Geomagnetic storms are disturbances of the Earth’s magnetic field, caused by solar and interplanetary events such as coronal mass ejections (CMEs), fast solar winds, and corotating interaction regions [1] [2] . They are often considered signatures of the dynamics of the Sun-Earth relationship [3] .

Geomagnetic storms disrupt terrestrial and space technologies [4] - [6] . Indeed, they affect satellite technologies and disrupt communications systems [7] - [9] , radio signals and GPS, space missions, geophysical exploration, power grids, and many other technologies.

There are many studies on geomagnetic storms. Among these, there are studies on 1) the origin of geomagnetic storms [10] - [13] , 2) their impact on the terrestrial environment [14] - [16] , 3) their occurrence as a function of solar cycles and phases [2] [3] [17] - [20] , 4) their classification from indices [1] [6] [11] [21] [22] , 5) their relationships to solar wind parameters [23] - [25] and many other topics.

For example, and [10] showed that at Earth, most intense geomagnetic storms are caused by southerly interplanetary magnetic fields (IMFs), carried by a high-speed solar wind. later pointed out that the main causes of geomagnetic storms on Earth are strong dawn-dusk electric fields, accompanied by southerly IMFs near Earth for a sufficiently long duration. [12] studied the solar sources of geomagnetic storms during solar cycle 24. He concluded that the weak geomagnetic activity during cycle 24 is related to the weak dawn-dusk electric field of the solar wind. This author also concludes that the relatively slow CMEs contributed to the geomagnetic storms during cycle 24. [3] studying the occurrence of geomagnetic storms as a function of seasons and time during solar cycles 21-24, observed a higher probability of occurrence of large storms around 21-8 UT during the equinoxes. [20] also studied the occurrence of geomagnetic storms during solar cycles 23 and 24. They found that weak and moderate storms, caused by fast solar winds, are more prevalent in the descending phase of the solar cycle, while strong storms, which are caused by coronal mass ejections (CMEs), are more frequent at solar maximum and then in the descending phase. To classify geomagnetic storms, [11] defined criteria that were taken up and adopted by [26] and [27] . According to these criteria, four classes of geomagnetic storms are distinguished, namely, 1) major storms defined by Kp_max ≥ 8 and Kp ≥ 6 lasting at least 3 hours during a 24-hour period, 2) large storms defined by 7 ≤ Kp_max ≤ 7+ and Kp ≥ 6 lasting at least 3 hours during a 24-hour period; 3) medium storms which include all other cases with Kp_max ≥ 6- and 4) weak storms characterized by 5- ≤ Kp_max ≤ 5+. , identified three classes of geomagnetic storms according to the minimum values of Dst; namely 1) intense storm (Dst ≥ −100 nT), 2) moderate storms (−100 ≤ Dst ≤ −50 nT) and weak storms (−50 ≤ Dst ≤ −30 nT). Later, [28] extended this classification to five classes by distinguishing, 1) weak storms (−50 ≤ Dst ≤ −30 nT); 2) moderate storms (−100 ≤ Dst ≤ −50 nT), 3) strong storms (−200 ≤ Dst ≤ −100 nT), 4) severe storms (−350 ≤ Dst ≤ −200 nT) and 5) major storms > −350 nT. [25] analyzed the correlation between geomagnetic storm intensity and solar wind parameters from 1996 to 2023. They found that storm intensity is correlated with the peak values and/or time integral values of the southward interplanetary magnetic field (IMF Bs), twilight electric field (Ey), Akasofu function (ε), and dynamic pressure (P_sw) to varying degrees.

The occurrence of geomagnetic storms as a function of solar phases has been widely studied. However, the influence of solar phases on the characteristics of geomagnetic storms is poorly addressed. Thus, to understand the influence of solar phases on the intensity of geomagnetic storms, this study analyzes the characteristics of intense storms (Dst < −100 nT) recorded during different solar phases.

In this study, hourly OMNIWEB values of Dst and AE indices, as well as the B_z, Ey, V_sw, and P_sw parameters, were used to characterize storm intensity. In addition, the Rz index was used to define the solar phases for the years studied. All these indices and parameters are available on the OMNIWEB website at: https://omniweb.gsfc.nasa.gov/form/dx1.html .

SSC dates were used to identify the onset of storms. These dates are available at: https://isgi.unistra.fr/data_download.php .

The three storms studied are intense storms selected on the basis of the Dst index and the criterion defined by [1] . With these criteria we select intense storms having almost the same min Dst and belonging to different solar phases. The Rz values and the criterion defined by [20] made it possible to identify the solar phases of the years of occurrence of the storms considered. Table 1 gives the dates of occurrence of the three storms and their position in the solar cycle.

The extreme values of the AE, Dst indices and the parameters Bz, Ey, V_sw and P_sw were used to characterize the intensity of storm [24] . The variations of Bz during the main phase of storm allow to characterize its structure in the IMF. Indeed, according to [29] , Bz variations are the magnetic signature of the internal structure of the IMF. Thus, a smooth and continuous variation of Bz indicates a well-organized internal structure while abrupt or disordered variations of Bz may signal a disturbed or incomplete structure. The polarities of the Bz allow to identify its orientation. Thus, a positive/negative Bz is a Bz with a North/South orientation [30] . The limits of the phases of a storm were identified on the basis of the SSC and the hourly variations of the Dst index. Thus, Figure 1 presents the limits of the phases of the three storms studied.

To observe the evolution of the characteristic parameters of the storms studied, we considered one day before the storm, the day of the storm and two days after the storm to plot the profiles.

Figures 2-4 present the variations in geomagnetic indices (AE, Dst), solar wind parameters (B_z, V_sw, nP, E_y), and magnetospheric parameters (P_sw) during the storms of November 6, 1997, August 17, 2001, and January 7, 2015, respectively. These storms occurred during an ascending phase, a solar maximum, and a descending phase of the sun, respectively. All graphs were plotted over a period of four (04) days.

The three geomagnetic storms (storm 1, storm 2, and storm 3), although all intense, exhibit distinct characteristics related to their position in the solar cycle and the nature of the interplanetary disturbances that triggered them. This diversity is well consistent with the findings of [31] , who distinguished between storms caused by coronal mass ejections (CMEs) and those due to high-speed streams from coronal holes (HSSs).

Storm 1 is typical of a storm caused by a CME occurring during a solar upswing phase. We observe a strong persistent negative Bz component (~ −15 nT) over 04 hours, a minimum Dst value close to −110 nT, and an Ey energy > 5 mV/m, corresponding well to an efficient coupling between the solar wind and the magnetosphere. These extremes appear during the main phase, except for the dynamic pressure and particle density which peak at the time of the SSC. This event illustrates a storm caused by a slow CME. According to [1] , such a configuration (prolonged southern Bz + Ey > 5 mV/m) is sufficient to cause a moderate energy transfer inducing an intense storm, even in the upswing phase. The simultaneous presence of high particle densities and high dynamic pressure reinforces the compression of the magnetopause, as confirmed by [32] . This situation well illustrates the classic scenario described by [33] where a slow CME with a strong and stable southerly magnetic field can produce a significant thunderstorm.

Storm 2 is the most intense of the three (Dst ~ −105 nT). It reflects maximum solar activity, with a very strongly negative Bz field (Bzmin = −20 nT) over ~10 hours; which is much greater than the negative Bz extension of the first storm (storm 1); an extreme Ey (>10 mV/m) and a fast solar wind (>500 km/s). It is therefore a fast and violent CME. According to [34] , these conditions favor major auroral disturbances, which is here confirmed by extreme values of the AE index (>1500 nT). The high interplanetary electric field induces a massive magnetospheric energy transfer, in accordance with the model of [35] . This configuration is typical of major geomagnetic storms associated with fast CMEs, as shown by [11] and [31] . It illustrates the impact of a structured interplanetary field on the intensity of a storm.

Compared to the first storm (storm 1), the intensity of this one reflects a fast, highly structured CME with a prolonged southern Bz field. The energy transfer to the magnetosphere is maximal, explaining the extreme values of the geomagnetic and auroral indices.

Storm 3 is less intense (Dst ~ −107 nT), which could be due to a less durable southern Bz component and a more moderate Ey (~8 mV/m) thus limiting the magnetosphere-solar wind coupling. The CME at the origin of this storm is probably less organized or oriented in a way less favorable to the coupling. In addition, the auroral activity is intense but over a short period (AE peak ~ 1300 nT at around 1000 UT).

Table 2 summarizes the extreme values of the parameters and indices used to characterize the intensity of the three geomagnetic storms.

Analyzing the three (3) storms, we note that storm 2, which occurred at solar maximum, is the most intense. It is distinguished by a prolonged (~10 h), well-structured and strongly negative (−20 nT) southern Bz component, a high Ey electric field (~10 mV/m), a fast solar wind (>500 km/s), strong compression on the magnetosphere (>20 nPa), and strong auroral electrojet activity (AE > 1500 nT). Storm 1, which occurred during the ascending solar phase, is a relatively less intense storm than storm 2. It is characterized by a prolonged (~12 h), strongly negative (~−15 nT) southern Bz but less structured than the previous one. The extreme values of the characteristic parameters and indices of this storm (storm 1) are lower than those of storm 2 (AE = 1125 nT; Ey = 5.8 mV/m; V_sw = 468 km/s; Psw = 7.6 nPa). Storm 3, which occurred during the descending phase, is the least intense. It is characterized by a well-structured and strongly negative South Bz component (−17.3 nT) but less prolonged compared to the other two (~5 h); a relatively intense auroral electrojet activity (AE = 1327 nT) over a short duration (~4 h); a weak fluctuation of the Ey field (−1 to 8.16 mV/m), a solar wind speed and a dynamic pressure relatively almost identical to those of storm 1 (475 km/s −8.39 nPa).

The results of these case studies may not apply to all solar cycles. To this end, a larger statistical study involving several solar cycles and several geomagnetic storms could lead to a good generalization of the results.

The geomagnetic storms studied exhibit strong variability in intensity, linked to the phase of the solar cycle. The interplanetary magnetic field Bz, its duration in southerly polarity, the electric field Ey, and the dynamic pressure of the solar wind are the main factors influencing storm intensity. The importance of prolonged southerly Bz plus high Ey can cause strong magnetosphere-solar wind coupling. The Dst and AE indices provide a coherent interpretation of storm evolution and its ionospheric impacts. These results confirm the importance of solar phases as well as that of the Bz component of the interplanetary magnetic field (IMF), particularly its structure in CMEs and the duration of its southerly polarity, in determining the intensity of geomagnetic storms.