

The principal pattern of the large-scale field-aligned current (FAC) system, also known as Birkeland currents, which form the circumpolar belts of Region-1 (on the poleward side) and Region-2 FACs (on the equatorward side), was disclosed by the work of . On the dayside adjacent to the cusp region, so-called Region-0 FACs are observed . Using MAGSAT satellite data, showed the existence of a particular FAC system in the dayside sector of the polar cap, the so-called NBZ Birkeland currents for intervals of positive IMF Bz.

From ground-based magnetometer observations, the high-latitude electrojets have already been studied prior to the space era cf.. The particularities of high-latitude ionospheric current systems during magnetic disturbances were known empirically . revealed high-latitude current systems for summer conditions, which are controlled by the IMF components and solar wind parameters. Based on such equivalent current systems and considering information about the anisotropic ionospheric conductivity, showed the possibility to determine a full current system, including FACs and horizontal currents in the ionosphere. Such a full current system can be estimated as a combination of the equivalent currents obtained both from ground-based and satellite observations of the magnetic variations .

An intense study of the polar electrojet (PE) at the high-latitude daytime ionosphere was initiated by the works of and . They demonstrated that its characteristic magnetic field variation depends on the sector structure of the IMF that is much like the average magnetic field of the solar photosphere. The IMF sector structure does not always correspond to the expected magnetic field variations in the near-polar region. showed that during periods of discrepancy between the expected magnetic variations and the sector structure from satellite observations, an essential deviation of the IMF from the usual spiral structure always existed. During these cases, the azimuthal IMF By component was oppositely directed to the expected direction of the spiral. This implies that the magnetic variation on the ground is not primarily controlled by the sector structure (toward or away the sun), but by the azimuthal component of the IMF (eastward or westward).

Various methods have been developed for the extraction of the PE magnetic field variations from ground-based observations in the near-polar region . The most effective approach appeared to be the correlation method . It is based on the fact that both the direction of the PE and its intensity depend on the IMF By component. The method allows for the separation of the magnetic variations of the PE from variations of other sources and shows the spatial–temporal variation of the PE vector variations very clearly. described the findings of a geomagnetically quiet interval in summer 1965 and the characteristics of the equivalent current system controlled by the IMF By component. In a first step, time intervals with correlations of the magnetic X(H), Y, and Z components with IMF By were identified for observatories with Φ>65∘. In case of existing correlations, they always appeared to be practically close to a linear dependence with a correlation coefficient r. Correlation was assumed to exist for values of r>0.4; otherwise (for r≤0.4) it was assumed as non-existing. Such a boundary for significant r values is justified by the correlation correction Sr=(1-r2)/(n-1). For values of |r/Sr|≥3, the relation between the X(H), Y, and Z components with the IMF By cannot be regarded as accidental. With n∼50 the correlation is not randomly distributed for r>0.4 (corresponding to 95 % confidence interval).

Regression lines, which relate the ground magnetic variations with the IMF By component, were estimated for all MLTs, based on the observed intervals with r>0.4. They were used to describe the spatial–temporal distribution of the surface magnetic variations in the horizontal and vertical plane, and were finally used for the estimation of the equivalent current system for IMF By=6 nT. Its integral intensity amounts to 180 kA, with a maximum current intensity of the electrojet in the dayside sector of ∼0.5 A m-1 at 80∘<Φ<81∘. An analogous estimation for July–August 1966 resulted in a value of ∼0.35 A m-1 at the same latitudes .

The PE in the dayside sector does not disappear during magnetic disturbances . The PE shifts equatorward to 72∘ <Φ<74∘ in the longitudinal range of 08:00 < MLT < 17:00 during intense substorms (with AL ∼-800 nT), and during periods of geomagnetic storms with AL ∼-1200 nT and Dst ∼-150 nT, it is situated at 66∘ <Φ<68∘ between 09:00 < MLT < 15:00. The current intensities of the PE increase only slightly to about ∼0.5 A m-1.

The variations of the magnetic field at the Earth's surface at high latitudes, which were derived with the method of regression analysis, allowed for the determination of the IMF By control of the spatial–temporal distributions of the electric field potential at ionospheric altitudes as well as the ionospheric and field-aligned currents (FACs; ). The electric field potential for an inhomogeneous ionospheric conductivity is obtained by solving a second-order partial differential equation. used magnetic observations of the summer seasons in 1972 and 1973, while obtained it for summer 1968. The potential differences at cusp latitudes in the daytime sector are ∼20 kV for IMF By∼±6 nT.

used MAGSAT magnetic field data in a height range of 350< h <550 km to determine the strength and location of the auroral electrojets at 115 km altitude. For the first time, he showed the possibility of estimating the horizontal ionospheric currents from scalar magnetic measurements only. The ionospheric currents were modelled by hundreds of infinite linear currents perpendicular to the orbital plane of the spacecraft, with discretization intervals of 111 km. The problem of ionospheric current estimation is underdetermined, and its solution is not unique. In order to constrain the solution, a regularization method is used. The comparison of modelled and measured variations of the magnetic field along the satellite orbit on 04 December 1979 at 17:00 UT demonstrates the good agreement for the field-aligned component but a significant discrepancy for the field-perpendicular one. The discrepancy is mainly caused by magnetic fields of the FACs. The integral amplitude of the ionospheric currents during the interval from 28 November to 10 December 1979 yielded a correlation of r=0.88 with the AE-index.

The IMF By orientation influences not only the PE but also the movements of the auroral forms at cusp latitudes . Simultaneous with permanently poleward-moving discrete auroral forms at the equatorward boundary of the cusp, which are controlled by the IMF Bz component, east–west moving auroral forms exist. This azimuthal movement is controlled by IMF By, such that for By>0, the discrete forms move westward, and for By<0 they move eastward. The movement of the auroral forms is in an opposite direction to the PE current flow direction. This can be expected, because the discrete auroral forms and the channels of enhanced ionospheric conductivity are both due to precipitating electrons into the upper atmosphere. A detailed consideration of the interrelation between auroral luminosity, auroral particle precipitation, and the PE during magnetic disturbances was given by . As shown there, the strong convection channel is located on the dawn side of the polar cap for IMF By>0 and on the dusk side for By<0 conditions. The electron precipitation in the regime of the convection channel in the morning sector consists of a band (∼500 km) of structured precipitation. The PE is located on the high-latitude boundary of the structured luminosity region in the vicinity of the strong flow channel of magnetospheric convection close to the bright auroral arc. For By>0, this channel is located in the morning sector on the poleward side of the polar cap boundary, with FAC out of the ionosphere and FAC into the ionosphere equatorward of the polar cap boundary.

investigated variations in the location and density of the auroral electrojets, which were independently determined from both the ground-based (IMAGE magnetometer network) and satellite (CHAllenging Minisatellite Payload – CHAMP) measurements.

made use of the Hall current estimations for the intense magnetic storms on 31 March to 01 April 2001 and 17 April–21 April 2002 to investigate the position and current densities of auroral electrojets (westward electrojet, WE, and eastward electrojet, EE) as well as the relations of the electrojets to the Dst index and the IMF Bz component. The characteristics of the PE have not been considered by these authors. The currents were determined from scalar magnetic field measurements of the CHAMP satellite (orbit in the meridional plane of 15:00–03:00 and 16:00–04:00 MLT) according to the method of . The intensity of the WE on the nightside is, on average, 2 times larger than the EE on the dayside.

In this study we investigate not only the auroral electrojet, but also the polar electrojet characteristics during six intense magnetic summer storms. In Sect.  we present an overview of the CHAMP data used as well as the indices, which characterize the electromagnetic conditions in the near-Earth space during the geomagnetic storms under study. Section  provides a short description of the method for the determination of the Hall currents from CHAMP scalar magnetic records. In Sect.  we consider the latitudinal variation of the strength and position of the electrojets during different phases of the magnetic storm on 29 May 2003–30 May 2003. Particular attention is drawn to the polar electrojet (PE). The subsequent Sect.  provides detailed correlation analyzes and the discussion of the control of the current direction in the electrojets, its strength, and its latitudinal position by various indices. The Conclusion's Sect.  summarizes the main results of the study with respect to the Hall current variations during the various storm phases.

The CHAllenging Minisatellite Payload (CHAMP) spacecraft was launched on 15 July 2000 into a circular, near-polar orbit with an inclination of 87.3∘. From its initial orbital height at ∼460 km, it has decayed to ∼400 km in 2003 and ∼350 km after 5 years. The orbital plane precesses to earlier local times at a rate of about 1 h per 11 days, so that the orbit covers all local times within about 131 days. The data used in this study are scalar magnetic field measurements obtained with the Overhauser magnetometer (OVM) at the boom tip with a resolution of 0.1 nT. In order to isolate the magnetic effect of ionospheric currents in the satellite data, the contributions from all other sources have been removed from the scalar field readings, as described in the study of .

The CHAMP orbital intervals during various storm periods used for this study are listed in Table . The quantity, locations, and intensity of the peaks along the latitudinal current intensity distribution vary over the course of the storm development. For the description of the storm development, we utilize various solar and geomagnetic indices.

First, we employ the auroral electrojet index (AE), which is derived from geomagnetic variations in the horizontal component observed at 12 selected observatories along the auroral zone in the Northern Hemisphere (http://wdc.kugi.kyoto-u.ac.jp/aedir/index.html, last access: August 2018). The upper (AU) and lower envelope (AL) of the superposed plots of all the data from these stations are used in this study as functions of UT.

Further, we employ the SymH and AsyH indices, which describe the geomagnetic disturbances at midlatitudes in terms of longitudinally asymmetric (ASY) and symmetric (SYM) disturbances for the H component (http://wdc.kugi.kyoto-u.ac.jp/aeasy/index.html, last access: August 2018 or, alternatively, https://omniweb.gsfc.nasa.gov/ow_min.html, last access: August 2018). SymH is essentially the same as the Dst index, but with a different time resolution (1 min cadence).

Finally, proposed a new solar wind coupling function, representing the rate of magnetic flux opened at the magnetopause, dΦMP/dt, which is referred to here as Index N (IndN). It is used for the correlation analysis in the solar-terrestrial physics and is expressed as follows; IndN=dΦMP/dt=v4/3BT2/3sin⁡8/3(θc/2).

Here, Φ (or ΦPC) is the (open) magnetic flux that constitutes the polar cap, v describes the solar wind speed, or more precisely, the transport velocity of IMF field lines that approach the magnetopause. BT is the magnitude of the IMF, sin⁡8/3(θc/2) is the percentage of field lines, which subsequently merge, and the IMF clock angle θc is defined by θc=arctan⁡2(By/Bz). This function best describes the interaction between the solar wind and the magnetosphere over a wide variety of magnetospheric activity. IndN has a strong correlation with other indices that characterize both the plasma and the IMF in the solar wind as well as the processes in the magnetosphere. By means of a statistical study of the electrojet characteristics, the new function IndN was used together with the classical indices SymH, AsyH, and AL. For the determination of all indices throughout this study we used time averages of the overflight intervals.

Ionospheric currents at high latitudes, which are recorded by low-Earth orbiting (LEO) satellites as magnetic field deviations, represent the sum of FACs between the magnetosphere and ionosphere (Birkeland currents) and predominantly horizontal ionospheric currents, which flow mainly in the highly conducting ionospheric E layer below the satellite orbit.

The horizontal sheet currents are commonly decomposed in two different ways. The classical fundamental theorem of vector calculus, known as Helmholtz's theorem, states that any vector field can be decomposed into the sum of a curl-free and a divergence-free part. On the other hand, considering the relation to an electric field, the sheet current is composed of Pedersen currents, which flow in the direction transverse to the magnetic field and parallel to the electric field in the neutral wind frame of reference e.g., and Hall currents, which are perpendicular to both fields. The latter decomposition requires, however, the knowledge of the electric field in the neutral wind frame of reference, which is not given in our case.

Using the Helmholtz theorem, we assume the Hall currents to be divergence-free, i.e. they are supposed to close entirely within the ionosphere, while the Pedersen currents are curl-free, connecting essentially various branches of FACs. showed (see their Fig. 14) that during summer conditions, which is the case for the six storm intervals analyzed in this study, the divergence-free and curl-free ionospheric currents are mainly represented by the Hall and Pedersen currents, respectively.

The Hall current at high latitudes are derived from CHAMP scalar magnetometer records along the satellite orbits according to the method that was presented by . This method of Hall current estimation from scalar magnetometer records of satellites was proposed for the first time by . These calculations make use of a current model consisting of a series of 160 infinite current lines at an altitude of 110 km and separated by 1∘ in latitude. The magnetic field of the line currents were related to the current strength I according to the Biot–Savart law. The strength of each of the 160 current lines were derived from an inversion of the observed field residuals using a least-squares fitting approach. The model does not take into account the contributions from field-aligned and Pedersen currents, measured at CHAMP altitudes. The comparison with ground-based geomagnetic variations of the horizontal component that considers only the contributions from the ionospheric Hall current field, because the contributions from the field-aligned and the Pedersen currents largely cancel each other out , showed the applicability of the modelling assumptions by with high reliability, particularly for the estimation of the Hall currents.

The level of ionization in the near-noon hours at latitudes of 75∘ <Φ<80∘ decreases from the summer to winter season by about 1 order of magnitude . The PE current strength amounts to ∼0.1 A m-1 during winter, which makes it difficult to be measured adequately by magnetometers aboard satellites. Because of that we investigate only summer storms in this study: three storms with CHAMP orbits in the midday–midnight plane and three in the dawn–dusk plane (listed in Table ). Here, we describe only one of these storms, namely that of 29 May–30 May 2003. The five other storms are described in the Appendix of this paper.

The storm phases are identified in this study according to the SymH index, which describes, together with the AsyH index, the large-scale variations of the geomagnetic field with a 1 min cadence. In essence, SymH represents the mean value of the magnetic field deviation from the quiet-time level for a longitudinally distributed chain of six midlatitude stations.

The intensity of the ring current varies with longitude. This variability, denoted by the AsyH index, is determined as the range between the maximum and minimum magnetic field values of the disturbance field minus the SymH from the longitudinal chain of midlatitude stations.

The orbit of the CHAMP satellite in its ascending branch was on the dayside (∼14:00–16:00 MLT), while its descending branch was in the nighttime sector (∼02:00–04:00 MLT). Figure  shows various geomagnetic indices and the variation of the By and Bz components of the IMF during the storm progression together with the times of CHAMP satellite observations during crossings of the northern polar cap regions, indicated by dashed vertical lines. The respective CHAMP orbit numbers are given above the uppermost panel, with the first three digits on the left side and the last two digits in between the two vertical dashed lines that indicate the corresponding observation intervals.

The beginning of the main magnetic storm phase was identified during orbit 16233 at 22:24 UT, with an average SymH value of -61.6 nT for the overflight interval, while the minimum value of SymH was recorded during orbit 16234 at 23:59 UT (-123.5 nT) and orbit 16235 at 01:33 UT (-139.5 nT). The four orbits prior to the main phase (16229–16232) at 16:18–20:53 UT are characterized by the SymH values of -1.6, -35.6, -59.6, and -27.0 nT as well as the occurrence of three substorms with intensities according to AL values in the range of ∼-1600 to ∼-2400 nT. AsyH increases sharply prior to the beginning of the main phase (208.3 nT during orbit 16231) and during the beginning of the main phase (290.7 nT during orbit 16233). In the maximum of the main phase, the values of this index decrease to 75.5 nT during orbit 16234 and 145.0 nT during orbit 16235. Following the main phase, the recovery phase develops (orbits 16236–16240) at 03:03–09:21 UT, in the course of which the SymH values return to the initial values at ∼-60 nT, and AsyH decreases to 51 nT during orbit 16239.

Let us now consider the structure and the latitudinal variation of the position and strength of the electrojet during the various phases of the analyzed storm. The eastward (EE) and westward electrojet (WE) can exist in the daytime sector at latitudes of the auroral zone (∼60∘ < MLat <70∘), while poleward of it, at latitudes of the auroral oval (∼73∘ < MLat <79∘), the currents of the polar electrojet (PE) can appear. The direction of the PE, however, can be eastward or westward. This is determined by the sign of the IMF By component; the eastward current in the PE is By>0 and the westward is By<0. In the nighttime sector, the current is directed westward (WE) in the majority of cases at auroral latitudes. Figure  shows the direction, MLat, and strength of the Hall currents along the orbit for dayside (left column) and nightside (right column) sectors as obtained from the scalar measurements of the geomagnetic variations corresponding to the modelled current variations of . The current direction is related to the orientation of the satellite orbit; positive currents point eastward for the descending orbital parts and westward for the ascending. The auroral electrojet current flow is assumed to be in a strict east–west direction due to method constraints. It is obvious that the quantity, locations, and intensity of the peaks along the latitudinal current intensity distribution vary in the course of the storm development. A close correlation of the EE with the WE can be expected for the AU and AL indices, respectively, which are regarded as a measure of the auroral electrojets from the ground. We are considering, however, magnetic records along the satellite orbit well above the ionospheric current layer.

In the Sect.  and in Appendix –, we have investigated several geomagnetic storm periods based on magnetometer measurements onboard the CHAMP satellite. The Hall currents in the high-latitude upper ionosphere of the Northern Hemisphere were analyzed for various MLT sectors with regard to their position in geomagnetic latitude, their strength, and their direction. The empirical description concerned the appearance of the EE, the WE, and the PE during various storm phases and was carried out primarily qualitatively.

Below we are going to analyze the current directions, their densities, and MLat positions for various MLT sectors with regard to solar wind parameters and some indices of the planetary magnetic activity (SymH, AsyH, AL, and IndN). We use activity indices, which characterize the occurrence and dynamics of the large-scale plasma domains in Earth's magnetosphere that are responsible for the existence of concrete variations in the geomagnetic field at Earth's surface.

In this paper we investigated the strength and spatial–temporal distribution (versus magnetic latitude MLat and MLT) of Hall currents at high latitudes. The currents were determined from measurements of scalar magnetic field data, sampled on board the CHAMP satellite at ionospheric altitudes of ∼430 km during a selection of six magnetic storms (see Table ). The main findings obtained are as follows.

The current intensity of the PE increases with the magnitude of the IMF By component, while no correlation at all could be found between the MLat position of the PE and the IMF By component. The PE is directed eastward for IMF By>0 and westward for IMF By<0. Changes of current flow direction in the PE can occur manifold during the storm, but only due to changes in the IMF By orientation. There is a strong correlation between the PE current strength and the extent of the ring current asymmetry as indicated by the AsyH index, while there is no connection with the SymH index, the symmetric part of the ring current. There is an IMF By control of the magnetic field asymmetry inside the magnetosphere that manifests in the high correlation between AsyH and the PE current intensity.

Auroral electrojets are located at auroral latitudes (MLat <72∘ during daytime hours and MLat <68∘ during nighttime) and exist during every MLT. The number of electrojets in a certain latitude range, the structure of the currents in them, and the interconnection with concrete magnetospheric plasma domains depend on the disturbance level, which is controlled by UT as well as local time (MLT) at the observational points. Around midnight, the WE is predominant, and it exists almost exclusively in the morning sector. During daytime hours, the MLat positions of the auroral electrojets, both WE and EE, correlate with the activity indices AsyH, AL, and IndN. The correlation with the current intensities, however, is relatively small for all indices. The largest correlations (r∼0.6–0.7) exist between the AsyH index and the current intensity of the electrojets in the evening sector.

Certain characteristic features of the electrojets appear during the different phases of a geomagnetic storm. With the development of the main phase, both the daytime EE and the nighttime WE shift to sub-auroral latitudes of MLat ∼56∘, while they increase in strength up to I∼1.5 A m-1. During evening hours, the WE is located ∼6∘ closer to the pole than the EE. A splitting of the WE is possible in the morning hours during the recovery phase, analogous to the splitting of auroral luminescence in the auroral oval.

During evening and nighttime hours the EE is located in the region of diffuse aurora, equatorward of the discrete auroral forms, and projects along magnetic field lines into the inner magnetosphere between the plasmasphere and the central plasma sheet of the magnetospheric tail . In addition to this basic term, an appreciable contribution to the EE comes during daytime hours from the PRC, which is situated in the near-noon sector of the equatorial magnetosphere near the magnetopause. The WE comprises nighttime MLT from the morning to evening hours and is located in the central plasma sheet, projecting along the magnetic field lines into the auroral oval. The generation of the WE takes place deep inside the plasma sheet, far from magnetic field lines that form the polar cap boundary on the nightside. The PE is controlled by the IMF By component and is closely related to dayside reconnection processes, which cause the increase in open magnetic flux in the polar cap.