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Preliminary empirical model of inner boundary of ion plasma sheet
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Preliminary empirical model of inner boundary of ion plasma sheet J.B. Cao a,b,⇑, D. Zhang b,c, H. Reme d,e, I. Dandouras d,e, J.A. Sauvaud d,e, H.S. Fu a,b, X.H. Wei b a
Space Science Institute, School of Astronautics, Beihang University, 100190 Beijing, China b Key laboratory for space weather/NSSC, 100190 Beijing, China c Graduate University of Chinese Academy of Sciences, Beijing 100039, China d University of Toulouse, UPS-OMP, IRAP, Toulouse, France e CNRS, IRAP, BP 44346, F-31028 Toulouse cedex 4, France
Received 31 January 2015; received in revised form 16 June 2015; accepted 17 June 2015 Available online 25 June 2015
Abstract The penetration of the plasma sheet into the inner magnetosphere is important to both ring current formation and spacecraft charging at geosynchronous orbit. This paper, using hot ion data recorded by HIA of TC-1/DSP, establishes an empirical model of the inner boundary of ion plasma sheet (IBIPS) on the near equatorial plane. All IBIPS are located inside geocentric radial distance of 9 RE. We divided local times (LT) into eight local time bins and found that during quiet times (Kp 6 2), the IBIPS is closest to the Earth on the pre-midnight side (LT = 1930–2130) and farthest on the dawn side (LT = 0430–0730), which differs from previous spiral models. The geocentric radius of IBIPS in each local time bin can be described by a linear fitting function: Rps = A + Bkp Kp. The changing rate Bkp of the radius of IBIPS relative to Kp index on the midnight side (LT = 2230–0130) and post-night side (LT = 0130–0430) are the two largest (0.66 and 0.67), indicating that the IBIPS on the night side (LT = 2230–0430) moves fastest when Kp changes. Since the IBIPSs in different local times bins have different changing rates, both the size and shape of IBIPS change when Kp varies. The correlation coefficients between the radius of IBIPS and the instantaneous Kp increase with the increase of DT (the time difference between IBIPS crossing time and preceding Kp interval), which suggests that with the increase of DT, the radius of IBIPS is more and more controlled by instantaneous Kp, and the influence of preceding Kp becomes weaker. The response time of IBIPS to Kp is between 80 and 95 min. When DT > 95 min, the correlation coefficient basically keeps unchanged and only has a weak increase, suggesting that the IBIPS is mainly determined by the convection electric field represented by instantaneous Kp. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Plasma sheet; Inner boundary; Magnetospheric convection; Kp index; Alfven layer; Empirical model
1. Introduction The penetration of plasma sheet into the inner magnetosphere is not only important to the magnetospherical dynamics, especially to the ring current formation and substorm energetic particle injection (Fok et al., 1996; Li et al., 1998; Jordanova et al., 1998; Kozyra et al., 1998; ⇑ Corresponding author at: Space Science Institute, Beihang University, 100191 Beijing, China. E-mail address: [email protected] (J.B. Cao).
http://dx.doi.org/10.1016/j.asr.2015.06.017 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Ganushkina et al., 2005; Dandouras et al., 2009), but also to the spacecraft charging at and outside geosynchronous orbit (Lanzerotti et al., 1998; Davis et al., 2008). Usually, the large scale penetration of the plasma sheet is represented by earthward movement of the inner boundary of the plasma sheet. The inner boundary of plasma sheet is a spatial demarcation boundary that separates the plasma sheet ions on open orbits from those ions on closed orbits and is closely associated with the Alfven layers of plasma sheet ions. Since the ions and electrons in the plasma sheet have separate orbits when they approach the Earth from
J.B. Cao et al. / Advances in Space Research 56 (2015) 1194–1199
the tail due to charge dependent drifts (magnetic field gradient and curvature drifts), the inner boundary of plasma sheet can be divided into two types: the inner boundary of electron plasma sheet and the inner boundary of ion plasma sheet (IBIPS). Mauk and Mcilwain (1974) have established a model which mapped the inner boundary of the plasma sheet as a function of Kp for the region from the premidnight sector to 0100 LT (local time). They found that the radius, Rb of inner boundary of plasma sheet is Rb = (122– 10 Kp)/(LT-7.3) under the assumption that the radial position of the boundary has the same linear dependence as the plasmapause position. Kaye and Kivelson (1979) established a substorm associated, time dependent demarcation boundary for the electrons in the plasma sheet by using data of low energy (0 to 7.1 keV) electron flux recorded by Explorer 45. Up to the present, however, there has been no model of the inner boundary of the plasma sheet based on direct observations of plasmas sheet ions in the near equatorial plane (Mauk and Mcilwain,1974; Korth et al., 1999). In the past decade, the Double Star Program (DSP) of China–Europe and the THEMIS mission of NASA were successfully implemented. Since these two missions operated in the near equatorial plane and have apogees larger than 10 RE, they provide excellent opportunities to study the inner boundary of plasma sheet (Wang et al., 2008; Runov et al., 2008; Cao et al., 2011; Jiang et al., 2011). Using the data of hot ions recorded by HIA/DSP, Cao et al. (2011) performed a statistical study of spatial distributions of IBIPS. They found that the correlation coefficients between the radial distances of the IBIPS, Ri, and Kp are 0.58 on average and can reach 0.72 in the local time range 2100–0300, while the correlation coefficients between Ri and AE or Dst are very low, only around 0.2. This result indicates that the radial distance of IBIPS is best ordered by Kp, which motivates us to establish an empirical model of IBIPS versus Kp. The purpose of this paper is to use hot ion data recorded by HIA/TC-1 to establish an empirical model of the IBIPS, which permits us to roughly estimate the positions of IBIPS in the near equatorial plane and discuss in more detail the correlation between IBIPS and Kp. Throughout this paper, the GSM coordinates are used.
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sheet is defined as the point where ion temperature is equal to 2 keV during rapid increase of temperature. The reason to choose the ion temperature not ion flux as the criterion of IBIPS is that the slope of rapid increase of ion temperature from tens –hundreds eV to 3–6 keV (i.e. the transition layer of IBIPS) corresponds very well to the slope of rapid increase of ion flux in the energy range 5–15 keV. In addition, ion temperature is also a parameter which is more readily accessible than ion flux. The transition layer of IBIPS is usually 0.2–0.6 RE wide. Since the error of ion temperature measured by HIA is about 18%, the uncertainty of Rps induced by temperature measurement error is usually between 0.02 and 0.04 RE, which depends on the sharpness of temperature slope. The dataset of IBIPS crossing events used here consists of 385 IBIPS crossing events which are determined by using the hot ion data of HIA from 2004 to 2007. These IBIPS crossing events have an inclination angle smaller than 14°. Fig. 1 shows the radius of IBIPS versus instantaneous Kp for all events. The radius of IBIPS has a clear tendency to decrease with increasing of Kp, which is consistent with the theory of Alfven layers (Korth et al., 1999; Zhang et al., 2015). This result is reasonable because the increase of Kp actually indicates the enhancement of the convection electric field (Thomsen, 2004), and an enhanced electric field can cause the Alfven layers of plasma sheet ions to move earthward. Fig. 1 also shows that even during quiet times when Kp < 1, the IBIPS can still penetrate into geosynchronous orbit. When Kp exceeds 3.67 (4), the IBIPS are all inside geosynchronous orbit. The geocentric radius of IBIPS is found to be dependent on local time, which is responsible for the spread of Rps for each Kp in Fig. 1. To reveal this, we divided all events into eight local time bins defined as 2230–0130, 0130–0430, 0430–0730, 0730–1030, 1030–1330, 1330–1630, 1630–1930 and 1930–2230. Fig. 2 shows the radius of IBIPS Rps versus Kp index for the post-midnight bins (LT = 0130–0430). We use a least-square polynomial fitting technique to fit these
2. Empirical model of inner boundary of ion plasma sheet The TC-1/DSP satellite is in an eccentric near equatorial orbit with an apogee radial distance of about 13.4 RE, a perigee radial distance of about 6934 km, and an inclination of 28.5° (Liu et al., 2005). The HIA instrument on board the TC-1 spacecraft is an ion spectrometer identical to the HIA sensor of the CIS instrument on board the 4 Cluster spacecraft (Reme et al., 2001, 2005). This instrument measures the 3-D distribution functions of the ions between 5 eV/q and 32 keV/q without mass discrimination. As in Cao et al. (2011), the inner boundary of ion plasma
Fig. 1. Radius of inner boundary of ion plasma sheet versus Kp on near Equatorial plane for all events (LT = 0000–2400).
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IBIPS: LT=0130-0430 10 9 8
Rps(Re)
7 6 5 4
Rps=7.81-0.66Kp
3 2 1 0 0.0
0.5
1.0
1.5
2.0 Kp
2.5
3.0
3.5
4.0
Fig. 2. Radius of inner boundary of ion plasma sheet versus Kp on near Equatorial plane for post-night events (LT = 0130–0430). A Kp dependence is evident. The black line represents the linear fitting curve Rps = 7.81–0.66 Kp.
points. We try the linear and second degree polynomial fittings and obtain the following expressions: Linear :
Rps ðReÞ ¼ 7:81 0:66 Kp
Second degree : Rps ðReÞ ¼ 7:83 0:68 Kp þ 0:0041 Kp2 It can be easily seen that the two expressions are very close. The Rps difference between them is less than 0.02 for Kp 6 4. Other higher degree polynomial fits give a similar result. Therefore, the linear fit is a suitable fit for Rps. The meanings of the coefficients in the linear fit Rps = A + Bkp Kp can be understood physically, such that the parameter A represents the radial distance of IBIPS when Kp = 0 and the parameter Bkp represents the rate of change of the radius of IBIPS with respect to Kp. Using the same method, we obtained the two parameters A and Bkp for the other 7 bins. Table 1 gives two parameters A and Bkp as well as the standard errors r for eight local time bins. It is worth noting that the standard errors on the dayside are larger than on the nightside. This is because when plasma sheet ions drift from nightside to the dayside, they will encounter some loss mechanisms, such as wave-particle interaction and charge exchange. Such an ion flux loss will thus make the ion boundary less sharp.
Fig. 3 shows the inner boundaries of ion plasma sheet calculated using the parameters in Table 1 at Kp = 0, 1, 2 and 3. In Fig. 3, we used a simple bilinear interpolation technique so as to link smoothly the two values at the centers of two neighboring MLT bins. As seen in Table 1, the rates of change of Rps in the LT bins 2230–0130 and 0130– 0430 are the two largest (Bkp = 0.66 and 0.67). This means that when Kp changes, the IBIPS on the pre-midnight and post-midnight sides move fastest (see Fig. 3). During quiet times (Kp 6 2), the IBIPS on the dawn side (LT = 0430–0730) is the farthest from the Earth and the IBIPS on the premidnight side (LT = 1930–2230) is the closest to the Earth. Since the IBIPSs in different local times bins have different changing rates, both the size and shape of the IBIPS change when Kp varies. For example, when Kp = 0, the radius of IBIPS is 7.05 Re on the premidnight side (LT = 1930–2230) and 7.39 RE on the midnight side (LT = 2230–0130), which means that the IBIPS on the premidnight side is closer to the Earth than that on the midnight side. When Kp increases, they move together toward the Earth. Since the changing rate of IBIPS on the midnight side (0.66) is larger than that on the premidnight side (0.49), the IBIPS on the midnight side will be closer to the Earth than the IBIPS on the premidnight side when Kp P 2. Previous studies based on data obtained at geosynchronous orbit have shown that the inner boundary of plasma sheet can be seen to be a structure that spirals radially inward from dusk to postmidnight (Mauk and Mcilwain, 1974). According to these models of spiral structures, the IBIPS on the midnight side is always closest to the Earth. However our results show that the IBIPS position closest to the Earth is changeable and not always
Table 1 Two parameters A and B in the function of Rps = A + B Kp for eight local time bins. r is the standard error between points and linear fit. Bins
LT
A
Bkp
r
Midnight Post midnight Dawn Morning Noon Afternoon Dusk Premidnight
2230–0130 0130–0430 0430–0730 0730–1030 1030–1330 1330–1630 1630–1930 1930–2230
7.39 7.81 7.91 7.79 7.46 7.48 7.29 7.05
0.66 0.67 0.42 0.49 0.43 0.54 0.47 0.48
0.67 0.70 0.70 0.69 0.77 0.76 0.72 0.69
Fig. 3. The inner boundaries of ion plasma sheet at Kp = 0, 1, 2 and 3 in the equatorial plane. The blue dashed line is the geosynchronous orbit.
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located on the midnight side. The main reason for this difference may be that previous studies made an assumption that the radial position of the boundary depended linearly in the same manner as the plasmapause positions. This conclusion obtained by our IBIPS model is consistent with previous hot ion observations at geosynchronous orbit. The IBIPS often passes the geosynchronous orbit (6.6 Re) when it moves to the Earth in response to enhanced convection (Borovsky et al., 1998; Korth et al., 1999; Thomsen et al., 2003; Denton et al., 2005; and Lavraud et al., 2006), Using the empirical model presented in Table 1, we can roughly analyze the temporal order of penetration of plasma sheet ions into the geosynchronous orbit. Provided that Kp starts to increase smoothly from zero, the IBIPS will move earthward from outside geosynchronous orbit. The IBIPS at different local time bins will arrive at geosynchronous orbit at different Kp values. Table 2 shows the Kp indexes which correspond to the arrivals of IBIPS at geosynchronous orbit for eight local time bins. In order to see more clearly, we also give the temporal order of the arrivals of IBIPS at geosynchronous orbit in Table 2. The IBIPS first crosses the pre-midnight geosynchronous orbit (LT = 1930–2230) at Kp = 0.93, then the midnight geosynchronous orbit (LT = 2230–0130) and finally the dawn side geosynchronous orbit (LT = 0430–0730) at Kp = 3.12. Korth et al. (1999) showed that the 10.647 keV protons are first observed in the local time bin of 1800–2300 at Kp = 0.67 (see their Plate 2). In addition, Zhang et al. (2006) reported that the plasma sheet ions (intermediately hot ions in their paper) can have more frequent access to geosynchronous orbit in the pre-midnight sector. 3. Response time of IBIPS to the Kp index The IBIPS is determined by the drift of plasma sheet ions towards and around the Earth. Thus the IBIPS will change when Kp index (i.e. convection electric field) changes. Since the time resolution of the Kp index is three hours, the response of IBIPS at different times within a three-hour-interval of the Kp index may be different. It is meaningful to determine the response time of IBIPS to Kp index. Fig. 4 shows the correlation coefficients of the radius of IBIPS and instantaneous Kp index as a function of DT = Ti T0, where Ti is the time of IBIPS crossing
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and T0 is the start time of the 3-hour interval of instantaneous Kp index, i.e., one of the values of 0,3,6,9,12,15,18 and 21. The correlation coefficient is calculated within a window of 60 min for every 5 min in the range of DT from 30 to 150 min. As seen in Fig. 4, the correlation coefficient basically increases with increase of DT. The correlation coefficient is 0.52 at DT = 30 min and about 0.63 at DT = 150 min. This result is reasonable because the larger DT is, the closer connection with the instantaneous Kp index the radius of IBIPS has and the smaller the influence of previous Kp index is. In fact, if DT is closest to zero, the IBIPS is mainly decided by the preceding Kp index rather than the instantaneous Kp index. The most interesting point in Fig. 3 is that between DT = 80 min and 95 min, the correlation coefficient sharply increases from 0.54 to 0.61. When DT >95 min, the correlation coefficient only weakly increase and keeps almost unchanged. Therefore DT = 80 min possibly corresponds to the response time of IBIPS to Kp index. This response time is related to the time needed for inner magnetospheric electric field shielding to readjust to convection electric field change. Wolf et al. (2007) pointed out that when Kp index increases, the inner-magnetosphere shielding effect will change and the inner magnetospheric electric field needs some time to reach its final stable state. It just means that the inner edge of the plasma sheet needs time to readjust to a change in convection. The theoretical results show that ten minutes after the enhancement of convection electric field, the shielding effect enhances considerably, and two hours later, shielding has reasserted itself quite effectively and the inner magnetospheric electric field reaches its final stable state (Jaggi and Wolf, 1973). Therefore, the correlation coefficient for DT >95 min basically remains unchanged and only has a weak increase. Here one question arises naturally. If DT is close to zero and the IBIPS is completely determined by the preceding Kp, why can the correlation coefficient at DT = 0 still reaches 0.51? This is because generally, the difference
Table 2 Kp index corresponding to the arrivals of IBIPS at geosynchronous orbit for eight local time bins. Bins
LT
Kp
Temporal order
Midnight Post midnight Dawn Morning Noon Afternoon Dusk Premidnight
2230–0130 0130–0430 0430–0730 0730–1030 1030–1330 1330–1630 1630–1930 1930–2230
1.20 1.81 3.12 2.42 2.00 1.62 1.46 0.94
2 5 8 7 6 4 3 1
Fig. 4. Correlation coefficients of radius of IBIPS and instantaneous Kp index as a function of DT = Ti T0, where Ti is the time of IBIPS crossing and T0 is the start time of the 3-hour interval of instantaneous Kp index.
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between two neighboring Kp indexes is very small, and the correlation coefficient between IBIPS and instantaneous Kp index to some extent approximately represents the correlation coefficient between IBIPS and preceding Kp index. However during the period of rapidly changing Kp index, the influence of preceding Kp index is not ignorable, particularly for those IBIPS with DT <80 min. 4. Conclusions This paper, using the hot ion data of HIA of TC-1, establishes an empirical model of IBIPS for Kp 6 4. We collected 402 IBIPS crossing events based on the data recorded by HIA of TC-1 from 2004 to 2007. All IBIPS are located inside geocentric radial distance of 9 RE. Since the geocentric radius of IBIPS is dependent on local time, we divided the IBIPS crossing events into eight local time bins. The radius of IBIPS for each local time bin is described by a linear function: Rps = A + B Kp where B represents the rate of change of Rps relative to Kp. During quiet times (Kp < 2), the IBIPS is closest to the Earth on the premidnight side (LT = 1930–2130) and farthest on the dawn side (LT = 0430–0730). The changing rate of radius of IBIPS relative to Kp on the midnight side (LT = 2230–0130) and post-midnight side (LT = 0130– 0430) are the two largest (0.66 and 0.67), indicating that the IBIPS on the night side (LT = 2230–0430) moves fastest when Kp changes. Since the changing rate on the midnight side (LT = 2230–0130) is larger than that on the pre-midnight side (LT = 1930–2130), the IBIPS on the midnight side will become the closest to the Earth when Kp P 2. Since the radius of IBIPS in different local times bins have different changing rates, both the size and shape of IBIPS change when Kp varies. The correlation coefficients between the radius of IBIPS and instantaneous Kp index increase with the increase of DT (the time difference between IBIPS crossing time and preceding Kp interval), which suggests that with the increase of DT, the radius of IBIPS is more and more controlled by instantaneous Kp index, and the influence of preceding Kp index is weaker and weaker. The response time of IBIPS to Kp index is between 80 and 95 min. This response time is comparable to the time needed for inner magnetospheric electric field shielding to readjust to convection electric field change. When DT >95 min, the correlation coefficient basically remains unchanged and only has a weak increase, suggesting that the IBIPS is mainly determined by the convection electric field represented by instantaneous Kp. It must be pointed out that the model presented in this paper is based upon the data collected at Kp 6 4. Whether this model is still applicable for larger Kp index needs to be verified in the future when more data at large Kp indexes are available. In addition, it may be better to include the data of THEMIS in the future. With larger dataset, we can select the crossing events with smaller inclination angle in GSM coordinates, which make the
observation points closer to GSM equatorial plane and allows us to have a more accurate model. Acknowledgement This work was supported by NSFC Grants 41431071, 41474124 and 41174141, 973 Program Grant 2011CB811404 and the Specialized Research Fund for State Key Laboratories for space weather. References Borovsky, J.E., Thomsen, M.F., Elphic, R.C., Cayton, T.E., McComas, D.J., 1998 (The transport of plasma sheet material from the distant tail to geosynchronous orbit). J. Geophys. Res. 103, 20297–20331. Cao, J.B., Ding, W.Z., Reme, H., Dandouras, I., Dunlop, M., Liu, Z.X., Yang, J.Y., 2011. The statistical studies of the inner boundary of plasma sheet. Ann. Geophys. 29, 289–298. http://dx.doi.org/10.5194/ angeo-29-289-2011, 2011; Corrigendum to“The statistical studies of the inner boundary of plasma sheet”, Ann. Geophys., 29, 349, doi:10.5194/angeo-29-349-2011. Davis, V.A., Mandell, M.J., Thomsen, M.F., 2008. Representation of the measured geosynchronous plasma environment in spacecraft charging calculations. J. Geophys. Res. 113, A10204. http://dx.doi.org/10.1029/ 2008JA013116. Dandouras, I., Cao, J., Vallat, C., 2009 (Energetic ion dynamics of the inner magnetosphere revealed in coordinated Cluster-Double Star observations). J. Geophys. Res. 114, A01S90. http://dx.doi.org/ 10.1029/2007JA012757. Denton, M.H., Thomsen, M.F., Korth, H., Lynch, S., Zhang, J.C., Liemohn, M.W., 2005. Bulk plasma properties at geosynchronous orbit. J. Geophys. Res. 110, A07223. http://dx.doi.org/10.1029/ 2004JA010861. Fok, M.-C., Moore, T.E., Greenspan, M.E., 1996. Ring current development during storm main phase. J. Geophys. Res. 101, 15311–15322. Ganushkina, N.Y., Pulkkinen, T.I., Fritz, T., 2005. Role of substorm associated impulsive electric fields in the ring current development during storms. Ann. Geophys. 23, 579–591. Jaggi, R.K., Wolf, R.A., 1973. Self-consistent calculation of the motion of a sheet of ions in the magnetosphere. J. Geophys. Res. 78, 2852–2866. Jiang, F., Kivelson, M.G., Walker, R.J., Khurana, K.K., Angelopoulos, V., Hsu, T., 2011. A statistical study of the inner edge of the electron plasma sheet and the net convection potential as a function of geomagnetic activity. J. Geophys. Res. 116, A06215. http://dx.doi.org/ 10.1029/2010JA016179. Jordanova, V.K., Farrugia, C.J., Janoo, L., Quinn, J.M., Torbert, R.B., Ogilvie, K.W., Lepping, R.P., Steinberg, J.T., McComas, D.J., Belian, R.D., 1998. October 1985 magnetic cloud and accompanying storm activity: Ring current evolution. J. Geophys. Res. 103, 79–92. Kaye, S.M., Kivelson, M.G., 1979. Time dependent convection electric fields and plasma injection. J. Geophys. Res. 84 (A8), 4183–4188. http://dx.doi.org/10.1029/JA084iA08p04183. Korth, H., Thomsen, M.F., Borovsky, J.E., McComas, D.J., 1999 (Plasma sheet access to geosynchronous orbit). J. Geophys. Res. 104, 25047. Kozyra, J.U., Jordanova, V.K., Borovsky, J.E., et al., 1998. Effects of a high-density plasma sheet on ring current development during the November 2–6, 1993, magnetic storm. J. Geophys. Res. 103, 26285– 26306. Lanzerotti, L.J., Breglia, C., Maurer, D.W., Johnson III, G.K., Maclennan, C.G., 1998. Studies of spacecraft charging on a geosynchronous telecommunications satellite. Adv. Space Res. 22 (1), 79–82. Lavraud, B., Thomsen, M.F., Wing, S., Fujimoto, M., Denton, M.H., Borovsky, J.E., Asnes, A., Seki, K., Weygand, J.M., 2006. Observations of two distinct cold, dense ion populations at geosynchronous orbit: local time asymmetry, solar wind dependence and origin. Ann. Geophys. 24, 3451–3465.
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ScienceDirect Advances in Space Research 56 (2015) 1194–1199 www.elsevier.com/locate/asr
Preliminary empirical model of inner boundary of ion plasma sheet J.B. Cao a,b,⇑, D. Zhang b,c, H. Reme d,e, I. Dandouras d,e, J.A. Sauvaud d,e, H.S. Fu a,b, X.H. Wei b a
Space Science Institute, School of Astronautics, Beihang University, 100190 Beijing, China b Key laboratory for space weather/NSSC, 100190 Beijing, China c Graduate University of Chinese Academy of Sciences, Beijing 100039, China d University of Toulouse, UPS-OMP, IRAP, Toulouse, France e CNRS, IRAP, BP 44346, F-31028 Toulouse cedex 4, France
Received 31 January 2015; received in revised form 16 June 2015; accepted 17 June 2015 Available online 25 June 2015
Abstract The penetration of the plasma sheet into the inner magnetosphere is important to both ring current formation and spacecraft charging at geosynchronous orbit. This paper, using hot ion data recorded by HIA of TC-1/DSP, establishes an empirical model of the inner boundary of ion plasma sheet (IBIPS) on the near equatorial plane. All IBIPS are located inside geocentric radial distance of 9 RE. We divided local times (LT) into eight local time bins and found that during quiet times (Kp 6 2), the IBIPS is closest to the Earth on the pre-midnight side (LT = 1930–2130) and farthest on the dawn side (LT = 0430–0730), which differs from previous spiral models. The geocentric radius of IBIPS in each local time bin can be described by a linear fitting function: Rps = A + Bkp Kp. The changing rate Bkp of the radius of IBIPS relative to Kp index on the midnight side (LT = 2230–0130) and post-night side (LT = 0130–0430) are the two largest (0.66 and 0.67), indicating that the IBIPS on the night side (LT = 2230–0430) moves fastest when Kp changes. Since the IBIPSs in different local times bins have different changing rates, both the size and shape of IBIPS change when Kp varies. The correlation coefficients between the radius of IBIPS and the instantaneous Kp increase with the increase of DT (the time difference between IBIPS crossing time and preceding Kp interval), which suggests that with the increase of DT, the radius of IBIPS is more and more controlled by instantaneous Kp, and the influence of preceding Kp becomes weaker. The response time of IBIPS to Kp is between 80 and 95 min. When DT > 95 min, the correlation coefficient basically keeps unchanged and only has a weak increase, suggesting that the IBIPS is mainly determined by the convection electric field represented by instantaneous Kp. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Plasma sheet; Inner boundary; Magnetospheric convection; Kp index; Alfven layer; Empirical model
1. Introduction The penetration of plasma sheet into the inner magnetosphere is not only important to the magnetospherical dynamics, especially to the ring current formation and substorm energetic particle injection (Fok et al., 1996; Li et al., 1998; Jordanova et al., 1998; Kozyra et al., 1998; ⇑ Corresponding author at: Space Science Institute, Beihang University, 100191 Beijing, China. E-mail address: [email protected] (J.B. Cao).
http://dx.doi.org/10.1016/j.asr.2015.06.017 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Ganushkina et al., 2005; Dandouras et al., 2009), but also to the spacecraft charging at and outside geosynchronous orbit (Lanzerotti et al., 1998; Davis et al., 2008). Usually, the large scale penetration of the plasma sheet is represented by earthward movement of the inner boundary of the plasma sheet. The inner boundary of plasma sheet is a spatial demarcation boundary that separates the plasma sheet ions on open orbits from those ions on closed orbits and is closely associated with the Alfven layers of plasma sheet ions. Since the ions and electrons in the plasma sheet have separate orbits when they approach the Earth from
J.B. Cao et al. / Advances in Space Research 56 (2015) 1194–1199
the tail due to charge dependent drifts (magnetic field gradient and curvature drifts), the inner boundary of plasma sheet can be divided into two types: the inner boundary of electron plasma sheet and the inner boundary of ion plasma sheet (IBIPS). Mauk and Mcilwain (1974) have established a model which mapped the inner boundary of the plasma sheet as a function of Kp for the region from the premidnight sector to 0100 LT (local time). They found that the radius, Rb of inner boundary of plasma sheet is Rb = (122– 10 Kp)/(LT-7.3) under the assumption that the radial position of the boundary has the same linear dependence as the plasmapause position. Kaye and Kivelson (1979) established a substorm associated, time dependent demarcation boundary for the electrons in the plasma sheet by using data of low energy (0 to 7.1 keV) electron flux recorded by Explorer 45. Up to the present, however, there has been no model of the inner boundary of the plasma sheet based on direct observations of plasmas sheet ions in the near equatorial plane (Mauk and Mcilwain,1974; Korth et al., 1999). In the past decade, the Double Star Program (DSP) of China–Europe and the THEMIS mission of NASA were successfully implemented. Since these two missions operated in the near equatorial plane and have apogees larger than 10 RE, they provide excellent opportunities to study the inner boundary of plasma sheet (Wang et al., 2008; Runov et al., 2008; Cao et al., 2011; Jiang et al., 2011). Using the data of hot ions recorded by HIA/DSP, Cao et al. (2011) performed a statistical study of spatial distributions of IBIPS. They found that the correlation coefficients between the radial distances of the IBIPS, Ri, and Kp are 0.58 on average and can reach 0.72 in the local time range 2100–0300, while the correlation coefficients between Ri and AE or Dst are very low, only around 0.2. This result indicates that the radial distance of IBIPS is best ordered by Kp, which motivates us to establish an empirical model of IBIPS versus Kp. The purpose of this paper is to use hot ion data recorded by HIA/TC-1 to establish an empirical model of the IBIPS, which permits us to roughly estimate the positions of IBIPS in the near equatorial plane and discuss in more detail the correlation between IBIPS and Kp. Throughout this paper, the GSM coordinates are used.
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sheet is defined as the point where ion temperature is equal to 2 keV during rapid increase of temperature. The reason to choose the ion temperature not ion flux as the criterion of IBIPS is that the slope of rapid increase of ion temperature from tens –hundreds eV to 3–6 keV (i.e. the transition layer of IBIPS) corresponds very well to the slope of rapid increase of ion flux in the energy range 5–15 keV. In addition, ion temperature is also a parameter which is more readily accessible than ion flux. The transition layer of IBIPS is usually 0.2–0.6 RE wide. Since the error of ion temperature measured by HIA is about 18%, the uncertainty of Rps induced by temperature measurement error is usually between 0.02 and 0.04 RE, which depends on the sharpness of temperature slope. The dataset of IBIPS crossing events used here consists of 385 IBIPS crossing events which are determined by using the hot ion data of HIA from 2004 to 2007. These IBIPS crossing events have an inclination angle smaller than 14°. Fig. 1 shows the radius of IBIPS versus instantaneous Kp for all events. The radius of IBIPS has a clear tendency to decrease with increasing of Kp, which is consistent with the theory of Alfven layers (Korth et al., 1999; Zhang et al., 2015). This result is reasonable because the increase of Kp actually indicates the enhancement of the convection electric field (Thomsen, 2004), and an enhanced electric field can cause the Alfven layers of plasma sheet ions to move earthward. Fig. 1 also shows that even during quiet times when Kp < 1, the IBIPS can still penetrate into geosynchronous orbit. When Kp exceeds 3.67 (4), the IBIPS are all inside geosynchronous orbit. The geocentric radius of IBIPS is found to be dependent on local time, which is responsible for the spread of Rps for each Kp in Fig. 1. To reveal this, we divided all events into eight local time bins defined as 2230–0130, 0130–0430, 0430–0730, 0730–1030, 1030–1330, 1330–1630, 1630–1930 and 1930–2230. Fig. 2 shows the radius of IBIPS Rps versus Kp index for the post-midnight bins (LT = 0130–0430). We use a least-square polynomial fitting technique to fit these
2. Empirical model of inner boundary of ion plasma sheet The TC-1/DSP satellite is in an eccentric near equatorial orbit with an apogee radial distance of about 13.4 RE, a perigee radial distance of about 6934 km, and an inclination of 28.5° (Liu et al., 2005). The HIA instrument on board the TC-1 spacecraft is an ion spectrometer identical to the HIA sensor of the CIS instrument on board the 4 Cluster spacecraft (Reme et al., 2001, 2005). This instrument measures the 3-D distribution functions of the ions between 5 eV/q and 32 keV/q without mass discrimination. As in Cao et al. (2011), the inner boundary of ion plasma
Fig. 1. Radius of inner boundary of ion plasma sheet versus Kp on near Equatorial plane for all events (LT = 0000–2400).
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IBIPS: LT=0130-0430 10 9 8
Rps(Re)
7 6 5 4
Rps=7.81-0.66Kp
3 2 1 0 0.0
0.5
1.0
1.5
2.0 Kp
2.5
3.0
3.5
4.0
Fig. 2. Radius of inner boundary of ion plasma sheet versus Kp on near Equatorial plane for post-night events (LT = 0130–0430). A Kp dependence is evident. The black line represents the linear fitting curve Rps = 7.81–0.66 Kp.
points. We try the linear and second degree polynomial fittings and obtain the following expressions: Linear :
Rps ðReÞ ¼ 7:81 0:66 Kp
Second degree : Rps ðReÞ ¼ 7:83 0:68 Kp þ 0:0041 Kp2 It can be easily seen that the two expressions are very close. The Rps difference between them is less than 0.02 for Kp 6 4. Other higher degree polynomial fits give a similar result. Therefore, the linear fit is a suitable fit for Rps. The meanings of the coefficients in the linear fit Rps = A + Bkp Kp can be understood physically, such that the parameter A represents the radial distance of IBIPS when Kp = 0 and the parameter Bkp represents the rate of change of the radius of IBIPS with respect to Kp. Using the same method, we obtained the two parameters A and Bkp for the other 7 bins. Table 1 gives two parameters A and Bkp as well as the standard errors r for eight local time bins. It is worth noting that the standard errors on the dayside are larger than on the nightside. This is because when plasma sheet ions drift from nightside to the dayside, they will encounter some loss mechanisms, such as wave-particle interaction and charge exchange. Such an ion flux loss will thus make the ion boundary less sharp.
Fig. 3 shows the inner boundaries of ion plasma sheet calculated using the parameters in Table 1 at Kp = 0, 1, 2 and 3. In Fig. 3, we used a simple bilinear interpolation technique so as to link smoothly the two values at the centers of two neighboring MLT bins. As seen in Table 1, the rates of change of Rps in the LT bins 2230–0130 and 0130– 0430 are the two largest (Bkp = 0.66 and 0.67). This means that when Kp changes, the IBIPS on the pre-midnight and post-midnight sides move fastest (see Fig. 3). During quiet times (Kp 6 2), the IBIPS on the dawn side (LT = 0430–0730) is the farthest from the Earth and the IBIPS on the premidnight side (LT = 1930–2230) is the closest to the Earth. Since the IBIPSs in different local times bins have different changing rates, both the size and shape of the IBIPS change when Kp varies. For example, when Kp = 0, the radius of IBIPS is 7.05 Re on the premidnight side (LT = 1930–2230) and 7.39 RE on the midnight side (LT = 2230–0130), which means that the IBIPS on the premidnight side is closer to the Earth than that on the midnight side. When Kp increases, they move together toward the Earth. Since the changing rate of IBIPS on the midnight side (0.66) is larger than that on the premidnight side (0.49), the IBIPS on the midnight side will be closer to the Earth than the IBIPS on the premidnight side when Kp P 2. Previous studies based on data obtained at geosynchronous orbit have shown that the inner boundary of plasma sheet can be seen to be a structure that spirals radially inward from dusk to postmidnight (Mauk and Mcilwain, 1974). According to these models of spiral structures, the IBIPS on the midnight side is always closest to the Earth. However our results show that the IBIPS position closest to the Earth is changeable and not always
Table 1 Two parameters A and B in the function of Rps = A + B Kp for eight local time bins. r is the standard error between points and linear fit. Bins
LT
A
Bkp
r
Midnight Post midnight Dawn Morning Noon Afternoon Dusk Premidnight
2230–0130 0130–0430 0430–0730 0730–1030 1030–1330 1330–1630 1630–1930 1930–2230
7.39 7.81 7.91 7.79 7.46 7.48 7.29 7.05
0.66 0.67 0.42 0.49 0.43 0.54 0.47 0.48
0.67 0.70 0.70 0.69 0.77 0.76 0.72 0.69
Fig. 3. The inner boundaries of ion plasma sheet at Kp = 0, 1, 2 and 3 in the equatorial plane. The blue dashed line is the geosynchronous orbit.
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located on the midnight side. The main reason for this difference may be that previous studies made an assumption that the radial position of the boundary depended linearly in the same manner as the plasmapause positions. This conclusion obtained by our IBIPS model is consistent with previous hot ion observations at geosynchronous orbit. The IBIPS often passes the geosynchronous orbit (6.6 Re) when it moves to the Earth in response to enhanced convection (Borovsky et al., 1998; Korth et al., 1999; Thomsen et al., 2003; Denton et al., 2005; and Lavraud et al., 2006), Using the empirical model presented in Table 1, we can roughly analyze the temporal order of penetration of plasma sheet ions into the geosynchronous orbit. Provided that Kp starts to increase smoothly from zero, the IBIPS will move earthward from outside geosynchronous orbit. The IBIPS at different local time bins will arrive at geosynchronous orbit at different Kp values. Table 2 shows the Kp indexes which correspond to the arrivals of IBIPS at geosynchronous orbit for eight local time bins. In order to see more clearly, we also give the temporal order of the arrivals of IBIPS at geosynchronous orbit in Table 2. The IBIPS first crosses the pre-midnight geosynchronous orbit (LT = 1930–2230) at Kp = 0.93, then the midnight geosynchronous orbit (LT = 2230–0130) and finally the dawn side geosynchronous orbit (LT = 0430–0730) at Kp = 3.12. Korth et al. (1999) showed that the 10.647 keV protons are first observed in the local time bin of 1800–2300 at Kp = 0.67 (see their Plate 2). In addition, Zhang et al. (2006) reported that the plasma sheet ions (intermediately hot ions in their paper) can have more frequent access to geosynchronous orbit in the pre-midnight sector. 3. Response time of IBIPS to the Kp index The IBIPS is determined by the drift of plasma sheet ions towards and around the Earth. Thus the IBIPS will change when Kp index (i.e. convection electric field) changes. Since the time resolution of the Kp index is three hours, the response of IBIPS at different times within a three-hour-interval of the Kp index may be different. It is meaningful to determine the response time of IBIPS to Kp index. Fig. 4 shows the correlation coefficients of the radius of IBIPS and instantaneous Kp index as a function of DT = Ti T0, where Ti is the time of IBIPS crossing
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and T0 is the start time of the 3-hour interval of instantaneous Kp index, i.e., one of the values of 0,3,6,9,12,15,18 and 21. The correlation coefficient is calculated within a window of 60 min for every 5 min in the range of DT from 30 to 150 min. As seen in Fig. 4, the correlation coefficient basically increases with increase of DT. The correlation coefficient is 0.52 at DT = 30 min and about 0.63 at DT = 150 min. This result is reasonable because the larger DT is, the closer connection with the instantaneous Kp index the radius of IBIPS has and the smaller the influence of previous Kp index is. In fact, if DT is closest to zero, the IBIPS is mainly decided by the preceding Kp index rather than the instantaneous Kp index. The most interesting point in Fig. 3 is that between DT = 80 min and 95 min, the correlation coefficient sharply increases from 0.54 to 0.61. When DT >95 min, the correlation coefficient only weakly increase and keeps almost unchanged. Therefore DT = 80 min possibly corresponds to the response time of IBIPS to Kp index. This response time is related to the time needed for inner magnetospheric electric field shielding to readjust to convection electric field change. Wolf et al. (2007) pointed out that when Kp index increases, the inner-magnetosphere shielding effect will change and the inner magnetospheric electric field needs some time to reach its final stable state. It just means that the inner edge of the plasma sheet needs time to readjust to a change in convection. The theoretical results show that ten minutes after the enhancement of convection electric field, the shielding effect enhances considerably, and two hours later, shielding has reasserted itself quite effectively and the inner magnetospheric electric field reaches its final stable state (Jaggi and Wolf, 1973). Therefore, the correlation coefficient for DT >95 min basically remains unchanged and only has a weak increase. Here one question arises naturally. If DT is close to zero and the IBIPS is completely determined by the preceding Kp, why can the correlation coefficient at DT = 0 still reaches 0.51? This is because generally, the difference
Table 2 Kp index corresponding to the arrivals of IBIPS at geosynchronous orbit for eight local time bins. Bins
LT
Kp
Temporal order
Midnight Post midnight Dawn Morning Noon Afternoon Dusk Premidnight
2230–0130 0130–0430 0430–0730 0730–1030 1030–1330 1330–1630 1630–1930 1930–2230
1.20 1.81 3.12 2.42 2.00 1.62 1.46 0.94
2 5 8 7 6 4 3 1
Fig. 4. Correlation coefficients of radius of IBIPS and instantaneous Kp index as a function of DT = Ti T0, where Ti is the time of IBIPS crossing and T0 is the start time of the 3-hour interval of instantaneous Kp index.
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between two neighboring Kp indexes is very small, and the correlation coefficient between IBIPS and instantaneous Kp index to some extent approximately represents the correlation coefficient between IBIPS and preceding Kp index. However during the period of rapidly changing Kp index, the influence of preceding Kp index is not ignorable, particularly for those IBIPS with DT <80 min. 4. Conclusions This paper, using the hot ion data of HIA of TC-1, establishes an empirical model of IBIPS for Kp 6 4. We collected 402 IBIPS crossing events based on the data recorded by HIA of TC-1 from 2004 to 2007. All IBIPS are located inside geocentric radial distance of 9 RE. Since the geocentric radius of IBIPS is dependent on local time, we divided the IBIPS crossing events into eight local time bins. The radius of IBIPS for each local time bin is described by a linear function: Rps = A + B Kp where B represents the rate of change of Rps relative to Kp. During quiet times (Kp < 2), the IBIPS is closest to the Earth on the premidnight side (LT = 1930–2130) and farthest on the dawn side (LT = 0430–0730). The changing rate of radius of IBIPS relative to Kp on the midnight side (LT = 2230–0130) and post-midnight side (LT = 0130– 0430) are the two largest (0.66 and 0.67), indicating that the IBIPS on the night side (LT = 2230–0430) moves fastest when Kp changes. Since the changing rate on the midnight side (LT = 2230–0130) is larger than that on the pre-midnight side (LT = 1930–2130), the IBIPS on the midnight side will become the closest to the Earth when Kp P 2. Since the radius of IBIPS in different local times bins have different changing rates, both the size and shape of IBIPS change when Kp varies. The correlation coefficients between the radius of IBIPS and instantaneous Kp index increase with the increase of DT (the time difference between IBIPS crossing time and preceding Kp interval), which suggests that with the increase of DT, the radius of IBIPS is more and more controlled by instantaneous Kp index, and the influence of preceding Kp index is weaker and weaker. The response time of IBIPS to Kp index is between 80 and 95 min. This response time is comparable to the time needed for inner magnetospheric electric field shielding to readjust to convection electric field change. When DT >95 min, the correlation coefficient basically remains unchanged and only has a weak increase, suggesting that the IBIPS is mainly determined by the convection electric field represented by instantaneous Kp. It must be pointed out that the model presented in this paper is based upon the data collected at Kp 6 4. Whether this model is still applicable for larger Kp index needs to be verified in the future when more data at large Kp indexes are available. In addition, it may be better to include the data of THEMIS in the future. With larger dataset, we can select the crossing events with smaller inclination angle in GSM coordinates, which make the
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