Even if the DP2 current intensity is not varied, the value of magnetic disturbance, fixed at near-pole station, constantly changes because the station rotating around the geographic pole moves relative to the Sun-oriented ionospheric current system. It means that value of disturbance observed at station will be determined by disposition of station in regard to current system, i.e., by geographic coordinates of the point and UT time. This situation is illustrated schematically in Figure 3, which demonstrates disposition of the northern polar cap and station Thule in the invariant geomagnetic coordinate system (thin black lines) at noon and midnight hours in summer (upper panel) and winter (lower panel) seasons, the geographic coordinate system being shown by thin green lines.

The sun-oriented equivalent DP2 current system is shown in Figure 3 by thick black lines. Red arrows present the corresponding magnetic disturbance vectors δF (with δX and δY components in upper right figure). In the summer near-pole region these currents are oriented along the Sun–Earth line, in the winter near-pole area the equivalent currents can diverge more 45°C from this direction (Troshichev et al., 1979b). The matter is that magnetic disturbances in the sunlit high-conductivity summer hemisphere are generated by the ionospheric Hall currents, since magnetic effect of the ionospheric Pedersen currents is compensated by magnetic effect of the field-aligned currents, in full agreement with theorem of Fukushima (1969). Consequently, the equivalent DP2 currents are identical to the actual Hall currents flowing in the summer ionosphere. To the contrary, the intensity of ionospheric Hall and Pedersen currents in the dark winter polar cap is marginal, and the polar cap magnetic activity is produced mainly at the account of the R1 FAC distant effect. It means that the winter DP2 system presents the equivalent current system describing mainly the distant effect of the field-aligned currents on the ground surface. Because of this, the equivalent winter DP2 currents are deflected towards dawn through angles 20°C–60°C relative to summer DP2 currents (Maezawa, 1976; Troshichev et al., 1979b).

To take into account the regular variation of magnetic activity, caused by daily rotating the station around the geographic pole, the magnetic disturbance vector δF is calculated according to formula: δ F = δ X s i n ⁡ γ ± δ Y c o s ⁡ γ (3) γ = λ + UT + φ (4) where δX·and δY are alterations of the geomagnetic northern X and eastern Y components observed at the station (see Figure 3), λ is the geographic longitude, UT is the universal time, and φ is the UT-dependent angle between the DP2 transpolar currents and the noon-midnight meridian (which is equivalent to angle between the ionospheric electric field and dawn-dusk meridian); signs (+) and (-), valid correspondingly for Vostok and Thule station, are taken to make allowance for opposite polarity of geomagnetic field in the northern and southern hemispheres. Only the horizontal components X and Y are taken into account since the ionospheric currents, flowing above the station, cause horizontal magnetic disturbances underneath the current, likewise the vertical field-aligned currents, flowing in and flowing out of the ionosphere, produce horizontal magnetic deviation on the ground surface. The meaning of expressions (3) and (4) is very simple: they are assigned to arrange the magnetic disturbance vector δF in alignment with DP-2 currents while daily rotating the station under this current system. Since angle φ is subjected to strong daily and seasonal variations, the values of φ should be available for each moment of every day.

Expression (2) implies that the disturbance value F is determined by the E _KL field value, the relationship between values δF and E _KL being strongly dependent on seasonal transformation of the equivalent DP2 currents and disposition of station in regard to the current system. If the scale parameters, i.e., angle φ and the calibration coefficients α and β determining linear connection between δF and E _KL , are statistically justified for any moment of day during the year, they can be taken to calculate the PC index (designed to estimate the E _KL field value) for any actual moment of time with use of δFactual value fixed in this actual time P C a c t u a l = δ F a c t u a l − β α (5)

Thus, the PC index can be calculated at any actual moment UT on conditions that (a) the δX and δY values in expression (3) represent effect of the solar wind influence on magnetosphere, and (b) the scale parameters α, β and φ, determining the relationship between values of E _KL and δF, are statistically justified and always available. The first problem reduces to determining the quiet daily curves (QDC)x and (QDC)y, which serve as level of reference to account off the disturbance values δX and δY related to the solar wind effect. The second problem is correct evaluation of coefficients α (slope) and β (intersection) in expression (2) and angle φ in expression (4) determining the statistically justified relationship between E _KL field and magnetic disturbance value δF for any UT time of every day of year. A line of attack on these problems was put forward in (Troshichev et al., 2006) as “the unified PC derivation metod”, which includes the “QDC running calculation” procedure and determination of statistically justified scale parameters α, β and φ.

The polar cap magnetic observatory constantly registers the geomagnetic field changes, which are separated into two types: regular variations the “quiet” geomagnetic field and accidental magnetic disturbances (magnetic activity) of various origin. The regular daily and seasonal geomagnetic variations are caused by regular change of solar UV irradiation above the observatory in course of daily rotation of station around the geographic pole and seasonal changes in the polar caps illumination in course of the Earth’s rotation around the Sun. The higher UV irradiation is, the larger is conductivity of the polar ionospheric and intensity of electric currents flowing in the ionosphere, and correspondingly, the larger is geomagnetic variations on the ground level. As a result, the QDC magnitude occurred to be maximal at noon during the summer season and to be minimal at midnight during the winter season. Besides, the geomagnetic field demonstrates the regular long-term (∼27 days) variation related to effect of the IMF sector structure (SS effect). In addition, the polar cap ionosphere conductivity is affected also by irregular and powerful solar UV irradiance, related to solar flares in periods of high solar activity, and by the solar proton injections in periods of solar proton events (SPE).

To estimate correctly the polar cap magnetic activity produced by the solar wind impact on magnetosphere it is necessary to separate this activity from the geomagnetic alterations related to solar UV irradiation. The question is easily resolved for regular variation of quiet geomagnetic field: this variation (QDC) is taken as a level of reference to count off the magnetic activity. The SS effect, related to regular changes of the radial IMF component, has not essential action on magnetic activity and may be also included in QDC owing its long duration (∼27 days). The problem is separation of irregular effects of the solar UV irradiance rises, related to solar flares and effects of solar proton events (SPE), which exert a strong influence on the polar cap ionospheric conductivity. If these irregular effects are identified, they can be distinguished and incorporated in QDC which is used as level of reference to evaluate the magnetic activity produced by the solar wind.

The problem with the irregular solar UV irradiation rises related to solar flares was solved taking into account the crucial distinction between typical duration of the E _KL field changes produced by the geoeffective solar wind (from minutes to hours) and the duration of effects produced by the irregular UV irradiation rises (several days). Consideration of the solar flares effect as the long-term factor in comparison with the short-term solar wind (E _KL ) factors made it possible to distinguish this irregular effect and to include it in the level of reference (QDC) (Troshichev et al., 2006). The problem with SPE effect, with duration from 1 day to some days, remains unresolved.

Figures 4A–D illustrates, on the example of geomagnetic X component for the Vostok station, the operations forming the “QDC running calculation” procedure. The upper panel shows the real run of geomagnetic X component (B_x) during year 2000 (the summer months at Vostok station are November/December/January/February and the winter months are May/June/July/August). Figure 4B demonstrates separation of the SS effect in X component (ss_x). Taking into account the strong periodicity (∼27 days) of the IMF sector structure, the SS effect is separated on the basis of data for 3 previous months, using a 7-days smoothing window. One can see that SS effect at Vostok station is noticeable in period from October to March and negligible in period from April to September. Figure 4C shows the difference B_x-ss_x, the essential changes being seen in value of geomagnetic alterations in summer months after subtraction of the SS effect. The same procedure is performed for geomagnetic Y component registered at station.

Just geomagnetic variation shown in Figure 4C was used for separation of 5 quiet days (or quietest segments) within the interval of 30 previous days to deduce the QDC for current day. The QDC is automatically recalculated for each particular day, the results being extrapolated for the subsequent day with aim of the on-line estimation of QDC and derivation of the quicklook PC index in this day (preliminary PC index is obtained after recalculation of QDC for elapsed day). Figure 4D shows the QDC shape for X component for each particular day in period from September 2000 to January 2001 (the different scale of quantities on panels (A)–(D) should be taken into account). It is seen that the QDC amplitude systematically increases during this period (from minimum in September to maximum in December/January), but some less-scale variations travel in waves against the background of this regular seasonal variation, since the QDC time evolution includes the irregular increases in UV irradiation related to solar flares. It implies that the QDC behavior is changed from year to year, the QDC amplitude being maximal on years of solar activity maximum and being minimal on years of solar activity minimum.

The “QDC running calculation” procedure was used in AARI from the outset. In Danish Meteorological Institute (DMI), which was responsible for magnetic observations at Thule stations up to 2011, the distinct method, described by Vennerstrøm (1991), was used for the PCN index production. The “quiet level” in this method is determined by interpolation between the absolute values of geomagnetic field, established at nighttime hours of quiet winter days in the two consecutive years. Unfortunately, the “unified PC derivation method” (Troshichev et al., 2006) has not been adopted in DMI since the competitive method, named as a solar rotation weighted (SRW) method, was suggested by Stauning (2011).

The SRW method makes allowance for “the steady or recurrent variations in the magnetic field components during quiet conditions with time-of-day, day-of-year, and solar activity level”. According to concept of Stauning (2011), the solar influence on the geomagnetic activity is regularly repeated due to solar rotation, resulting in steady or recurrent variations (with period ∼27 days) in the IMF sector structure, in the solar wind velocity and in the 10.7 cm radio flux (F.10.7). The SRW method includes the weight factors, which promote the samples separated by one solar rotation “having the same face on the Sun turned toward the Earth” and enhance the importance of nearby samples, but minimises “the samples measured with the opposite face of the Sun turned toward the Earth”. It means that the SRW-method emphasizes the regular 27-days periodicity (“sector structure”) and levels off the irregular effects without this periodicity. As a result, the effects of the irregular solar UV rises related to solar flares can be automatically attributed to the PC index value, which is counted off from QDC, determined by SRW method. It should be noted that the “unified method” (Troshichev et al., 2006) has been recommended by IAGA Division V-DAT, as the best, for the IAGA endorsement and has been approved by IAGA in 2013.

Analysis of the QDC amplitude changes conditioned by the solar UV irregular variations has been fulfilled in (Troshichev et al., 2021) basing on yearly values of QDC magnitude and solar UV irradiance for period of 23/24 solar activity cycles. It is well known that the ionosphere conductivity is ensured by the solar X and UV irradiation with wavelength 100 nm–200 nm, which is absorbed in the Earth’s upper atmosphere and ionosphere (50 km–500 km), the radiation being varied in range of 20% (0.1 W/m² ± 0.02 W/m²) in connection with solar flares. The data on UV (100 nm–200 nm) irradiance (https://lasp.colorado.edu/lisird/data/lasp_gsfc_composite_ssi/) were used to examine the relation between the QDC magnitude and the solar irradiance level. The yearly-averaged amplitudes of QDC for X and Y components at stations Thule and Vostok were taken and their summary values (QDCtotal_X and QDCtotal_Y) were counted for each year. It turned out that the yearly values QDCtotal_X and QDCtotal_Y demonstrate the same regularity in alterations from year to year.

Figure 5 shows run of the yearly values of QDCtotal_X, QDCtotal_Y (a) and UV irradiation 150 nm–200 nm (b) in 1998–2018. One can see the well correspondence between the alterations of yearly values of QDCtotal magnitude and appropriate UV irradiance during this period. Figure 5C shows, as example, the correlation between values of the QDC magnitude and UV irradiance 160 nm, which is as high as R = 0.943. This perfect correspondence between the alterations of UV and QDC quantities demonstrates strong dependence of the QDC magnitude on solar activity (solar flares) and verifies correctness of the “running QDC calculation” procedure (Troshichev et al., 2006) used for derivation of the PC index.

To determine calibration parameters, the E _KL values were calculated according Eq. 1 by data on solar wind parameters presented at OMNI site (http://omniweb.gsfc.nasa.gov). The appropriate δF values, representing the DP2 disturbances at near-pole stations Thule and Vostok, were evaluated with use of the “running QDC” as a proper level of reference. The coefficients α and β, determined linear connection between δF and E _KL , were calculated for all values of angle φ in the range of ± 90°C from the suggested dawn-dusk orientation of DP2 vector. The “true” angle φ was chosen as angle value providing the best correlation between values δF and E _KL , and the quantities α, β corresponding to this “true” angle φ, were regarded as optimal, statistically justified parameters.

At first, the statistically justified parameters α, β and φ were calculated for epochs of solar maximum (1998–2001) with use of the GSE (Geocentric Solar Ecliptic) representation (Troshichev et al., 2006). In 2009 the parameters were recalculated with use of the GSM (Geocentric Solar Magnetosphere). Then the justified parameters were determined (with use of the GSM presentation) for epoch solar minimum (1997, 2007–2009) and for a complete cycle of solar activity (1995–2005) (Troshichev et al., 2006). Figure 6 shows these 3 series of parameters determined for Vostok station in these epochs (left, middle and right columns) as function of UT time (axis of abscises) and month (axis of ordinates). One can see that patterns for angles φ (denoted here as Φ) and coefficients α and β, derived at a quite different level of solar activity, are in good conformity by character and amplitude in course of UT and season changes (the difference in scales for three columns should be taken into account), testifying that the relationship between E _KL and δF remains basically the same irrespective of solar activity cycle. As a result, α, β and φ parameters obtained with use of the GSM representation for the full cycle of solar activity 1995–2005 (right column in Figure 6) were applied in all subsequent analyses.

The main peculiarity in behavior of calibration parameters is a seasonal dependence of parameters α (slope), β (intersection) and Φ (angle between the DP2 transpolar currents and noon-midnight meridian). Parameter α reaches the maximal value during summer months at Vostok station (January/February and November/December) and reduces in half during the winter months (May/June/July/August) suggesting the strong dependence of δF value on ionospheric conductivity. Transpolar currents are close (Φ ∼ 20°C) to noon-midnight meridian during 0–12 UT in summer and deviate up to 60°C from the meridian in winter, the seasonal distinction being conditioned by the different nature of the magnetic disturbances in the summer and winter polar caps. Availability of statistically justified parameters α, β and φ made it possible to calibrate the δF quantities by E _KL values. As a result, the stations Thule and Vostok, located in different points of the northern and southern polar caps and referred to different α, β and φ parameters, yield the similar PCN and PCS indices, consistent with value of E _KL field affecting the magnetosphere.

Figure 4E shows, in a large scale, the run of values δX = Bx-ss_x (where ss_x is the SS effect for X component) and QDC_x (which were presented in Figures 4C,D) for period from November 19 to 02 December 2000 at Vostok station. The deviations of values δX = B_x-ss_x and δY = B_y-ss_y from the appropriate values of QDC_x and QDCy at the Thule and Vostok stations were taken for calculation of the corresponding PCN and PCS indices with use of the statistically justified parameters α, β and φ available for any current moment of any day of year. Figure 4F demonstrates the PCN (blue) and PCS (red) indices derived by “unified method” for the indicated period. Figure 4G shows, for comparison, the run of magnetic disturbances in the auroral zone (AL index). One can see a good conformity between alterations of the AL and PCN, PCS indices, in spite of fact that these indices, derived from absolutely independent series of magnetic data, characterize magnetic activity in quite different regions of the magnetosphere. It implies that PC index really estimates input of solar wind energy into the magnetosphere (Troshichev and Janzhura, 2012; Troshichev, 2017).

In spite of the fact that the R1 FAC system acts at all times, irrespective of the IMF B_Z sign, the PC index in summer polar cap (PCsummer) often demonstrates the negative meanings (see Figure 4F). The negative PC indices are related to NBZ FAC system acting in the limited sunlit near-pole region (Armstrong and Zmuda, 1970; Zmuda and Armstrong, 1974; Iijima and Potemra, 1976b; Iijima et al., 1978). Corresponding DP3 current system is generated in borders of this area on the background of DP2 current system. As a result, the forth-vortices current system is formed in the summer polar cap without essential changes in structure of DP2 currents at latitudes below 75°C (see Figure 2A, upper panel). Under these conditions, the PCsummer index is incapable to elucidate situation in the entire polar cap. At the same time, the R1 FAC structure in the winter hemisphere remains invariable and intensity of the DP2 disturbances is taken into account by the corresponding PCwinter index. It means that the solar wind impact on the magnetosphere under conditions of the northward IMF should be estimated by the PCwinter index, the negative PCsummer indices can be used only for identification of current situation in the summer polar cap (for example, as indicator of magnetic quiescence).

The relationship between the 1-min E _KL and PC values during active periods was studied by Troshichev and Sormakov (2015) on the basis of isolated and expanded substorms for 1998–2001 listed in (Troshichev et al., 2014). Values of E _KL field were calculated using the data on solar wind parameters reduced to magnetopause (OMNI/Web interface http://omniweb.gsfc.nasa.gov). To level off an occassional magnetic activity asymmetry in the opposite polar caps, the PC index was taken as an average value of the PCN and PCS indices. The total number of examined events with data available for both stations turned out to be N = 163 for the isolated substorms, N = 983 for the expanded substorms, and N = 261 for the coordinated events for the period of 1998–2001.

Two approaches were used while performing the analysis. In the first approach the correlation between the E _KL and PC quantities was calculated in the 1-h interval preceding the sudden onset (SO) of each isolated or expanded substorm, the SO moment being used as a key date T₀. In the second approach the events with the conforming PC and E _KL deviations on the 2-h interval preceding SO were separated as coordinated events, the E _KL field raise commencement was taken as a key date (T₀), and the correlation between the E _KL and PC quantities over the time period T₀ ± 30 min was examined. In both cases the correlation between E _KL and PC was described by linear function, the coordinated E _KL and PC increases being followed by the substorm onsets.

Figure 7 shows degree of correlation between the E _KL field and PC index for all three types of substorms (upper panel) and distribution of delay times in response of PC index to changes in E _KL field (lower panel). To reveal the optimal time of the PC response to E _KL changes, the consideration of delay time was restricted to the most representative events demonstrating the correlation R > 0.75 between the PC and E _KL quantities smoothed with use of the 15-min running window. As Figure 7 demonstrates, the delay times are extended in the range from 0 min to 40 min with the pronounced peak at ΔT = 10 min–18 min for isolated substorms, ΔT = 10 min–20 min for extended substorms and ΔT = 13 min–18 min for coordinated events. The presented results testify that the PC index growth preceding the substorm onset is strongly related to the appropriate raise of E _KL field.

The comparative analysis of the substorm behavior in relation to the E _KL field and PC index was also fulfilled in (Kullen et al., 2010; Despirak et al., 2016). 874 substorms with and without growth-phase pseudobreakups were studied by Kullen et al. (2010). It was shown that the E _KL field rise can be observed about 1 h–2 h before the substorm onset. However, in this case the E _KL rise is slow and gradual (growth rate <0.04 mV/m/min) and does not exceed the critical level ∼1.5 mV/m, whereas the substorm demonstrates very low intensity (AE ∼ 200 nT). The substorms appear as isolated events after some hours of low geomagnetic activity. According to classification given in (Troshichev et al., 2014), these events refer to category of isolated substorms with growth phase lasted long time without sharp increases of the PC index.

Over 1,700 substorms, observed during two solar cycle maxima (1999–2000 and 2012–2013) were studied by Despirak et al. (2016). The substorms were divided into 3 types according to auroral oval dynamic: substorms which were observed only at auroral latitudes (“usual” substorms), substorms which propagate from auroral latitudes (< 70°C) to polar geomagnetic latitudes (> 70°C) (“expanded” substorms) and substorms which are observed only at latitudes above ∼70°C in the absence of simultaneous disturbances below 70°C (“polar” substorms). It was found that different PC values were typical of these types of substorms: the highest PC index values were observed before the “expanded” substorms, the lowest PC values were observed before the “polar” substorms.

To determine factors controlling the delay time in the PC response to E _KL field changes, Troshichev and Sormakov (2015) examined relation of the delay time value ΔΤ to such solar wind parameters, as the IMF vertical (B _Z ), azimuthal (B _Y ), and horizontal (B _T ) components, the solar wind speed (V _X ) and dynamic pressure (Pdyn), the parameters being averaged for the 1 h term preceding the SO moment (T₀). Contrary to expectations, the role of any separate solar wind parameter in the substorm development occurred to be insignificant. As this takes place, correlation between PC index and E _KL field was evident. Thereafter the “coordinated events”, with conforming behavior of PC index and E _KL field on the 2-h interval preceding SO, were examined.

Coordinated events were divided into different groups according to value of delay time ΔT. Figure 8 shows behavior of the smoothed values of V _X , B _Z , E _KL and PC in course of coordinated events for the statistically justified groups with ΔT = 10 min–12 min (N = 33), ΔT = 13 min–15 min (N = 53), ΔT = 16 min–18 min (N = 60), and ΔT = 19 min–21 min (N = 38), the font size shown on the left side is the same for all intervals of ΔT. Thin red lines represent the time evolution of V _X , B _Z , E _KL and PC in course of individual events. Solid black lines show the behavior of the mean V _X , B _Z , E _KL and PC quantities for each ΔT group. Vertical lines mark the delay time interval boundaries T₀ and T₀ + ΔT, the latter corresponds to the moment when the PC index starts to increase.

Figure 8 (upper panel) shows that the delay time tends to increase while the mean value of solar wind │V _X │ decreases. Nevertheless, the solar wind speeds V _X , as large as −800 km/s and as small as −300 km/s, are common for any ΔΤ group. Besides, the time evolution of V _X is not responsive to moment T₀. The IMF vertical B _Z component (2nd panel) starts to turn down (southward) just at moment T₀, the regularity being evident for individual events, as well as for mean B _Z in each ΔΤ group: the higher the B _Z alteration magnitude (ΔB _Z ) is, the shorter the delay time ΔT is. However, the larger ΔB _Z values are built up at the expense of positive (northward) B _Z preceding the moment T₀, whereas the base level of negative (southward) B _Z after the T₀ was ∼ −3.5 nT for all ΔΤ groups. At the same time, correlation between ΔΤ and E _KL field (3rd panel) turns out to be quite explicit: the higher the E _KL rise (ΔE _KL ) during the ΔT interval, the shorter is the delay time ΔT in response of PC to the E _KL rise. The actual delay time is determined by the E _KL field growth rate, not by such solar wind parameters, as IMF B _Z component or solar wind speed V _X (averaged for 1-h interval preceding the substorm sudden onset). The shortest delay times (ΔΤ < 10 min) were related to significant strengthening of southward IMF and a rather low speed of solar wind (V _X ∼ 350 km/s–450 km/s).

General link between the E _KL field and PCN, PCS indices is determined by parameters α, β and φ , characterizing relationships between the disturbances values δF, observed at stations Thule and Vostok, and values of E _KL , estimated by data presented at site (http://omniweb.gsfc.nasa.gov). These parameters were derived for period from 1995 to 2005 (Troshichev et al., 2011a) and are regarded as statistically justified. Nevertheless, in particular events the relationship between PC index and E _KL field can strongly deviate from statistical regularity. Troshichev and Sormakov (2019b) have analyzed relationship between the E _KL and PC values for 1,302 substorm events and found that well correlation (R>0.5) between E _KL field and PC index was observed in only ∼80% of the examined substorms. Typical examples of consistency and inconsistency between E _KL field and PC index are presented in Figure 9, where the upper panel shows behavior of E _KL field (green) and index PCmean = (PCN + PCS)/2 (violet), the middle panel is for PCN and PCS indices (blue and red lines), the lower panel shows the magnetic disturbance indices AL/AU, the substorm onsets being marked by vertical dotted line.

Figure 9A demonstrates coordinated changes of E _KL , PC and AL values in course of isolated magnetic substorm on 29 November 2004, when the disturbance started against the background of quiet magnetic field in connection with the PC growth responding to the E _KL field increase. Figure 9B demonstrates specific event on 17 August 2001, when jump in PC index was registered ∼10 min ahead of the appropriate E _KL field increase on the magnetopause. Since E _KL field is estimated by data on the solar wind parameters measured by spacecrafts far upstream of the magnetosphere, it is logically suggest that the actual solar wind, fixed by distant monitors, traveled in space with acceleration in this case. As a consequence, the real contact of solar wind with magnetosphere (and jump of PC index) occurred ahead of the “estimated” contact.

Figures 9C,D give examples of events when the magnetic activity (PC and AU/AL indices) was not consistent at all with the E _KL field alterations. In case of events on 20 February 1998 electric field E _KL was unchanged and quiet (E _KL ∼1 mV/m), whereas PCN and PCS indices demonstrated jump above 2 mV/m, which was accompanied by development of substorm with intensity of AL ∼ -400 nT. In case of event on 06 March 2006 the E _KL field demonstrated sharp increase above 2 mV/m for long, but this increase was not followed by the PC index growth and substorm development. As analysis (Troshichev and Sormakov, 2019b) has demonstrated, correlation between the PC and E _KL field was poor or even negative in about 20% of examined events, in spite of the evident consistency in variations of PC and AL indices. It means that IMF, measured by the distant solar wind monitors, did not encounter the Earth’s magnetosphere at all in these cases or impact on the magnetosphere by side-flow.

This conclusion is in full agreement with results (Vokhmyanin et al., 2019), which have demonstrated that the solar wind parameters measured in the Lagrange point and in vicinity of the magnetosphere (data of Geotail spacecraft in front of the magnetosphere bow shock obtained for 10 409 intervals available in both datasets over the period from 1997 to 2016) were distinguished in ∼25% of the examined intervals irrespective of the space weather conditions. It is particularly remarkable that according to Vokhmyanin et al. (2019), both sets of data (the OMNI database and the Geotail measurements) turn out to be in a good agreement in those cases when the PC index correlated well with the E _KL field derived from the OMNI data.

Thus, the correspondence between PC index and E _KL field is often missing details or disappears, in spite of statistical conformity of these two quantities. This circumstance seems to be quite reasonable since the estimation of the E _KL value is based on measurements of the solar wind parameters far upstream of the Earth, usually near the Lagrange point (at distance of ∼1.5 million km). The actual E _KL field coupling with the magnetosphere can be distinct from the “estimated” E _KL field for the following reasons:

1) The IMF has a small correlation distance (within 60 Earth radiuses of the Sun-Earth line) compared to solar wind plasma properties (King and Papitashvili, 2005). The spacecrafts should be positioned within this distance to monitor correctly the solar wind components.

Analysis of general relationship between the PC and E _KL values for 24 years (1997–2020) was fulfilled in (Troshichev et al., 2022) basing on the daily averaged quantities of E _KL field and definitive indices PCN and PCS. Figure 10 shows, as example, variations of the daily quantities of E _KL field and definite PCN, PCS indices in years of increased solar activity (2000 and 2015) and in years of solar minimum (2008 and 2019).

One can see that the daily E _KL and PCN, PCS quantities in periods with increased solar activity (upper panels) often exceed the value ∼1.5 mV/m, which presents a threshold level for development of magnetic disturbances (Troshichev et al., 2014). In epochs of solar minimum (lower panels) the daily PCN, PCS and E _KL quantities were generally lower this level. The daily PC and E _KL quantities alter (leap or drop) in perfect correspondence: the traces of PCN (blue) and PCS (red) usually do not go beyond the olive trace of E _KL . The relationship between the daily values of E _KL field and PCN, PCS indices is described by the linear function (with coefficient of correlation R) irrespective of the epoch and phase of solar activity.

2000 PCN = 0.039 (± 0.048) + 0.822 (± 0.029) *E _KL (R = 0.833)

As study (Troshichev et al., 2022) showed, decrease of correlation between E _KL field and PC indices below 0.85 was observed in periods of solar maximum, involving intervals of high magnetic activity with daily quantities of PCN, PCS and E _KL exceeding the value ∼4 mV/m. These intervals were related to solar proton events (SPE), when invasion of the high-energy solar protons produces the extreme increase of ionosphere conductivity in both polar caps. Strong correlation (R = 0.88) between the geomagnetic deviations at the polar stations Thule and Resolute Bay and PC and AE indices during major SPE events was demonstrated by Khan et al. (2013). In Figure 10 intervals with SPE in 2000 and 2015 are marked by horizontal black strips (according to catalogs of Logachev Yu et al., 2016; 2022), the solar proton events being absent in 2008 and 2019. If the intervals with SPE events are excluded from examination, the correlation between the daily quantities of E _KL field and PC index is increased up to R = 0.875 in 2000 and up to R = 0.87 in 2015. The SPE related effect is not identified by the “QDC running calculation” procedure as the extreme increase of ionospheric conductivity in view of short duration of the phenomenon (from hours to tens hours). As a result, effect of the ionospheric conductivity increase is attributed to the solar wind influence that led to decrease of correlation between the E _KL field and PCN/PCS indices in these cases.

Results of the analyses (Troshichev et al., 2022) testify that relationship between the solar wind electric field E _KL and the polar cap magnetic PC index (correlation on level R > 0.875 with decrease to R < 0.80 in epochs of solar maximum) was not changed when passing from 23rd to 24th solar cycle, in spite of high difference of these cycles in activity. It means that calibration parameters, determining these relationships, can be regarded as valid irrespective of the solar activity cycle.

Keeping in mind the evident link between E _KL field and PCN, PCS indices, the alteration of the yearly values of E _KL and index PCmean = (PCN + PCS)/2 during the 23/24 cycles was examined by Troshichev et al. (2021) in relation to such solar wind parameters, as solar wind velocity Vsw, total IMF field |B|, southward IMF Bz component, solar wind density Nsw, velocity Vsw ² and the solar wind dynamic pressure Pdyn = mNswVsw ² . The yearly values of the solar wind parameters Vsw, Nsw, Pdyn, IMF B|, By, Bz, E _KL were counted from the corresponding hourly (or daily) data presented on website http://omniweb.gsfc.nasa.gov. The “relative” yearly values of these parameters (i.e., the yearly quantities of various indicators, normalized by their averaged value for 22 years) were used to ensure the descriptive comparison of parameters with quite divergent scales of magnitude. It should be remembered in this connection that correlation between the compared quantities remains the same whether absolute or relative values are taken.

Results presented in Figure 11A (Troshichev et al., 2021) show that the yearly values of PCmean are closely related to such solar wind parameters as the solar wind velocity Vsw (R = 0.86) and the IMF intensity |B| (R = 0.84), resulting in high correlation of PCmean with their product, field E _KL (R = 0.92). It is remarkable that yearly PC index correlate with IMF |B| value much better than with the IMF Bz component (R = 0.72), much like E _KL field, which correlation with |B| is as high as R = 0.96 compared to correlation with B _Z (R = 0.81). The magnetospheric disturbance indices, AE and Dst, demonstrate the same regularity: the correlation of AE and Dst with |B| is equal to R = 0.88 and R = 0.86, whereas their correlations with Bz is equal to R = 0.69 and R = 0.74, correspondingly. It implies that dependence of magnetic disturbances on value of total IMF field |B| is stronger than their dependence on the IMF Bz component, in spite of high geoefficiency of the IMF southward (Bs) component.

The yearly PCmean values well correlate also with yearly Pdyn (R = 0.83) values (Figure 10B), however this linkage is evidently provided by solar wind velocity Vsw (R = 0.86). The other constituent, the solar wind density Nsw, demonstrates negative correlation with PCmean (R = -0.27) as well as with Vsw (R = -0.42) and E _KL (R = -0.08). This regularity is consistent with results presented in Section 7, which show that the PC index correlates with the Pdyn impulses only if these pulses are accompanied by corresponding changes in E _KL field, the inconsistency between the Pdyn and PC alterations becoming evident when the E _KL and Pdyn courses diverge.

Interrelation between PC index and cross-polar cap voltage (and diameter) was examined firstly in (Troshichev et al., 1996) with use of data of the particle and electric field measurements on board EXOS-D (Akebono) satellite for period January-June 1990. As results of the analysis showed, both parameters, polar cap diameter and voltage, well correlate with PC index. The same result was obtained (Troshichev et al., 2000) when examining the ionospheric electric field derived from the ion drift measurements made by DMSP satellites over the near-pole region, the PCN and PCS indices being used in the analysis (Figure 12). According to Chun et al. (2002), the cross polar cap potential is linearly proportional to the positive PCN index (with correlation R = 0.99) irrespective of season.

Good correlation (R = 0.88) between values of Φpc and PCN index was found by Bankov and Vassileva (2005) (with using data of measurements on board DMSP-F13 satellite in course 549 North Pole passes under various IMF conditions during spring of 1998), by Moon (2012) (correlation between Φpc and E _KL field, PCN index during 1996–2003 with peaks R = 0.82 in the equinoctial season), by Adhikari et al. (2017) (the relationships between Φpc and the solar wind parameters Vsw, B_X, B_Y, B_Z, the electric field E _KL , and geomagnetic indices PC, AL, SymH during the high intensive long duration auroral activity (HILDCAA) and supersubstorm (SSS) events). It was shown also (Chun et al., 1999, 2002) that PC index can serve as a proxy for the hemispheric Joule heating production rate.

Effect of the PC index “saturation” in response to solar wind electric field E _K was noted in (Nagatsuma, 2002; Troshichev et al., 2006; Stauning and Troshichev, 2008; Fiori et al., 2009). Term “saturation” in this context means that PC index practically stops to rise when E _KL field exceeds some critical value. The E _KL level that is necessary and sufficient for PC saturation was determined as 4 mV/m–5 mV/m by Nagatsuma (2002) and Troshichev et al. (2006), and as 2 mV/m by Fiori et al. (2009) (correlation between the PCN index and cross-polar cap velocity based on data of the Super DARN radars measurements).

Since the PC index is directly related to transpolar potential, saturation of PC index implies saturation of the cross-polar cap potential, which is commonly regarded, as a good proxy of the energy input into magnetosphere. In study (Ridley and Kihn, 2004) the assimilative mapping of ionosphere electrodynamics (AMIE) technique was used to calculate the cross polar cap potential and the polar cap electric field during 53 intervals with exceptionally large values of interplanetary electric field (10 mV/m) in 1997–2001. It was found that the transpolar potential estimated by linear extrapolation between the solar wind electric field and polar cap potential turned out to be overestimated as compared with the actually observed potential for values E _KL > 5–10 mV/m. Different mechanisms were proposed to explain this phenomenon (see reviews in Kivelson and Ridley, 2008; Borovsky et al., 2009); none of them was defined as the deciding factor.

In exploring the physical mechanism of the cross polar cap potential saturation, Kivelson and Ridley (2008) took into account the SuperDARN radar data and put forward the “transmitted potential” (E _KR function), which incorporates saturation of the cross polar potential. Analyses of relationship between the E _KR function and PC index (Gao et al., 2012a; Gao et al., 2012b; Gao, 2012) showed that correlation between the PC index and E _KR function is better than correlation between PC and E _KL field, especially when E _KR significantly differs from E _KL . The mechanisms, which are likely responsible for the discrepancy between the E _KL field and E _KR function effects were categorized by Gao (2012) as the following: 1) sources that effectively change the baseline values of magnetic field H and D components in deriving the PC index; 2) solar wind conditions that produced negative PC indices; 3) anomalous poleward excursions of the auroral oval; and 4) shifts of flow patterns arising from very strong IMF B_Y.

Thus, all above-listed analyses are evidence for relation of the cross polar cap voltage to the PC index value even though they are inconsistent in details. It should be noted in this connection that the PCN indices used in studies fulfilled before 2008 were derived by traditional method adopted in DMI (Vennerstrøm, 1991), which is strongly different from “unified method” (Troshichev et al., 2006) adopted in AARI for derivation of the PC index. The PCN indices, used in studies from 2008 to 2012, were, possibly, obtained by method described in (Stauning, 2011). After 2012 all PC indices, provided by the DTU Space Institute and AARI, were calculated by the “unified method” (Troshichev et al., 2006) approved by IAGA in 2013. Discrepancy of the described above results can account for difference in the methods of the PCN index calculation before 2012 and, correspondingly, for distinction of the used PCN indices.