We statistically analyzed severe magnetic fluctuations in the nightside
near-Earth plasma sheet at 6–12
Substorms, which are important geomagnetic and auroral disturbances with timescales of 2 to 3 h, were first identified by Akasofu (1964). The
detailed description of substorms in that paper triggered a tremendous
upsurge in related studies. Our understanding of substorms and their onsets
has dramatically changed in the past few decades. As one approach to
understand substorm onset, magnetic fluctuation is regarded as one possible
instability to trigger substorms in the inner magnetosphere. Takahashi et
al. (1987) reported strong magnetic fluctuations in the magnetotail at
After the identification of auroral substorms, many studies were conducted
using ground-based magnetometers and all-sky cameras. With the development of
space technology, an increasing amount of satellite data has also become
available for scientific research. Hones (1973) showed an important finding
of both tailward and earthward plasma flows in the magnetotail, which suggests
the formation of two magnetic neutral lines located near the Earth and far
away in the tail. This study and related works formed the near-Earth neutral
line (NENL) model of substorms (e.g., Baker et al., 1996; Shiokawa et al.,
1997, 1998). Shiokawa et al. (1997, 1998) clarified the time sequence of
substorm-related phenomena. From the appearance of a new
Some researchers have focused on current disruption in the near-Earth tail rather than magnetic reconnection when exploring the origin of substorms (Lui, 2001). Lui et al. (1990) pointed out that kinetic cross-field instability can occur in the near-Earth tail before the substorm expansion phase. This instability can cause the formation of a substorm current wedge by reducing the cross-tail current. Lui (1991a, b) proposed a synthetic model in which instabilities in the near-Earth magnetotail may be the initial trigger of substorms. Some substorm-related features, including pseudo-breakups and the localized region of substorm initiation, could be explained by this model (Lui et al., 1991). These ideas came to be known as the inside-out model.
The formation of a new near-Earth neutral line (outside-in model) and current disruption in the near-Earth tail (inside-out model) have become the two dominant approaches when considering substorm onset. Recognizing the importance of both down-tail and near-Earth activities may become a feasible approach in future studies (Henderson, 2009). For both of these two approaches, magnetic fluctuations in the near-Earth tail are involved as a phenomenon that requires more research. Ohtani et al. (1995, 1998) used Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) data and fractal analysis to investigate substorm-related magnetic fluctuations, which are considered to be strongly related to plasma instabilities and current disruption. Ono et al. (2009) pointed out that during magnetic field dipolarization, ions in the near-Earth plasma sheet are non-adiabatically accelerated due to the induced electric field by these magnetic fluctuations. Nosé et al. (2010) revealed that dipolarization is accompanied by the appearance of magnetic fluctuations with a timescale of 3–5 s.
The importance of studying these magnetic fluctuations in the inner magnetotail also lies in the fact that they are strongly related to non-magnetohydrodynamics (non-MHD) processes in the magnetotail, during which the kinetic effect of ions plays an important role (Consolini et al., 2005). From the beginning of its development, MHD simulation has been a useful tool to study plasma in the magnetotail. Birn et al. (1996) used resistive MHD simulations to investigate the current disruption and diversion properties. By using a global MHD magnetosphere model, Wiltberger et al. (2000) unveiled many fast flow channels in the magnetotail with plasma and magnetic field properties that are consistent with observations conducted by Angelopoulos et al. (1992). On the other hand, Lui and Najmi (1997) showed that during the current disruption, the spectrum of accompanied magnetic fluctuations becomes intermittently broad, covering timescales from below to above the ion gyroperiod. In such a particular circumstance, the collapse of the MHD condition causes continuous challenges for the study of magnetotail dynamics.
Despite the above various importance of magnetic field fluctuations for the dynamics of the magnetosphere, to our knowledge, there have been no comprehensive statistical analyses of magnetic fluctuations in the near-Earth plasma sheet. In this study, we conducted a statistical analysis of occurrence rate and substorm-related properties of severe magnetic fluctuations at periods shorter than the local ion gyroperiod in the near-Earth plasma sheet.
Three subregions chosen for analysis. The subregions are divided by
GSM-
The two-step calculation to identify severe magnetic fluctuation events.
In this study, we used 2-year magnetic field data from 2013 and 2014
(sampling rate: 4 Hz) obtained by the fluxgate magnetometer (FGM; Auster
et al., 2008) aboard the Time History of Events and Macroscale Interactions
during Substorms E (THEMIS-E) satellite (Angelopoulos, 2008). The plasma flow
data were obtained by the electrostatic analyzer (ESA) aboard the same
THEMIS-E satellite (McFadden et al., 2008). Figure 1 shows the region we
chose for our analysis, which is located in the near-Earth tail at
(
Figure 2 shows the two-step calculation we used to identify severe magnetic
fluctuation events. In the first step, we calculated the average background
magnetic field intensity (
Example multiple-fluctuation events on 28 August 2013. There were 19 severe magnetic fluctuation events.
Enlarged plot for example multiple-fluctuation events on 28 August 2013. It shows the 1 min time interval after 06:21 UT. There were nine severe magnetic fluctuation events.
Since relatively long-lasting magnetic fluctuations are more relevant to
substorm onset (Lui, 1991a), we defined three continuous severe magnetic
fluctuation events that happen within 10 min as a multiple-fluctuation event.
In our calculation of the background magnetic field intensity during the
first step, we abandoned the sections with
We should note that the present approach can include all kinds of magnetic fluctuations with large amplitudes comparable to or larger than the ambient magnetic field intensity and with periods shorter than the local ion gyroperiod. It can contain both incoherent structures, such as current disruptions caused by waves and instabilities, and coherent structures, such as sharp magnetic field change during dipolarization fronts (e.g., Runov et al., 2011) or the flapping of plasma sheet. Thus, the occurrence rates calculated by our criteria demonstrate the maximum values of the severe magnetic fluctuations caused by instabilities.
Figure 3 shows an example of 6 multiple-fluctuation events including
18 severe magnetic fluctuation events (the last severe magnetic fluctuation
event in Fig. 3 was excluded). Note that the magnetic fluctuations occurred
when the ion velocities were high. In order to show the property of severe
magnetic fluctuation in more detail, we enlarged the 1 min time interval
from 06:21 UT in Fig. 3, as shown in Fig. 4. There were nine severe magnetic
fluctuation events during this 1 min time interval. The total magnetic field
intensity shows a strong variation with an amplitude of
Distribution of duration time for severe magnetic fluctuation events.
Our statistical analysis of the magnetic field intensity data from 2013 and 2014 yielded 1283 severe magnetic fluctuation events, among which there were 389 multiple-fluctuation events containing 1167 severe magnetic fluctuation events. For all the severe magnetic fluctuation events, 1 % of them are located in Region A, 19 % of them are located in Region B, and 80 % of them are located in Region C. For 99 % of the severe magnetic fluctuation events, the plasma beta values were greater than 1 (21 % were between 1 and 10, and 78 % were greater than 10), indicating that they were located in the plasma sheet (e.g., Baumjohann et al., 1990; Schmid et al., 2011).
Figure 5 shows the distribution of the duration time of these severe magnetic fluctuations. The duration was defined as the length of time during which the 1 s severe magnetic fluctuation events occurred sequentially. Nearly all fluctuations had duration times of less than 15 s, with one exception (24 s).
We estimated the occurrence rates of severe magnetic fluctuation events and
multiple-fluctuation events for each subregion in the tail and for the
entire region by calculating the ratio between the duration time of events
and the total observation time taken for the corresponding region. For
example, the occurrence rate of severe magnetic fluctuation events for Region
A was calculated as 19 s/1 608 118 s
Occurrence rate and inferred volume of the onset region (
The occurrence rates of severe magnetic fluctuations calculated for multiple-fluctuation events are also shown in brackets in Table 1 (0.114, 0.620, and 1.15 % for Region A, Region B, and Region C, respectively). In this case, we utilized the 10 min time interval used in the definition of a multiple-fluctuation event as the numerator and the observation time of satellite as the denominator. We set the time of the first severe magnetic fluctuation event that belongs to one multiple-fluctuation event as the start time and accumulated the following 10 min time interval in the calculation of the occurrence rate. We removed the overlapped time interval between two adjacent multiple-fluctuation events (10 min time intervals).
Using these occurrence rates of severe magnetic fluctuation, we made two
estimations. Firstly, magnetic fluctuation is considered as one possible
trigger mechanism for current disruption and substorm onset in the inside-out
substorm model. According to Borovsky et al. (1993), an average of four
substorms occur every day. If we assume that all the substorms are
accompanied by a 5 min current disruption (magnetic fluctuation with a
duration time of 5 min; e.g., Takahashi et al., 1987; Lui, 1991b), the
ratio between the current disruption time (5 min
However, the above estimation of 1 % contains the assumption that the
current disruption occurs everywhere in the plasma sheet observed by the
satellite. If we consider the possibility of localization of current
disruption in a small region, which is more likely to occur, we would miss a
lot of severe magnetic fluctuation events during the satellite measurement.
Then if we assume that all the substorms are caused by the severe magnetic
fluctuations, we can estimate the scale size of the current disruption region
from the ratio between the occurrence rate of the observed severe magnetic
fluctuations (0.0149 %) and the occurrence rate of substorms (1.4 %).
The estimated scale size of current disruption is about
3.83
Occurrence rate (
In order to check the dependence of the occurrence rate of magnetic
fluctuations on their amplitudes, we show the occurrence rate of magnetic
fluctuation events by changing the selection criterion to
It should be noted that there is ambiguity in the relative locations of
these fluctuation events with respect to the center of the plasma sheet in
the
We used the empirical Tsyganenko magnetospheric magnetic field model (T01) to
evaluate the distance between fluctuation event locations and the varying
neutral sheet (Tsyganenko, 2002a, b). This model is useful and valid at
Note that in order to calculate the spatial distributions of the occurrence
rates, we first needed to calculate
The spatial distribution of
Figure 6 shows the spatial distributions of (a) the number of severe magnetic
fluctuation events, (b) observation times when the satellite was in the given
GSM-
The spatial distributions of
Figure 7 shows the spatial distributions of (a) the number of severe magnetic
fluctuation events, (b) observation times, and (c) the occurrence rates of
the fluctuation events normalized by the observation times in the plane of
GSM-
Occurrence rates of the fluctuation events with distance
Figure 8 shows the occurrence rates of severe magnetic fluctuation events
with distance
The auroral electrojet lower (AL) index is often used to indicate the
occurrence of substorms (e.g, Shiokawa and Yumoto, 1993). In the calculation
of the auroral electrojet (AE) index, the lower envelope of the north–south
Superposed epoch analysis of the AL index 1 h before and after the time of severe magnetic fluctuation events.
Superposed epoch analysis of magnetic field intensity variations 1 h before and after the time of severe magnetic fluctuation events.
Figure 10 shows the superposed epoch analysis of magnetic field variations
1 h before and after the time of severe magnetic fluctuation events. A clear
decrease in
Figure 10 also shows abrupt decreases in total
Distribution of 10 s averaged ion velocities during magnetic fluctuation events.
The relationship between magnetic fluctuation and fast plasma flows in the
near-Earth plasma sheet has been previously studied (e.g., Bauer et al.,
1995; Vörös et al., 2004; Shiokawa et al., 2005a). Using superposed
epoch analysis, Frühauff and Glassmeier (2016) recently showed the
characteristics of fast flows and related magnetic disturbances in the
magnetotail. They revealed that during the entire flow burst timescale, the
directions of minimum magnetic field variations are perpendicular to the main
flow and the background magnetic field directions. In this section, in
order to investigate the relationship between severe magnetic fluctuation
events and high-speed ion flow, we compared magnetic fluctuation events with
plasma data obtained by the THEMIS-E satellite. Figure 11 shows the
distribution of 10 s averaged ion velocities
Superposed epoch analysis of ion velocity 1 h before and after the time of severe magnetic fluctuation events.
Figure 12 shows the superposed epoch analysis of ion flow velocities 1 h
before and after the time of severe magnetic fluctuation events. We can
observe an increase in ion velocity from
To determine whether the magnetic fluctuation can cause the high-speed ion flow (case 2), we made some further adjustments. First, we calculated the average ion velocity at 0–1 min before the time of severe magnetic fluctuation events and then selected those events with a 1 min averaged ion velocity greater than the ion velocity at the event time. The superposed epoch analysis of ion velocity 1 h before and after the event time for the selected 698 events is shown in Fig. 13a, from which we can observe an increase in ion flow velocity before the event time. Figure 13b shows the superposed epoch analysis for 303 selected events with an averaged velocity at 0–10 min before the event time greater than the velocity at the event time. Again, we cannot observe an increase in ion flow velocity after the event time.
Superposed epoch analysis of ion velocity 1 h before and after the
time of selected severe magnetic fluctuation events. In panel
Figure 13c and d are similar superposed epoch plots of ion velocity 1 h before and after the event time for those events with averaged ion velocities at 0–1 and 0–10 min after the event time greater than the velocities at the event time, respectively. In these two plots, enhancements in ion flow velocity are observed after the event time. However, these events are fewer in number (only 118 and 70 events, respectively), and the amplitudes of the velocity enhancements are relatively small. As a result, Fig. 13a–c show clear increases in the ion velocity before the severe magnetic fluctuation events, which indicates that for most cases the severe magnetic fluctuations cannot be the cause of the high-speed plasma flow.
Here, we should further discuss the increase in plasma flow speed before the magnetic fluctuation. Before the present severe magnetic fluctuation event observed by the satellite, another current disruption (severe magnetic fluctuation) may occur at the tailward side of the satellite because the thinned plasma sheet can be unstable everywhere at the end of the growth phase of substorms. Then, the former current disruption can cause the observed increase in earthward plasma flow before the time of the present magnetic fluctuation event. However, we believe that such a possibility is unlikely because the earthward flow is generally accompanied by the dipolar magnetic field that stabilizes the plasma instability due to the thinning of the plasma sheet. Thus, if the plasma instability that causes the current disruption is caused by the thinning of the plasma sheet, the present observation of flow enhancement before the magnetic fluctuation (current disruption) contradicts the idea that the earthward flow is caused by the current disruption.
On the contrary, another severe magnetic fluctuation may also occur at the earthward side of the satellite. The current disruption due to severe magnetic fluctuations can cause subsequent current disruptions to happen from the present site to more tailward locations, even without additional instabilities. That is, the earthward plasma flow associated with the current disruption causes depletion of the tailward pressure-gradient force at the site of the present plasma flow. This pressure decrease attracts plasma at the tailward side of the present location, causing the plasma to move earthward sequentially as a rarefaction wave (e.g., Haerendel, 1992; Hwang et al., 2014). Considering that the plasma flow can cause severe magnetic fluctuations, the possibility that the satellite detects the first current disruption (severe magnetic fluctuation) without plasma flow may become smaller. In that sense, we cannot deny the possibility that the current disruption in the inside-out model caused only the first earthward flow, and other earthward flows and associated severe magnetic fluctuations occur subsequently. Then the number of the severe magnetic fluctuation events after the flow may become dominant, as observed in Figs. 12 and 13.
We used magnetic field data from 2013 and 2014 obtained by THEMIS-E at a
sampling rate of 4 Hz to analyze severe magnetic fluctuation events. In
total, 1283 severe magnetic fluctuation events were identified with
The occurrence rates of severe magnetic fluctuation events in the
near-Earth plasma sheet ( We found that all the distances from the location of fluctuation events to
the T01-based neutral sheet are less than 1 The superposed epoch analysis of the AL index 1 h before and after the
time of severe magnetic fluctuation events shows an obvious decrease in index
value around the event time. An increase in Sixty-two percent of severe magnetic fluctuation events are accompanied by
ion flow velocity with
We used the IDL Geopack Dynamic Link Module (DLM) routines provided by H. Korth to run the Tsyganenko magnetospheric magnetic field model. This model
was developed by N. A. Tsyganenko
(
HX conducted the analysis for this study and wrote the paper. KS guided this study as the graduate-course supervisor of HX. DF contributed to conducting this study as a co-investigator of the THEMIS FGM. All authors have read and approved the final paper.
The authors declare that they have no conflict of interest.
We thank Vassilis Angelopoulos for his helpful suggestions and Yukinaga Miyashita for his support in SPEDAS/TDAS operation. We acknowledge support from the Leadership Development Program for Space Exploration and Research at Nagoya University. This work is supported by a Grant-in-Aid for Scientific Research (JP 16H06286) from the Japan Society for the Promotion of Science. We acknowledge the NASA contract NAS5-02099 and V. Angelopoulos for the use of data from the THEMIS mission. We specifically acknowledge C. W. Carlson and J. P. McFadden for the use of ESA data and K. H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. The topical editor, Georgios Balasis, thanks three anonymous referees for help in evaluating this paper.