**3. Response of** *PC* **index to the** *EKL* **field changes**

Comprehensive analysis of relationships between the *E*KL field and *PC* index in course of isolated and expanded substorms (see Section 3) observed in 1998–2001 was fulfilled by *Troshichev and Sormakov* [48] with use of the 1-min *E*KL and *PC* values. To exclude the possible effect of inconsistency between the "estimated" *E*KL field (that calculated by solar wind parameters fixed far upstream of the magnetosphere) and actual *E*KL field affecting the magnetosphere, in reality, the specific "coordinated" substorms (N = 261) were also examined, when the *PC* index and *E*KL field demonstrated the obviously corresponding variations on the 2-hour interval preceding the substorm onset (SO). The *E*KL field raise commencement was taken as a key date (T0) and correlation between the *E*KL and *PC* quantities over the time

**Figure 3.**

*Histograms of the substorm occurrence over the level of correlation between* EKL *and* PC *for isolated (a), expanded (b) and coordinated substorm events (c) [48].*

period T0 ± 30 minutes was analyzed. **Figure 3** shows distribution of the number of substorms with different coefficients of correlation (R) between the *E*KL field and *PC* index for various types of substorm events. For coordinated substorms, the correlation was so high as R > 0.7 in 98% of events, the delay time in response of *PC* to *E*KL field alterations being extended in the range from 0 to 40 minutes with the pronounced peak at ∆T = 10–20 minutes.

To ascertain possible influence of the solar wind parameters on the value of ΔT, the relationships between ΔT and such solar wind parameters as the IMF vertical (*B*Z), azimuthal (*B*Y) and horizontal (*B*T) components, the solar wind speed (*Vsw*) and solar wind dynamic pressure(*Pd*) were examined, the solar wind parameters being averaged for the interval T0 ± 30 min. Contrary to the expectations, any single solar wind parameter demonstrated a minor importance in the ΔΤ value setting. In case of the solar wind speed (R = -0.32), only a slight tendency for the decrease of ΔT value with the growth of Vsw was seen. Other solar wind parameters, such as the vertical, azimuthal, and tangential IMF components, did not show any relation to the ΔT value at all.

To reveal the solar wind parameter actually controlling the ΔΤ value, the 1-min values of *V*X, *B*Z, *E*KL and *PC* fixed in course of coordinated events were smoothed with the use of the boxcar average of the 15-min width, and then they were separated into different groups according to delay value ΔT. The smoothed values of *V*X*, B*Z, *E*KL, and *PC* were put afterwards through the superposed epoch analysis, the moment of the sudden jump of the 15-min smoothed *E*KL being taken as a zero time T0. The behavior of the smoothed values of *V*X*, B*Z, *E*KL, and *PC* in course of coordinated events is shown in **Figure 4** for the most statistically justified groups with ΔT = 10–12 min (N = 33), ΔT = 13–15 min (N = 53), ΔT = 16–18 min (N = 60) and ΔT = 19–21 min (N = 38). 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.

As **Figure 4** demonstrates, the solar wind speed by itself is not a decisive factor in the ΔT setting (1st panel): the speeds values, as large as *V*X *=* -800 km/s and as small as Vx = −300 km/s, are common for any ΔΤ group and the time evolution of *V*X is not responsive to the moment T0. The IMF vertical *B*Z component (2nd panel) starts to turn down (southward) just at the moment T0; however, the larger Δ*B*<sup>Z</sup> values are built up at the expense of positive (northward) *B*Z IMF preceding the moment T0, as a result, the delay times ΔT turn out to be shorter under conditions

*The Polar Cap Magnetic Activity (*PC *Index) as a Tool of Monitoring and Nowcasting... DOI: http://dx.doi.org/10.5772/intechopen.103165*

**Figure 4.**

*Time evolution of the 15-min smoothed values* VX*,* BZ*,* EKL *and* PC *observed in case of coordinated events with delay times ΔT = 10–12, 13–15, 16–18 and 19–21 min. [48].*

of the northward IMF (averaged for the 1-hour interval). At the same time, the correlation between ΔΤ and the *E*KL field (3rd panel) turns out to be quite explicit: the higher the *E*KL raise (Δ*E*KL) during the ΔT interval is, the shorter the delay time ΔT is. It means that the actual delay time in response of *PC* index to changes of *E*KL field is determined by the *E*KL growth rate, not by such solar wind parameters, as the IMF Bz component or the solar wind speed Vsw, contrary to the concept of *Dungey* [49].

## **4.** *PC* **index as an indicator of the magnetospheric substorms development**

Energy and dynamics of magnetic substorms are commonly estimated by *AL* index, which characterizes intensity of the negative magnetic deviations produced by westward ionospheric currents (auroral electrojets) in the auroral zone [3, 50]. In study [51], the 1-min *PCN* and *PCS* indices, calculated by the unified method [11], were used in analysis of substorms observed in 1998–2001 (N = 1798), the substorm sudden onset (SO) being identified as the *AL* increase by the value more than −100 nT within 15 minutes. It has been demonstrated that the development of magnetic substorms is always preceded by the *PC* index growth. If the *PC* index increases gradually and slightly for a long time, the *AL* index also slowly increases but without SO signatures. The substorm sudden onsets were related to a sharp increase of the *PC* growth occurring within the 10 min interval proceeding the SO moment. Usually, the *PC* index continues to grow after the substorm's sudden onset, the *PC* growth rate being unaffected by SO. The substorm occurrence sharply increases when the *PC* index exceeds the threshold level ~ 1 mV/m and reaches

the maximum when *PC* ~ 1.5 mV/m, irrespective of the substorm growth phase duration and type of substorm. Fall of *PC* value below the threshold level leads to substorm completion.

The following classes of magnetic substorms were selected in [8, 51]: **isolated** substorms (N = 194) – disturbances, which arise out of the background of quiet conditions (*AL* ≤ 200nT) lasting as a minimum during three hours prior to substorm sudden onset; **expanded** substorms (N = 1418) – disturbances which occurred against the background of noticeable magnetic activity in both the auroral zone and the polar cap; **delayed substorms (**N = 154) – disturbances with sudden onset occurring against the background of invariable, over a long time, magnetic activity substorms. Examples of isolated, expanded and delayed substorms are presented in **Figure 5.**

The results [8, 51] demonstrated that substorms commonly start when the *PC* index exceeds a certain threshold value, i.e. when the energy input into the magnetosphere exceeds a certain crucial level ("energy storage threshold"). It is very essential that this crucial level, dependent on the *PC* growth rate and the magnetospheric activity grade is not the constant value. If the *PC* index (i.e. solar wind energy input) grows gradually and slowly, the magnetic activity also steadily increases, but without substorm onset. It implies that the magnetosphere adapts to new conditions in case of slight energy input. It can occur at the expense of the higher energy dissipation (for example, in the absence of magnetic substorm the Joule heating in the auroral ionosphere is much higher in the periods of enhanced magnetospheric convection than in the periods of ordinary convection). Under these conditions, the balance between the incoming and dissipating energies is retained, but level of energy that is necessary and sufficient for substorm beginning is gradually raised. The substorm is generated by "jump of energy input" when the solar wind energy incoming into the magnetosphere suddenly exceeds the existing level of storage energy. It means that substorm can start with any level of magnetospheric activity and irrespective of how long the solar wind energy was entering into the magnetosphere, in contrast to "directly driven" and "loading-unloading" concepts of the substorm development [3, 52–55]

In case of minor dissipation, when the threshold level is low, the required excess of the energy input over the "storage" energy is insignificant and intensity of the corresponding magnetic substorm will be weak (isolated "magnetic bays" starting against the background of full magnetic quiescence). In case of major dissipation, when the energy crucial level is high, the required excess of the energy input should be significant and the intensity of magnetic disturbance will be, correspondingly, largest (powerful "sawtooth substorms"). In case, when the *PC* index remains unchangeable for tens of minutes after reaching the threshold level and then sharply raises, the "delayed substorm" are observed. Application of the *PC* index as a proxy of the solar wind energy that entered into the magnetosphere gives grounds for verification of the "threshold-dependent driven mode" in different manifestations of magnetospheric substorms.

**Figure 6** shows relationships between the *PC mean* and *AL* values in course of isolated, expanded, and delayed substorms obtained for time intervals before the substorm sudden onset SO (*T*0, *T*0-5min and *T*0-20min) and after sudden onset (*T*0 + 5 min, *T*0 + 10 min, and *T*0 + 20 min) [51]. One can see that the slope coefficient after SO turned out to be twice as much as before SO, as an evident consequence of the aurora particle precipitation leading to the rise of conductivity of the auroral zone ionosphere and formation of powerful westward auroral electrojet during the

*The Polar Cap Magnetic Activity (*PC *Index) as a Tool of Monitoring and Nowcasting... DOI: http://dx.doi.org/10.5772/intechopen.103165*

**Figure 5.**

*Examples of isolated, expanded and delayed substorms for different levels of* PC *index in moment of substorm sudden onset PC0 marked by vertical line [51].*

substorm expansion phase. The isolated, delayed, and expanded substorms demonstrate a similar linear dependency of *AL* on *PC* during the substorm expansive phase, with coefficients of correlations changing in range from 0.85 to 0.94.

**Figure 6.** *Relationships between the mean* PC *and* AL *values in course of isolated, expanded, and delayed substorms [51].*
