Journal of Geophysical Research: Space Physics

Joint responses of geosynchronous magnetic field and relativistic electrons to external changes in solar wind dynamic pressure and interplanetary magnetic field

Authors


Corresponding author: L. Y. Li, School of Astronautics, Beihang University, XueYuan Road No. 37, HaiDian District, Beijing 100191, China. (lyli_ssri@buaa.edu.cn)

Abstract

[1] This paper studied statistically the joint responses of magnetic field and relativistic (>0.5 MeV) electrons at geosynchronous orbit to 201 interplanetary perturbations during 6 years from 2003 (solar maximum) to 2008 (solar minimum). The statistical results indicate that during geomagnetically quiet times (HSYM > −30 nT, and AE < 200 nT), ~47.3% changes in the geosynchronous magnetic field and relativistic electron fluxes are caused by the combined actions of the enhancement of solar wind dynamic pressure (Pd) and the southward turning of interplanetary magnetic field (IMF) (ΔPd > 0.4 nPa and IMF Bz < 0 nT), and only ~18.4% changes are due to single dynamic pressure increase (ΔPd > 0.4 nPa, but IMF Bz > 0 nT), and ~34.3% changes are due to single southward turning of IMF (IMF Bz < 0 nT, but |ΔPd| < 0.4 nPa). Although the responses of magnetic field and relativistic electrons to the southward turning of IMF are weaker than their responses to the dynamic pressure increase, the southward turning of IMF can cause significant dawn-dusk asymmetric perturbations that the magnetic field and relativistic electron fluxes increase on the dawnside (LT ~ 00:00–12:00) but decrease on the duskside (LT ~ 13:00–23:00) during the quiet times. Furthermore, the variation of relativistic electron fluxes is adiabatically controlled by the magnitude and elevation angle changes of magnetic field during the single IMF southward turnings. However, the variation of relativistic electron fluxes is independent of the change in magnetic field in some magnetospheric compression regions during the solar wind dynamic pressure enhancements (including the single pressure increases and the combined external perturbations), indicating that nonadiabatic dynamic processes of relativistic electrons occur there.

1 Introduction

[2] Both the enhancement of solar wind dynamic pressure (Pd) and the southward turning of interplanetary magnetic field (IMF) are two important external driving sources of some geospace perturbations from ground to magnetopause. The response of magnetic field to the dynamic pressure enhancement has been confirmed by the satellite and ground observations [Wilken et al., 1982; Rufenach et al., 1992; Russell et al., 1999; Kim et al., 2004; Keika et al., 2008; Li et al., 2008, 2011a]. The magnetic field tends to increase (decrease) at the dayside (nightside) geosynchronous orbit when solar wind dynamic pressure increases [Sanny et al., 2002; Lee and Lyons, 2004; Borodkova et al., 2005; Wang et al., 2007, 2009]. The magnetic field response to the solar wind perturbations is mainly due to the variations of magnetospheric and ionospheric current systems such as Chapman-Ferraro (CF) current, cross-tail current (CTC), ring current (RC), and so on [Tsyganenko, 2000, 2002; Shi et al., 2006, 2008a, 2008b]. Moreover, the earthward transportation of magnetic flux by temporarily enhanced plasma flows is also suggested as a possible cause of the decrease of magnetic field at the nightside geosynchronous orbit after the impingement of an interplanetary (IP) shock [Wang et al., 2010; Sun et al., 2011, 2012].

[3] Another effect of the dynamic pressure increase is causing the flux enhancements of relativistic (>0.5 MeV) electrons and energetic ions in the magnetosphere [Li et al., 2003; Dandouras et al., 2009; Zong et al., 2009]. On the contrary, the fluxes of energetic particles at the geosynchronous orbit were also found to decrease in some dynamic increase events [Lee et al., 2005; Shi et al., 2009]. However, the relationship between the variations of energetic electron fluxes and magnetic field is not yet clear so far, and some nonadiabatic dynamic processes of particles are not fully considered in the previous studies. First, the dayside magnetopause can displace inward to the inside of geosynchronous orbit because of the large Pd increase and/or the strongly southward turning of IMF [Dmitriev et al., 2004, 2005]. Thus, the energetic particles initially at geosynchronous orbit can drift out of the magnetopause and lose to interplanetary space when the radial distance (r0) of the subsolar magnetopause is less than the geosynchronous altitude (~6.6 RE) [Green et al., 2004; Kim et al., 2010; Matsumura et al., 2011]; and meanwhile, the dayside geosynchronous orbit is filled with the magnetosheath magnetic field. This effect is termed “magnetopause shadowing”. Second, electromagnetic ion cyclotron (EMIC) waves and ELF/VLF waves (e.g., whistler-mode chorus) can be excited during the magnetospheric compression [Olson and Lee, 1983; Anderson and Hamilton, 1993; Arnoldy, 2005; Fu et al., 2012], and these waves are able to accelerate or scatter the energetic particles through the wave-particle interactions [Summers et al., 1998; Summers and Thorne, 2003; Albert, 2003; Meredith et al., 2003; Horne et al., 2003, 2005; Li et al., 2005; Jordanova et al., 2008; Su et al., 2009; Xiao et al., 2009a, 2009b, 2010a, 2010b; Liu et al., 2010].

[4] Besides the influence of solar wind dynamic pressure, the orientation of interplanetary magnetic field (IMF) Bz can also influence the state of magnetosphere. For example, the southward IMF (IMF BZ < 0) can enhance the cross-tail current, field-aligned currents (FAC) in the regions 1 and 2 (R1 and R2), and the partial ring current (PRC) closure FAC, and hence change the magnetic fields in the space and on the ground [Zanetti and Potemra, 1986; Kaufmann, 1987; Wing and Sibeck, 1997; Wing et al. 2002; Tsyganenko, 2002; Shi et al., 2008a, 2008b]. The hourly averaged z-component (Bz) of magnetic field at the dawnside and duskside geosynchronous orbit has a strong dependence on the southward IMF Bz [Wing and Sibeck, 1997], and the H-component of magnetic field in the low-latitude and mid-latitude ground stations displays the dawn-to-dusk asymmetric perturbations (H increases in the dawn sector but decreases in the dusk sector) during the southward IMF [Shi et al., 2006, 2008a,2008b]. Moreover, a strong and prolonged (>30 min) southward IMF can enhance magnetic storms and magnetospheric substorms [Arnoldy, 1971; Caan et al., 1977]. The continuous intense substorm activities (AE > 200 nT) can lead to the net increases of relativistic electron population in the outer radiation belt, whereas the storms (Dst < −30nT) without continuous intense substorms result in the net loss of the outer zone relativistic (>0.5 MeV) electrons [Li et al., 2009]. Although the geomagnetic activity driven by a southward IMF is suggested as a necessary condition for MeV electron enhancements at geosynchronous orbit [Li et al., 2011b], it is not clear whether the southward turning of IMF can cause the relativistic electron variations before the intensifications of storms and substorms.

[5] In this paper, we studied statistically the joint responses of geosynchronous magnetic field and relativistic electrons to 201 external perturbations, which include 37 Pd-increase events (ΔPd > 0.4 nPa, but IMF Bz > 0 nT), 69 southward-IMF events (IMF Bz < 0 nT, but |ΔPd| < 0.4 nPa), and 95 combined-perturbation events (ΔPd > 0.4 nPa and IMF Bz < 0 nT). In order to remove the influences of “magnetopause shadowing” and geomagnetic activities, all response events are required to satisfy the criteria (r0 > 6.6 RE, Dst > −30 nT, AE < 200 nT, and the response time t < 30 min). The data set is introduced in section 2. The cases studies and statistical results are presented in section 3. The discussions are performed in section 4, and the conclusions are summarized in the last section.

2 Data Set

[6] In this paper, the data of Pd, IMF Bz, AE index and the longitudinally symmetric horizontal component (HSYM) of geomagnetic field come from Coordinated Data Analysis Web (CDAWeb), and the radial distance (r0) of subsolar magnetopause is calculated through the position model of subsolar magnetopause [Shue et al., 1998]. The HSYM can approximately indicate the ring current's intensity (i.e., Dst index) [Li et al., 2011c].

[7] In addition, the data of geosynchronous magnetic field (B = (Bx2 + By2 + Bz2)1/2) and relativistic electron fluxes (J> 0.6 MeV for >0.6 MeV electrons, and J> 2 MeV for >2 MeV electrons) come from GOES 8, GOES 10, GOES 11, and GOES 12 satellites; and the elevation angle of geosynchronous magnetic field defined by θ = arctg(Bz/(Bx2 + By2)1/2) is used to examine the magnetospheric configuration change for different external perturbations. The increase (decrease) of elevation angle represents the corresponding magnetic dipolarization (stretching).

3 Case Studies and Statistical Results

3.1 Case Studies

[8] Figure 1 shows two examples of joint responses of geosynchronous magnetic field and relativistic electrons to the enhancement of solar wind dynamic pressure (ΔPd > 0.4 nPa, but IMF Bz > 0 nT). During the interval, ~16:39–17:00 UT on 27 January 2003, solar wind dynamic pressure increased remarkably (ΔPd > 4.2 nPa), but the IMF was still northward (IMF Bz > 0 nT), and geomagnetic activities are very weak (HSYM > 0 nT and AE < 100 nT). The dynamic pressure enhancement caused the inward displacement (Δr0 ~ −2 RE) of subsolar magnetopause, the compression (ΔB ~ 25 nT) and dipolarization (Δθ ~ 10°) of magnetic field, and the enhancement of relativistic electron fluxes (J> 0.6 MeV and J> 2 MeV) at the dayside geosynchronous orbit (LT ~ 11:39–12:00) (see Figures 1a–e in the left column). However, during the interval 05:44–06:00 UT on 7 June 2008, the dynamic pressure increase caused the decompression (ΔB ~ −2 nT) and stretching (Δθ ~ −2°) of magnetic field and the decrease of relativistic electron fluxes at the nightside geosynchronous orbit (LT ~ 20:44–21:00) (see Figures 1f–j in the right column).

Figure 1.

Joint responses of geosynchronous magnetic field (magnitude B, Bz, and elevation angle θ) and relativistic electron fluxes (J> 0.6 MeV and J> 2 MeV) to the enhancement of solar wind dynamic pressure (Pd) under the conditions of a northward IMF (IMF Bz > 0 nT) and weak geomagnetic activities (HSYM > 0 nT, and AE < 100 nT). r0 is the radial distance of subsolar magnetopause, and r0 > 6.6 RE during the enhancement of solar wind dynamic pressure.

[9] Figure 2 shows two examples of joint responses of geosynchronous magnetic field and relativistic electron fluxes to the southward turning of IMF (IMF Bz < 0 nT, but |ΔPd| < 0.4 nPa). Similar to the effect of dynamic pressure increase, the southward turning of IMF can also lead to obvious changes in the magnetic field and relativistic electron fluxes at geosynchronous orbit. During the geomagnetically quiet times (HSYM > 0 nT and AE < 100 nT) from 14:08 UT to 14:30 UT on 30 December 2006, the southward turning of IMF caused the compression (ΔB ~ 2.2 nT) and weak dipolarization (Δθ ~ 0.2°) of magnetic field at the dawnside geosynchronous orbit (LT ~ 05:08–05:30); and meanwhile, the fluxes of relativistic electrons increase there (see Figures 2a–e in the left column). However, during the interval 01:38–01:48 UT on 5 September 2008, the southward turning of IMF resulted in the decompression (ΔB ~ −3.5 nT) and slight stretching (Δθ ~ −0.7°) of magnetic field at the duskside geosynchronous orbit (LT ~ 16:38–16:48); and meanwhile, the fluxes of relativistic electrons decrease there (see Figures 2f–j in the right column).

Figure 2.

Joint responses of geosynchronous magnetic field (magnitude B, Bz, and elevation angle θ) and relativistic electron fluxes (J> 0.6 MeV and J> 2 MeV) to the southward turning of IMF (IMF Bz < 0 nT) under the conditions of a stable solar wind dynamic pressure (|ΔPd| < 0.4 nPa) and weak geomagnetic activities (HSYM > −10 nT and AE < 100 nT). r0 is the radial distance of subsolar magnetopause, and r0 >6.6 RE during the southward turning of IMF.

[10] Since the geosynchronous orbit was still inside the subsolar magnetopause (r0 > 6.6RE) during the periods of dynamic pressure enhancement and southward IMF, the variations of magnetic field and relativistic electron fluxes at geosynchronous orbit is not due to the “magnetopause shadowing”. The increase of relativistic electron fluxes is associated with the compression and dipolarization of magnetic field, whereas their flux decrease is associated with the decompression and stretching of magnetic field. This indicates that the responses (increase or decrease) of relativistic electron fluxes are adiabatically controlled by the magnitude-changes and configuration-changes of magnetic field. When the first adiabatic invariant (magnetic moment μ = E/B) of trapped electrons is conserved, they can gain (lose) some energies in a direction perpendicular to the magnetic field vector because of the increase (decrease) of magnetic field, which is termed “betatron acceleration (deceleration)”. When the second adiabatic (longitudinal) invariant inline image of trapped electrons maintains constant, they can gain (lose) some energies in a direction parallel to the magnetic field vector because of the shortening (stretching) of magnetic field lines, which is termed “Fermi acceleration (deceleration)”. These adiabatic variations are probably associated with the inward or outward radial diffusion process. However, the following statistical results indicate that the variations of the relativistic electron fluxes are not always controlled adiabatically by the magnetic field changes in some dynamic pressure increase events.

[11] In addition, the increase (decrease) of magnetic field is not always accompanied by its dipolarization (stretching), especially in the nighttime. In Figures 1h and 2h, the magnitude (B) and Z-component (Bz) of nighttime magnetic field decrease remarkably, whereas its elevation angle θ remains invariant sometimes even increase towards the dipolarization-like, indicating that the magnitude-changes and configuration-changes of magnetic field are independent of each other in some response regions. Therefore, only Bz variation cannot exactly reflect the configuration variation of magnetic field, although it is dominant in geosynchronous magnetic field. These conclusions are further proved by the following statistical results.

3.2 Statistical Results

[12] In order to investigate the correlation between electron flux variation and magnetic field change during different interplanetary perturbations, we chose 201 interplanetary perturbation events which satisfy the criteria (HSYM > −30 nT, AE < 200 nT, r0 > 6.6 RE, and the response time t < 30 min). As indicated in Figures 1 and 2, the quick changes (the response time t < 30 min) of magnetic field and electron fluxes after the external perturbations are evidently different from their normal spatial (local time) variations before the external perturbations, and each response of the magnetosphere is confirmed by observations from multi-satellites at geosynchronous orbit (including GOES 8, GOES 10, GOES 11, and GOES 12 at different local times). Since the magnetosphere is quite sensitive even to some small changes (ΔPd ~ 0.5 nPa) in the solar wind dynamic pressure [Li et al., 2011a], the dynamic pressure increase events are selected when ΔPd > 0.4 nPa but IMF Bz > 0 nT, whereas the southward-IMF events are selected when IMF Bz < 0 nT but |ΔPd| < 0.4 nPa.

[13] Figure 3 shows the perturbation (ΔPd = <Pd>after −<Pd>before) of solar wind dynamic pressure, the minimum value (Bz-min) of IMF Bz, the minimum radial distance (r0-min) of subsolar magnetopause, the minimum value (HSYM-min) of HSYM (i.e., Dst) index, and the maximum value (AEmax) of AE index during each external-perturbation. During 6 years from 2003 (solar maximum) to 2008 (solar minimum), there are ~37 (18.4%) events of solar wind dynamic pressure increase (ΔPd > 0.4 nPa, but IMF Bz > 0 nT), ~69 (34.3%) events of the southward turning of IMF (IMF Bz < 0 nT, but |ΔPd| < 0.4 nPa), and ~95 (47.3%) combined-perturbation events (ΔPd > 0.4 nPa and IMF Bz < 0 nT). The largest occurrence rate (percentage) of the combined-perturbation events indicates that during geomagnetically quiet times, the most of perturbations within the Earth's magnetosphere are caused by the combined external perturbations of solar wind dynamic pressure and IMF. Since the perturbations of solar wind dynamic pressure and IMF were not quite large (−0.4 nP < ΔPd < 15 nPa and IMF Bz-min > −10 nT), the geosynchronous orbit was still inside the subsolar magnetopause (r0-min > 6.6 RE), and the geomagnetic activities are also very weak (AEmin < 200 nT and HSYM-min > −30 nT) within 30 min after the external perturbations. Interestingly, there is a moderate negative correlation between the minimum value (HSYM-min) of geomagnetic field horizontal component and the minimum radial distance (r0-min) of subsolar magnetopause (their linear correlation coefficient cc ~−0.5), and their observational values can be approximately fitted by linear equation ((1)):

display math(1)
Figure 3.

(a) The minimum value (Bz-min) of IMF Bz versus the perturbation (ΔPd = <Pd>after −<Pd>before) of solar wind dynamic pressure. (b) The minimum value (HSYM-min) of HSYM (i. e., Dst) versus the minimum radial distance (r0-min) of subsolar magnetopause. The color of points denotes the maximum value (AEmax) of AE index in each event. The red lines in Figure 3a are the dividing lines of different kind perturbations. The black line in Figure 3b gives linear fits to the observations.

3.2.1 Joint Responses of Magnetic Field and Relativistic Electrons to the Enhancement of Solar Wind Dynamic Pressure

[14] Under the conditions of a northward IMF (IMF Bz > 0 nT) and weak geomagnetic activities (HSYM > −17 nT and AE < 173 nT), there are about 37 increases in solar wind dynamic pressure (ΔPd > 0.4 nPa) during 6 years from 2003 to 2008. Figures 4a–d display the responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to the 37 dynamic pressure increases. The responses of magnetic field and relativistic electron fluxes have a dependence on local time. In the dayside and flank regions of magnetosphere (LT ~ 04:00–20:00), the magnetic field increases remarkably (ΔB > 5 nT) and becomes dipolarization-like (Δθ > 1°) because of the magnetospheric compression by the increment (ΔPd > 0.5 nPa) of solar wind dynamic pressure; and meanwhile, the fluxes of relativistic electrons increase (ΔJ> 0.6 MeV > 0 and J> 2 MeV > 0) there. In the nightside magnetosphere (LT ~ 20:00–04:00 of next day), the magnetic field decrease (ΔB < 0 nT) and becomes depolarization-like (Δθ < 0°) during the magnetospheric compression, and meanwhile the fluxes of relativistic electrons decrease (ΔJ> 0.6 MeV < 0 and J> 2 MeV < 0) there.

Figure 4.

(a–d) The responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to the 37 increases in solar wind dynamic pressure. (e and f) The correlation between the electron flux variation (ΔJ> 0.6 MeV and ΔJ> 2 MeV) and the magnitude and elevation angle changes (ΔB and Δθ) of magnetic field. ΔPd is the increment of solar wind dynamic pressure and is denoted by the color of each point. cc is the linear correlation coefficient between ΔJ> 0.6 MeV or ΔJ> 2 MeV and ΔB.

[15] The local time dependence of magnitude change of magnetic field is similar to the variation of Z-component (Bz) of geosynchronous magnetic field observed by Wang et al., [2009]. The compression and dipolarization of magnetic field on the dayside and flank are mainly attributed to the enhanced Chapman-Ferraro current (i.e., magnetopause current), whereas its decrease and stretching on the nightside are probably due to the enhanced cross-tail currents [Wing et al., 2002; Lee and Lyons, 2004]. However, there is no one-to-one correspondence between the magnetic field increase (decrease) and its dipolarization (stretching) in Figures 4a–b, and the magnetic field also displays obvious stretching (Δθ < 0°) in the region of dayside magnetic field compression (ΔB or ΔBz > 0 nT at LT ~ 09:00–15:00 UT). This indicates that the magnitude-changes and configuration-changes of magnetic field are independent of each other in some magnetospheric compression regions. Therefore, only the Bz variation cannot exactly reflect the response of magnetic field configuration to the enhancement of solar wind dynamic pressure. The configuration change (dipolarization or stretching) of magnetic field is mainly determined by the magnetospheric current system and the direction of local plasma bulk flow, whereas its magnitude variation (increase or decrease) depends not only on both of them but also on the magnetospheric volume.

[16] In addition, the enhancement of relativistic electron fluxes on the dayside is consistent with the high occurrence rate of 1.1–1.5 MeV electron flux increase events there [Shi et al., 2009]. Since the influences of “magnetopause shadowing” and storms are removed in our statistical events, there is no flux decrease phenomenon around noon (LT ~ 08:00–14:00). The fluxes of relativistic electrons increase in the region of the magnetic field compression and dipolarization, whereas their fluxes decrease in the region of the magnetic field decompression and stretching, indicating that the adiabatic effect produced by the change in magnetic field is still an important cause of relativistic electron flux variation during the increase of solar wind dynamic pressure. However, the increase or decrease of relativistic electron fluxes are not completely determined by the magnitude or elevation angle changes of magnetic field at some local times. Figures 4e and 4f indicate the relationship between the electron flux variation and the magnetic field change for the dynamic pressure increase. The fluxes of relativistic electron also decrease in the some regions of the magnetic field compression and dipolarization (e.g., the event marked by the green and red points in the nether right quadrant of Figures 4e and 4f), although their fluxes usually decrease in the region of magnetic field decompression (ΔB < 0 nT). The linear correlation coefficient (cc) between ΔJ> 0.6 MeV and ΔB is about 0.36, and the cc between ΔJ> 2MeV and ΔB is about 0.31, indicating that there is only a weak linear correlation between the electron flux variation and the magnetic field change during the magnetospheric compression by the increasing dynamic pressure. Since EMIC waves can be amplified during the magnetospheric compression [Olson and Lee, 1983; Anderson and Hamilton, 1993; Arnoldy, 2005], and are also observed at geosynchronous orbit [Mauk et al., 1981; Halford et al., 2010; Clausen et al., 2011], it is possible that the relativistic electrons are quickly lost because of the wave-induced pitch angle scattering in some magnetospheric compression regions.

3.2.2 Joint Responses of Magnetic Field and Relativistic Electrons to the Southward Turning of IMF

[17] Under the conditions of a stable solar wind dynamic pressure (|ΔPd| < 0.4 nPa) and weak geomagnetic activities (HSYM > −25 nT and AE < 185 nT), there are about 69 southward turnings of IMF during 6 years from 2003 to 2008. Figures 5a–d show the responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to the 69 southward turnings of IMF (IMF Bz-min < −0.3 nT). Although the southward turning of IMF leads to the obvious increases or decreases of magnetic field and relativistic electron fluxes at the different local times, those increases or decreases are not determined by the southward turning extent of IMF (i.e., IMF Bz-min). Similar to the variation of ground magnetic field H-component caused by the southward IMF [Shi et al., 2006, 2008a, 2008b], the magnitude of magnetic field and the fluxes of relativistic electrons have also weak dawn-dusk asymmetric perturbations at geosynchronous orbit. The remarkable decreases of magnetic field and relativistic electron fluxes mainly occur in the sector of LT ~ 13:00–23:00, whereas their increases can take place any local time. The changes of field-aligned currents (R1 and R2) and partial ring current (PRC) are suggested as a primary cause of the dawn-dusk asymmetric perturbations of magnetic field [Shi et al., 2006, 2008a, 2008b]. However, the elevation angle of magnetic field can increase (Δθ > 0°) or decrease (Δθ < 0°) at all local times. Therefore, the variation of magnetic field configuration is also independent of its magnitude variation in some response regions for the southward turning of IMF.

Figure 5.

(a–d) The responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to the 69 southward turnings of IMF. (e and f) The correlation between the electron flux variation (ΔJ> 0.6 MeV and ΔJ> 2 MeV) and the magnitude and elevation angle changes (ΔB and Δθ) of magnetic field. IMF Bz-min is the minimum value of IMF Bz, and is denoted by the color of each point. The black curves in Figures 3b and 3f give linear fits to the observations.

[18] Figures 5e and 5f indicate the relationship between the electron flux variation and the magnetic field change for the southward turning of IMF. There is a moderate correlation between the variations of electron fluxes and magnetic field magnitude (cc ~0.61 for >0.6 MeV electrons and 0.45 for >2 MeV electrons), and the variation of relativistic electron fluxes is completely controlled by the magnitude-changes and configuration-changes of magnetic field during the period of southward IMF. When the change in magnetic field is large (|ΔB| > 2.5 nT), the fluxes of relativistic electrons increase (ΔJ> 0.6 MeV > 0 and ΔJ> 2 MeV > 0) in the region of magnetic field increase (ΔB > 2.5 nT), whereas their fluxes decrease (ΔJ> 0.6 MeV < 0 and ΔJ> 2 MeV < 0) in the region of magnetic field decrease (ΔB < −2.5 nT), indicating that the betatron acceleration (deceleration) is responsible for the flux enhancement (decrease) of relativistic electrons. When the change in magnetic field magnitude is small (|ΔB| < 2.5 nT), the fluxes of relativistic electrons increase in the region of magnetic field dipolarization (Δθ > 0°), whereas their fluxes decrease in the region of magnetic field stretching (Δθ < 0°), indicating that the Fermi acceleration (deceleration) is responsible for the flux enhancement (decrease) of relativistic electrons in the absence of strong betatron acceleration (deceleration). The magnetic field modification of relativistic electron fluxes is expressed as adiabatic equations ((2)) and ((3)):

display math(2)
display math(3)

[19] The numerical results of the adiabatic equations ((2)) and ((3)) are plotted as black curves in Figures 5e and 5f. Apparently, the numerical results of adiabatic equations can fit the observation data.

[20] Our statistical results for the first time indicate that the variation of relativistic electron fluxes at geosynchronous orbit are adiabatically controlled by the magnetic field response to the southward turning of IMF under the conditions of a stable solar wind dynamic pressure (|ΔPd| < 0.4 nPa) and weak geomagnetic activities (HSYM > −25 nT and AE < 185 nT). In comparison with the responses of the magnetic field and electron fluxes to the increase of solar wind dynamic pressure (−20 < ΔB < 60 nT, −6° < Δθ < 6°, −3.0 × 105 < ΔJ> 2 MeV < 2.0 × 105 (cm2.s.sr)−1, −2.0 × 103 < ΔJ> 0.6 MeV < 8.0 × 103 (cm2.s.sr)−1), their responses to the southward IMF are relatively small (−8 < ΔB < 8 nT, −3° < Δθ < 3°, −1.0 × 105 < ΔJ> 0.6 MeV < 1.0 × 105 (cm2.s.sr)−1, −6.0 × 103 < ΔJ> 2 MeV < 2.0 × 103 (cm2.s.sr)−1). However, the southward turning of IMF causes weak dawn-dusk asymmetric perturbations of the magnetic field magnitude and relativistic electron fluxes through the adiabatic dynamic processes. The relativistic electrons probably undergo adiabatic and nonadiabatic accelerations or losses during the period of solar wind dynamic pressure increase.

3.2.3 Joint Responses of Magnetic Field and Relativistic Electrons to the Combined External Perturbations

[21] When the increasing solar wind dynamic pressure and the southward IMF jointly act on the Earth's magnetosphere, the magnetospheric response simultaneously contains two effects of the dynamic pressure increase and southward IMF. Figures 6a–d display the responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to 95 combined external perturbations (ΔPd > 0.4 nPa and IMF Bz < 0 nT). Different from the responses of magnetic field and relativistic electrons to the single dynamic pressure increase in Figure 4, the variations of magnetic field magnitude and relativistic electron fluxes have a significant dawn-dusk asymmetry because of the influence of southward IMF. The increases of magnetic field and relativistic electron fluxes mainly occur in the sector from dawn to noon (LT ~ 02:00–12:00), whereas their decreases mainly occur in the sector from afternoon to nighttime (LT ~ 13:00–23:00). However, there is no such asymmetric variation in the elevation angle of magnetic field. This point confirms again that the magnitude-changes and configuration-changes of magnetic field are also relatively independent during the combined external perturbations.

Figure 6.

(a–d) The responses of geosynchronous magnetic field and relativistic electron fluxes at different local times to the 95 combined external perturbations. (e and f) The correlation between the electron flux variation (ΔJ> 0.6 MeV and ΔJ> 2 MeV) and the magnitude and elevation angle changes (ΔB and Δθ) of magnetic field. Δsd is the increment of solar wind dynamic pressure and is denoted by the color of each point.

[22] The similar local time response features of magnetic field magnitude and relativistic electron fluxes indicate that the betatron acceleration/deceleration induced by the magnetic field increase/decrease is still one important cause of the relativistic electron flux variations during the combined external perturbations. However, the variations of relativistic electron fluxes are not completely determined by the magnetic field changes in some magnetospheric compression regions. Figures 6e and 6f indicate the relationship between the electron flux variation and the magnetic field change for the combined external perturbations. The electron fluxes can decrease (ΔJ> 0.6 MeV < 0 and ΔJ> 2 MeV < 0) in one place where the magnetic field increase and evolve toward a dipolarization-like (ΔB > 0 and Δθ > 0) (e.g., the event marked by orange point in the nether right quadrant of Figures 6e and 6f), and they also increase (ΔJ> 0.6 MeV > 0 and ΔJ> 2 MeV > 0) in another place where the magnetic field decrease and is stretched (ΔB < 0 and Δθ < 0) (e.g., the event marked by blue disk in upper right quadrant of Figures 6e and 6f). The almost incorrelate (cc ~0.07 and 0.3) changes between the magnetic field and the relativistic electrons imply that some nonadiabatic dynamic processes (e.g., wave-particle interaction) of relativistic electrons occur in some magnetospheric compression regions, and these nonadiabatic variations are mainly due to the magnetospheric compression by the increasing solar wind dynamic pressure. Since both the EMIC and chorus waves can be enhanced during the magnetospheric compression [Olson and Lee, 1983; Anderson and Hamilton, 1993; Arnoldy, 2005; Fu et al., 2012], they are able to lead to the nonadiabatic variations of relativistic electron fluxes through the wave-particle interactions [Summers et al., 1998; Summers and Thorne, 2003; Albert, 2003; Meredith et al., 2003; Horne et al., 2003, 2005; Li et al., 2005; Jordanova et al., 2008; Su et al., 2009; Xiao et al., 2009a,2009b, 2010a,2010b; Liu et al., 2010].

4 Discussions

[23] The previous studies mainly use the Bz variation to indicate the response of geosynchronous magnetic field to solar wind dynamic pressure increase, and the influence of southward IMF on geosynchronous magnetic field was ignored. By analyzing the magnetic field elevation angle and magnitude changes for different external perturbation events, we found that only Bz variation cannot exactly reflect the response of magnetic field configuration to the external perturbations. The magnetic field compression (decompression) is not always accompanied by its dipolarization (stretching) in some external perturbation events, indicating that the magnitude-changes and configuration-changes of magnetic field are independent of each other in some magnetospheric response regions. The configuration variation (dipolarization or stretching) of magnetic field is mainly determined by the magnetospheric current system and the direction of local plasma bulk flow, but the magnitude change (increase or decrease) of magnetic field depends not only on both of them but also on the magnetospheric volume.

[24] Although the magnetospheric response to single southward turning of IMF is weaker than that to single dynamic pressure increase, the southward IMF can result in significant dawn-dusk asymmetric perturbations in the magnetic field magnitude and relativistic electron fluxes during both the single southward turning of IMF and the combined external perturbations. Therefore, the influence of southward IMF on the magnetosphere cannot be ignored for the most of external perturbations during the geomagnetically quiet times. Moreover, our statistical results for the first time indicate that the variation of relativistic electron fluxes at geosynchronous orbit are adiabatically controlled by the magnetic field response to the southward turning of IMF under the conditions of a stable solar wind dynamic pressure (|ΔPd| < 0.4 nPa) and weak geomagnetic activities (HSYM > −25 nT and AE < 185 nT), and there is a moderate correlation between the electron flux variation and the magnetic field change (cc ~0.61 and 0.45 for different-energy electrons).

[25] In addition, our statistical results indicate that the variation of relativistic electron fluxes is independent of the change in magnetic field in some local times during the periods of the single dynamic pressure increase and the combined external perturbations. The fluxes of relativistic electrons can increase even if the magnetic field is decreasing and stretched in one place, whereas their fluxes can also decrease even if the magnetic field is increasing and dipolarizing in another place. The independent changes between the magnetic field and the relativistic electrons imply that some nonadiabatic dynamic processes of relativistic electrons occur in some magnetospheric compression regions. In our statistical events, a little of magnetospheric responses at same local time are probably opposite for same external perturbations in the different intervals, this is probably due to the different action directions of external perturbations (e.g., different shock directions) or due to the different electromagnetic environments there.

5 Conclusions

[26] By using the criteria (HSYM > −30 nT, AE < 200 nT, r0 > 6.6 RE, and the response time t < 30 min) to remove the influences of “magnetopause shadowing” and geomagnetic activities, we analyzed statistically the joint responses of geosynchronous magnetic field and relativistic electron fluxes to 201 interplanetary perturbations during 6 years from 2003 to 2008. The main conclusions are summarized as follows:

  1. [27] During geomagnetically quiet times (HSYM > −30 nT and AE < 200 nT), ~47.3% changes in the geosynchronous magnetic field and relativistic electron fluxes are caused by the combined actions of the increase of solar wind dynamic pressure (Pd) and the southward turning of interplanetary magnetic field (IMF) (ΔPd > 0.4 nPa and IMF Bz < 0 nT), and only ~18.4% changes are due to single dynamic pressure increase (ΔPd > 0.4 nPa, but IMF Bz > 0 nT), and ~34.3% changes are due to single southward turning of IMF (IMF Bz < 0 nT, but |ΔPd| < 0.4 nPa).

  2. [28] The magnetic field increase (decrease) is not always accompanied by its dipolarization (stretching) in some external perturbation events, indicating that only Bz variation cannot exactly reflect the magnitude-responses and configuration-responses of geosynchronous magnetic field to the external perturbations. Therefore, the magnetic field elevation angle and magnitude variations are required for analyzing the response of geosynchronous magnetic field to the increase of solar wind dynamic pressure or the southward turning of IMF.

  3. [29] Although the responses of magnetic field and relativistic electrons to the southward turning of IMF are weaker than their responses to the dynamic pressure increase, the southward turning of IMF can cause significant dawn-dusk asymmetric perturbations that the magnetic field and relativistic electron fluxes increase on the dawnside (LT ~ 00:00–12:00) but decrease on the duskside (LT ~ 13:00–23:00) during the quiet times. Therefore, the influence of southward IMF on the magnetosphere cannot be neglected during the periods of single southward turning of IMF and combined external perturbations.

  4. [30] During the single IMF southward turnings, the variation of relativistic electron fluxes at geosynchronous orbit is adiabatically controlled by the magnitude and elevation angle changes of magnetic field. The increase or decrease of relativistic electron fluxes is mainly determined by the magnitude change (increase or decrease) of magnetic field when the magnitude change of magnetic field exceeds 2.5 nT, whereas their flux variations are mainly determined by the configuration change (dipolarization or stretching) of magnetic field when the magnitude change of magnetic field is less than 2.5 nT.

  5. [31] During the solar wind dynamic pressure enhancements (including the single pressure increases and the combined external perturbations), the variation of relativistic electron fluxes is independent of the change in magnetic field in some magnetospheric compression regions. The fluxes of relativistic electrons can increase even if the magnetic field is decreasing and stretched in one place, whereas their fluxes can also decrease even if the magnetic field is increasing and dipolarization in other place. The independent changes between the magnetic field and the relativistic electrons imply that nonadiabatic dynamic processes of relativistic electrons occur in some magnetospheric compression regions during the solar wind dynamic pressure enhancements (including the single pressure increases and the combined external perturbations). The detailed nonadiabatic dynamic processes (e.g., wave-particle interaction) will be further investigated in the future.

Acknowledgments

[32] This work is supported by NSFC (grants 41074119, 40604018, 41174141, 40904042) and 973 Program (grant 2011CB811404). We acknowledge the staffs working for the data from GOES 8, GOES 10, GOES 11, GOES 12 satellites, and OMNI database in CDAWeb.