Spatial Distribution and Semiannual Variation of Cold‐Dense Plasma Sheet

The cold‐dense plasma sheet (CDPS) plays an important role in the entry process of the solar wind plasma into the magnetosphere. Investigating the seasonal variation of CDPS occurrences will help us better understand the long‐term variation of plasma exchange between the solar wind and magnetosphere, but any seasonal variation of CDPS occurrences has not yet been reported in the literature. In this paper, we investigate the seasonal variation of the occurrence rate of CDPS using Geotail data from 1996 to 2015 and find a semiannual variation of the CDPS occurrences. Given the higher probability of solar wind entry under stronger northward interplanetary magnetic field (IMF) conditions, 20 years of IMF data (1996–2015) are used to investigate the seasonal variation of IMF Bz under northward IMF conditions. We find a semiannual variation of IMF Bz, which is consistent with the Russell‐McPherron (R‐M) effect. We therefore suggest that the semiannual variation of CDPS may be related to the R‐M effect.


Introduction
The formation of the cold-dense plasma sheet (CDPS) is considered a representative signature of solar wind entry under northward interplanetary magnetic field (IMF) conditions seen in the magnetosphere (e.g., Fujimoto et al., 1996;Stenuit et al., 2002;Terasawa et al., 1997;Wing & Newell, 2002). CDPS is generally characterized by high density (n > 1 cm À3 ) and low temperature (T < 2 keV) with a low ion bulk flow speed (|V x | < 100 km/s) (e.g., Baumjohann et al., 1989;Fujimoto et al., 1996Fujimoto et al., , 2002Li et al., 2005;Wing, Johnson, & Fujimoto, 2006). Observations have shown that a cold-dense plasma sheet forms after a long duration of northward IMF (e.g., Terasawa et al., 1997;Wing et al., 2005). A cold and dense plasma sheet can also be considered as a precondition for the strong ring current that forms during geomagnetic storms (Thomsen et al., 2003;Lavraud, Thomsen, Borovsky, et al., 2006;Chen et al., 2007) and also affects magnetosphere-ionosphere coupling (e.g., Gkioulidou et al., 2009). The magnetospheric flank regions are believed to be the source region of the CDPS. Plasmas with low temperature and high density in the flank region are source components of CDPS, provided by the solar wind entry during the northward IMF period. Double-lobe reconnection (Crooker, 1992;Fuselier et al. 2002;Lavraud, Thomsen, Lefebvre, et al., 2006;Le et al., 1996;Li et al., 2008;Onsager et al., 2001;Sandholt et al., 1999;Song & Russell, 1992;Shi et al., 2009Shi et al., , 2013 could be an important mechanism to transport cold and dense plasma from solar wind to the magnetosphere. Lavraud et al. (2005) found evidence of double-lobe reconnection at high latitudes. Shi et al. (2013) found a new region of solar wind plasma entry into the magnetosphere, in the lobes tailward of the cusp, and lobe reconnection was suggested to be the most probable mechanism of the entry. Based on OpenGGCM MHD simulations, Li et al. (2005) simulated the process of cold-dense plasma sheet transport from the solar wind into the magnetosphere through dual-lobe reconnection. The Kelvin-Helmholtz (K-H) instability in the magnetospheric flank regions is another mechanism for solar wind entry under northward IMF conditions (e.g., Fairfield et al., 2000;Fujimoto, Tonooka, & Mukai, 2003;Hasegawa et al., 2004Hasegawa et al., , 2009Miura, 1987). Other mechanisms such as impulsive penetration (e.g., Echim & Lemaire, 2002) and gradient drift (e.g., Olson & Pfitzer, 1985;Zhou et al., 2007) may also play a role in the plasma interchange between the solar wind and magnetosphere under northward IMF conditions. • We present the spatial distribution of plasma sheet temperature and density in GSM X-Y plane using 21 years of in situ Geotail data • Cold-dense plasma sheet occurrence rates have a semiannual variation, in keeping with the semiannual variation of the IMF + B z • The Russell-McPherron effect may therefore control these variations and hence modulate solar wind entry into the magnetosphere Supporting Information: • Supporting Information S1 • Figure S1 • Figure S2 Correspondence to: Q. Shi Wang et al., 2014;Wing et al., 2006). However, the seasonal variation of the CDPS occurrence has not been studied. Through the investigation of seasonal variation of the CDPS occurrence, we gain a basic understanding of the seasonal variation of the mass interchange rate between the solar wind and magnetosphere during quiet times.
Since the CDPS particle source has been considered to be from the solar wind, the variation of solar wind conditions should control the variation of CDPS occurrence. The semiannual variation of geomagnetic activity has been reported for over a hundred years (Sabine, 1851). Several hypotheses were proposed to explain this variation, such as the axial hypothesis (Cortie, 1912;Svalgaard, 1977), the equinoctial hypothesis (Bartels, 1932;Cliver et al., 2002Cliver et al., , 2000McIntosh, 1959) and the Russell-McPherron (R-M) effect (Russell & McPherron, 1973). The axial hypothesis attributes the semiannual variation to the variation of the Earth's heliographic latitude. During March and September the heliographic latitude of Earth approaches the range of values where sunspots appear frequently and the average solar wind velocity is higher (Hundhausen et al., 1971). The equinoctial hypothesis considers the φ angle between the Earth-Sun line and the dipole axis of the Earth as the key parameter that affects the field configuration in the Chapman-Ferraro current plane (Crooker & Siscoe, 1986). This suppresses the transfer of energy and further influences the coupling efficiency between solar wind and magnetosphere. The R-M effect proposes that the θ angle is a key parameter, which is defined as the angle between Y axis in geocentric solar equatorial (GSE) coordinate and Z axis in geocentric solar magnetospheric (GSM) coordinates, when examining components of the IMF. According to the R-M effect, the instantaneous IMF-Z GSM component increases in association with a decrease of the angle θ, whose range is smaller than 90°. The minimum of θ appears at spring and fall equinoxes. The maximum of angle θ is seen at summer and winter solstices, when the GSE B y projection effect minimizes and the magnitude of GSM B z reaches its maximum. Previous studies on R-M effect focused on understanding the role of R-M effect for southward IMF conditions (e.g., O'Brien & McPherron, 2002;Russell & McPherron, 1973;Siscoe & Crooker, 1996;Zhao & Zong, 2012) and for the dipole effect under various IMF orientations (Nowada et al., 2009;Russell, Wang, & Raeder, 2003), while no attempts have been made under northward IMF. However, several works have suggested the higher occurrence of solar wind entry with stronger northward IMF (Lavraud, Thomsen, Lefebvre, et al., 2006;Lin et al., 2014;Zhou et al., 2007). Therefore, in this paper, we investigate the seasonal variation of CDPS occurrences and the possible role that the R-M effect plays in the seasonal variation of northward IMF, and then build a possible link between the R-M effect and the CDPS occurrences.

Data Set
The CDPS events are identified by use of the magnetic field (MGF) experiment data (Kokubun et al., 1994) and the ion moment data in EA modes from the Low-Energy Particle (LEP) experiment with a covered energy range of 60 eV-40 keV (Mukai et al., 1994) and Comprehensive Plasma Instrumentation (CPI) onboard Geotail, with a covered energy range of 1.3 eV-48.2 keV (Frank et al., 1994) from 1996 to 2015. All the results are presented in GSM coordinates.
To investigate the seasonal variation of the northward IMF, IMF data with 1 h time resolution between 1996 and 2015 are used from the OMNI database. The OMNI 1 min resolution data are also used when we calculate the magnetopause location using the Shue et al. (1998) model.

Cold-Dense Plasma Sheet Observation
All our cases were found in the magnetosphere with the range of X GSM < À10 R E . To avoid the crossing events of the magnetosheath and low-latitude boundary layer, we only consider the plasma sheet (PS) and cold-dense plasma sheet (CDPS) events, whose radial distance is 3 R E away from the magnetopause location. The magnetopause location is calculated by Shue et al. (1998)  The CDPS events are defined as those PS events that have high ion densities (N ion > 1 cc À1 ) and low ion temperatures (T ion < 2 keV) (Fujimoto et al., 1996, and these two criteria were used for both LEP and CPI data. The plasma parameters data are taken from the LEP instrument when the events are observed by both LEP and CPI. We have not examined the consistency of the two kinds of data. However, for the events that were observed by both instruments, the ion density is close to each other, and the temperature observed by CPI is higher than the LEP value. Based on the criteria of the PS and CDPS crossings, we identified 636 CDPS events out of 3,770 plasma sheet crossing events. The occurrence rate of CDPS on the duskside is 15.29% and 18.20% on the dawnside, in which the occurrence rate is calculated only using the events on the corresponding side of magnetosphere. The locations of the PS (blue dots) and the CDPS crossing events (red dots), projected onto the GSM X-Y plane, are shown in Figure 1 (see Figure S1 in the supporting information for the detailed ion density and temperature of the PS and CDPS events, and the plasma Beta for PS events can be found in Figure S2). Wing & Newell, (2002) showed the projected spatial distribution of ion density and temperature of the plasma sheet from observations in the ionosphere and found a clear dawn-dusk asymmetry in both ion density and ion temperature in the inner magnetosphere. We also investigate the spatial distribution of ion density and temperature based on in situ observations. The spatial distribution of ion number density and temperature of Figure 1. The position of CDPS events (red dots) and PS events (blue dots). The horizontal axis is position of these events in X GSM direction, (a) the Y axis is the position in Y GSM direction, and (b) the Y axis is the radial distance to the magnetopause. Spatial distribution of (c) ion number density of all plasma sheet crossings events, (d) ion temperature of all plasma sheet crossings events, (e) ion number density of plasma sheet but not cold-dense plasma sheet crossing events, and (f) ion temperature of plasma sheet but not cold-dense plasma sheet crossing events. All observational event points are averaged over 2 R E × 2 R E bins. Some regions are left blank because of insufficient data points.
Journal of Geophysical Research: Space Physics

10.1002/2017JA024565
PS events projected onto the GSM X-Y plane using average values in each 2 R E × 2 R E bin are shown in Figures 1c and 1d, respectively. Figures 1e and 1f also show the spatial distribution of ion number density and ion temperature for PS events. Note that CDPS events are excluded from the PS events used to calculate the average values shown in Figures 1e and 1f. There is a clear dawn-dusk asymmetry of average ion density for PS events shown in Figure 1c; however, the difference in average ion temperature for plasma sheet crossing events in both flanks is not significant, as seen in Figure 1d. The dawn-dusk asymmetry of ion density is not seen in Figure 1e, which indicates that this asymmetry is brought by the CDPS events. The spatial distribution of the ion temperature with or without CDPS is quite similar shown in Figures 1d and 1f, and there is no significant dawn-dusk asymmetry. The number of CDPS/PS events in every month is given in Figure 2a. To examine the seasonal variation of the CDPS occurrence rate, we divided the number of CDPS events in every month by counting the monthly total number of PS events. The result is given in Figure 2a with error bars. The error bar is calculated using the propagation of error analysis and shows below, where n is the number of CDPS events and N is the number of PS events in every month. It seems likely that the CDPS occurrence has a semiannual variation with peaks at March and September and valleys at January and July. Borovsky, Thomsen, and Elphic (1998) reported that it took~4 h for the solar wind plasma to reach the nightside plasma sheet at geosynchronous orbit. Since the CDPS events we found are outside of geosynchronous orbit, here we investigate the solar wind conditions during a 4 h interval preceding the start of these events. We find that 87 CDPS events are excluded due to the lack of data in this 4 h interval, which leaves 549 events remaining. Figure 2b shows the distribution of the CDPS events as a function of the duration of northward IMF prior to the CDPS event start time. The IMF data are shifted to the CDPS position; the time shift is calculated by X/V sw , where X is the upstream distance of the spacecraft which monitored the IMF and V sw is the measured solar wind speed. The duration in Figure 2b is the sum of the northward IMF periods of time during 4 h before CDPS events. More than 85% (469 out of 549) of the CDPS events experienced at least 2 h of northward IMF within the previous 4 h. This is consistent with previous observations (e.g., Terasawa et al., 1997;Wing et al., 2005). Using these 85% of the CDPS events with at least 2 h of northward IMF prior to the CDPS event and the PS events shown in Figure 2a, we recalculated the CDPS occurrence rate, as shown in Figure 2c. The tendency that CDPS occurrences increased during March and September/October and dropped during January and July remains clear. We also found that most of the CDPS events in our study are during quiet times (Kp < 3 and AE < 150 nT; see Figure S2); therefore, the semiannual variation of CDPS occurrence should not be related to solar wind entry under southward IMF conditions prior to the identified events.

Observation of the Northward IMF Variations
It is suggested that the formation of cold-dense plasma sheet requires a long duration of northward IMF (e.g., Terasawa et al., 1997;Wing et al., 2005). Here we use the OMNI 1 h resolution data from 1996 to 2015 to investigate the seasonal variation of the magnitude of the northward IMF (GSM B z > 0) conditions. Figure 3 shows the seasonal (horizontal axis) and diurnal (vertical axis) variations of northward IMF data calculated on a grid of 24 × 24 bins (with 1 h × 15.25 days for a single bin) and smoothed by a 3 × 3 average. We only use solar wind data during northward IMF periods to calculate the result shown in Figure 3. Figures 3a shows the color contour maps for the probabilities of IMF B z component larger than 2 nT, and Figure 3b shows the average values of IMF B z . There are three main assumptions in the R-M effect: (i) the direction of IMF is always along the Parker spiral and its magnitude is constant; (ii) the possibility of meeting southward or northward IMF is equal; and (iii) the northward IMF has no effect on the geomagnetic activity. The R-M effect is put forward to explain the semiannual variation of geomagnetic activities after the solar wind entry under the southward IMF, such as geomagnetic storms and substorms, but the increased magnitude of B z caused by the projection of GSE B y could also be expected under northward IMF. The first and second hypotheses are used in this paper. Figure 3c shows the semiannual and diurnal variations of the angle θ under northward IMF conditions, which is the controlling parameter of the R-M effect. Figure 3d shows the semiannual and diurnal variations of the angle φ, which is considered as the key parameter of the equinoctial hypothesis. The peaks of the northward IMF probability are seen between 21:00 UT and 02:00 UT at spring equinox and around 10:00 UT at fall equinox. The valleys of the northward IMF probability existed at summer and winter solstices, and the θ angle reaches a minimum at the same time. The φ angle reaches a minimum at summer and winter solstices, but there is no clear peak or those calculated between the IMF B z and equinoctial hypothesis. Therefore, we suggest that the R-M effect is a more probable hypothesis to explain the seasonal and diurnal northward IMF variations shown in Figure 3 than the equinoctial hypothesis. According to the diurnal variation of the IMF B z shown in Figures 3a-3c, the period of high probability of the higher northward IMF should be larger in March and September, and therefore, it is likely that there will be long periods of northward IMF during the 2 months. Since the formation of CDPS is related to the long duration of periods of northward IMF and the increased positive B z magnitude, we consider that the semiannual variation of CDPS occurrence is also related to R-M effect.

Summary and Discussion
In this paper, we have performed a statistical analysis of the occurrence of the CDPS and the magnitude of the northward IMF B z . We find 636 CDPS events and 3,770 PS events, and the CDPS occurrence on the dawnside is slightly higher than that on the duskside, but the difference is not significant. Based on direct in situ observations, a clear dawn-dusk asymmetry of ion density within CDPS events is shown and this dawn-dusk asymmetry is not reflected in spatial distribution of ion temperatures. This indicates that the transport of CDPS events from the flanks to the central magnetotail is more efficient on the dawnside, which confirms previous works from indirect observations (e.g., Wing et al., 2005;Wing & Newell, 2002). Most of the CDPS events that we observed are during geomagnetic quiet times (Kp < 3, AE < 150 nT; see Figure S2) and experience a long duration of northward IMF prior to the event. The occurrence rate of CDPS shows a semiannual variation. This variation of CDPS occurrence is still clear using a subset of CDPS events with long intervals of northward IMF. Using the OMNI data set, we investigate the seasonal and diurnal variations of the magnitude of the IMF B z under northward IMF conditions. The magnitude of IMF B z peaks at spring and fall equinoxes and reaches the minimum at summer and winter solstices. The seasonal and diurnal variations of IMF B z are more consistent with the R-M effect than the equinoctial hypothesis.
The equinoctial hypothesis could also affect the CDPS occurrence by affecting the threshold of shear flow velocity (Boller & Stolov, 1970) and lead to a semiannual variation of CDPS occurrences. If the equinoctial hypothesis is more important, the dawn-dusk asymmetry of CDPS occurrence could be expected due to the dawn-dusk asymmetry of K-H instability (e.g., Nykyri, 2013). However, the difference between the duskside and dawnside in our CDPS occurrence is not so significant, and both K-H instability and the high-latitude reconnection are easier to occur when the magnitude of IMF B z is larger during northward IMF intervals. The long duration of northward IMF, which is often observed before the CDPS events, appears to be more likely to occur in March and September than in June and December. The axial hypothesis suggests that the variation of the average solar wind velocity is a key factor in the semiannual variation of geomagnetic activity during active times, but the CDPS events we observed are during quiet times, and not related to the solar wind entry under southward IMF conditions. We therefore suggest that both the equinoctial hypothesis and the R-M effect create better conditions than axial hypothesis for solar wind entry under northward IMF conditions in March and September. Of these two alternatives, our statistical study of IMF B z occurrence probability is consistent with the R-M effect, and clearly inconsistent with the equinoctial hypothesis. As a result, the cold and dense plasma sheet should be easier to form, which explains the higher occurrence rate of CDPS observed during spring and fall equinoxes. The CDPS is a critical component of storm time ring current dynamics (Chen et al., 2007;Lavraud, Thomsen, Borovsky, et al., 2006;Thomsen et al., 2003) and magnetosphere-ionosphere coupling (e.g., Gkioulidou et al., 2009). Here we show that the CDPS has a seasonal dependence, which in turn will be reflected in both the formation and generation of the ring current and more generally, magnetosphere-ionosphere coupling.