Magnetotail Variability During Magnetospheric Substorms

In this work, we present a statistical study of substorms covering a five‐year period 2016–2020. Substorm phases were identified from time series of the SuperMAG AL (SML) index using a list of 5,077 previously identified substorm onsets, the SML peak value marking transition from expansion to recovery phase, and the recovery identified as return to activity less than −100 nT in the SML index. Magnetic field observations from THEMIS, RBSP, and MMS missions were used to study the magnetotail characteristics during the substorm evolution. A superposed epoch analysis indicates that the substorm onset occurs almost simultaneously with a few minutes of uncertainty throughout the magnetotail, ranging from geostationary orbit to 20 RE. The onset in the transition region precedes the ground onset by a few minutes. The peak SML time coincides with the peak of the outer transition region ΔBZ, which suggests that the field‐aligned currents driving the SML activity arise from the outer transition region. Analysis of 2D maps of the tail magnetic field shows that the magnetotail current changes are limited to the center of the tail within |Y| < 10RE. The substorm recovery is fastest in the inner transition region and lasts longer when moving further out. We did not find major asymmetries in the substorm signatures associated with IMF BY or BZ.


Introduction
The term magnetospheric substorm is coined to a sequence of processes that represents one of the basic dynamic cycles in the solar wind-magnetosphere-ionosphere system, originally identified from their auroral (Akasofu, 1964) and auroral electrojet (Davis & Sugiura, 1966) signatures.Insightful analyses of the limited magnetotail data available at the time led to association of the ionospheric substorm with inner magnetotail magnetic field dipolarization and formation of the substorm current wedge (R. L. McPherron et al., 1973), and reconnection and plasmoid release in the mid-magnetotail (Hones Jr. et al., 1986).While the basic substorm elements have remained unchanged since the original works (D.N. Baker et al., 1996), considerable efforts have been devoted to establishing the spatio-temporal connectivity between the inner and midtail processes (Angelopoulos et al., 2009) and to deciphering the detailed relation between the solar wind driver and the magnetotail response (Pulkkinen et al., 2010).While the role of substorms is critical in generating the time-varying currents in the ionosphere and thereby driving ground-based space weather effects (Pulkkinen, 2007), neither the available space-based magnetotail observations (Juusola et al., 2011;M. Kubyshkina et al., 2011) nor the advancement of numerical simulations (Janhunen et al., 2012;Merkin et al., 2019;Tóth et al., 2012) have been able to provide closure to the problem.
The closed-field region of the magnetotail comprises the outer magnetosphere plasma sheet and the embedded cross-tail current sheet and the inner magnetosphere radiation belt (electron), ring current (ion) and plasmaspheric populations, in decreasing order of energy.The plasma sheet is highly structured and hosts a continuous sequence of both Earthward and tailward directed bursty bulk flows (Angelopoulos et al., 1993), which have been interpreted as signatures of particle acceleration by local reconnection (Sergeev et al., 2000).
The classical description of the substorm evolution includes the growth phase, expansion phase, and the recovery phase (D.N. Baker et al., 1996).The growth phase is initiated by southward turning of the interplanetary magnetic field (IMF) and consequently enhanced dayside reconnection (R. L. McPherron, 1970), thinning of the plasma sheet resulting in energetic electron precipitation (Pytte et al., 1978), and causes a slow enhancement of the diamagnetic cross-tail current from the transition region (8-12R E ) to the mid-magnetotail (∼20R E ) (Pulkkinen et al., 1992).In the ionosphere, the substorm onset is seen as an expansion of an auroral brightening (Frey et al., 2004) and an intensification of the westward electrojet (Gjerloev, 2012) often measured by the auroral electrojet (AL) index.In the inner magnetotail, the intensified current is disrupted (Lui, 2018;Lui et al., 1988) and a substorm current wedge couples the magnetotail to the ionosphere by a pair of field-aligned currents (Kepko et al., 2015).Further out, magnetic reconnection often creates an isolated plasmoid that is accelerated out from the magnetotail (Ieda et al., 1998).During the substorm recovery, the magnetosphere returns to its quiet-time configuration (Pulkkinen et al., 1994).
The location of the substorm processes in the magnetotail varies depending on the intensity of the preceding solar wind driving, the phase of the solar cycle, the orientation of the IMF and direction of the solar wind flow, and any large-scale fluctuations in the driver parameters (Baumjohann et al., 1989;Nagai, 2006).However, statistically, the substorm current wedge starts in the pre-midnight sector and opens to cover several hours in local time around the midnight sector (Nagai, 1982).Similarly, the flow bursts typically occur close to the tail center, within about |Y| < 8R E from the center of the tail (Sergeev et al., 2012), also with slight preference toward the evening sector.Based on techniques originally developed in Pulkkinen (1991) for analysis of individual cases, M. Kubyshkina et al. (2011) argued that using magnetic field models tuned to the substorm onset conditions, the auroral breakup location maps to the midtail region, connecting the breakup to the reconnection region rather than to the current disruption at the inner edge of the transition region.A statistical analysis by Miyashita et al. (2006) focused on the variations of magnetotail associated with the storm and nonstorm time substorm onsets using data from the Geotail spacecraft.They performed superposed epoch analysis of various plasma parameters and magnetic/ electric field data to establish a relationship between the dipolarization and magnetic reconnection and to understand the dynamics of magnetotail and triggering of substorms using multispacecraft observations (Miyashita et al., 2009).Juusola et al. (2011) studied the statistics of plasma flows during substorms and concluded that the occurrence frequency of bursty flows varies during the substorm evolution, enhancing toward the end of the growth phase, maximizing during the expansion phase, and then decreasing in frequency during the recovery phase.Recently, Stephens et al. (2019) used data mining techniques to reconstruct the substorm-associated current systems, and were able to reproduce the creation of the field minimum in the transition region as well as the dipolarization of the magnetic field and formation of the substorm current wedge at onset.
In this paper, we use the wealth of satellite measurements acquired in the past years, concentrating particularly on the period 2016-2020, when three of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft (Angelopoulos, 2008), the Magnetospheric Multiscale (MMS) satellites (Burch et al., 2016), and the two Radiation Belt Storm Probes (RBSP) (Mauk et al., 2013) were all making measurements in the magnetosphere.We focus particularly on the least studied substorm phase, the recovery from the peak activity back to the quiet state.For substorm identification and characterization, we use observations from the SuperMAG collaboration (Gjerloev, 2012) and the substorm onset list created using those observations (Ohtani & Gjerloev, 2020).We especially examine the time scales in different parts of the system: in the ionosphere, in the inner magnetosphere, and in the mid-magnetotail.The significant new data sets from these missions warrant revisiting the average characteristics of the magnetotail during the substorm process.This paper is organized as follows: Section 2 describes the observations and data analysis methods, Section 3 presents a superposed epoch analysis of the substorm evolution in the magnetotail, Section 4 presents twodimensional maps of the magnetic field evolution during substorms, and Section 5 discusses effects of the IMF B Y and B Z .Section 6 concludes with discussion.

Observations and Methods
SuperMAG (Gjerloev, 2012) is a collaboration of organizations and national agencies who operate and maintain over 500 magnetometers spanning the globe.The SuperMAG service (https://supermag.jhuapl.edu/)provides easy access to validated ground magnetic field perturbations displaying observations from each station in the same coordinate system, with identical baseline removal approaches, and a unified time resolution of 1 min (or for a subset, 1 s).The magnetometer data has been augmented by the OMNI (https://omniweb.gsfc.nasa.gov/)data set of solar wind and interplanetary magnetic field measurements time-shifted to the Earth's bow shock (King, 2005) for context.
The statistical substorm data set utilized in this study originates from Ohtani and Gjerloev (2020), who identified substorm onsets using the SuperMAG AL (SML) index.The SML index is constructed using data from all available stations above 50°magnetic latitude, but is otherwise formulated similarly to the AL index computed as a lower envelope of the north-south component from 12 auroral latitude observatories.These authors defined the substorm onset as the start of a decrease in the SML index characterized by a second derivative (Δ 2 SML/Δt 2 ≤ 1.5 nT/min 2 ).For the event to be counted as a substorm, the authors set limits for peak value and duration of the expansion phase.A step-by-step approach for identifying isolated substorms is described in Appendix A and shown in Figure A1 of Ohtani and Gjerloev (2020).A listing of these substorm onset times is also available at the SuperMAG website (https://supermag.jhuapl.edu/indices).
We focus on 5,077 substorms from the Ohtani and Gjerloev (2020) data set that occurred during the period 2016-2020 (Figure 1).Using the list of substorm onsets and the SuperMAG SML index, we identified substorm peak times by finding the time of minimum SML value following the substorm onset, and the end of the substorm defined as the time when the SML index increased to above the level of 100 nT (or as the time of the next substorm onset if that occurred before full recovery of the SML index).For prolonged intervals of geomagnetic activity, we defined the maximum expansion and recovery times to be 2 hr.The bottom five panels of Figure 1 show selected sample events with the three times marked and the expansion and recovery phases highlighted.
The magnetospheric analysis is carried out using data from multisatellite THEMIS mission, from the MMS-1 spacecraft, and from the two RBSP probes.We use data from three THEMIS spacecraft (A, D, and E), excluding the two outermost ones orbiting the Moon.We use 3-s (spin average) resolution data from the Fluxgate Magnetometer (FGM) (Auster et al., 2008) for this analysis.We also use observations from the MMS-1 (Burch et al., 2016) digital fluxgate magnetometer (Russell et al., 2016).While the MMS mission comprises four spacecraft, they fly in such close formation that including observations from more than one spacecraft is not relevant for the spatial and temporal scales of this study.Finally, we cover the inner magnetosphere region using the RBSP (Mauk et al., 2013) magnetometer that is part of the EMFISIS instrument suite onboard both spacecraft (Kletzing et al., 2013).
All magnetic field observations in this analysis are shown in geocentric solar magnetospheric (GSM) coordinates and as differences with the internal geomagnetic field subtracted using the International Geomagnetic Reference Field (IGRF-13) model (Alken et al., 2021).Removing the internal field contribution helps to reveal the signatures caused by variations of the external currents associated with the substorm processes, especially close to the Earth where the internal dipole field contribution to the total field is large.While the internal field is small for measurements in the magnetotail, we show all data as external field only for consistency.We denote the external field as ΔB Z , and calculate it as a difference between the observed and internal field model value Figure 2 shows magnetospheric data coverage for (a) RBSP-A, B, (b) THEMIS-A, D, E, (c) MMS-1, and (d) all spacecraft.Using 1-min averaged measurements, we compute average number of data points for each 1R E × 1R E bin in X and Y. Scales for the average number of data points is shown on the vertical color-bar.Analysis is limited to the region outside of 4R E (shown as the gray shaded disc around the Earth).The black circle at 6 R E marks roughly the distance of the geosynchronous orbit.For RBSP, all data points fall within this region, as the apogee of these spacecraft is close to 6R E .Due to orbital dynamics, the maximum number of data points occurs near the apogee of each of the spacecraft, shown as higher density around geostationary orbit (RBSP), and close to 12R E (THEMIS and MMS). Figure 2d shows a combination of measurements from all spacecraft for the complete 5year period in the Y Z plane to point out the near-equatorial orbits of the spacecraft.We point out the uneven data coverage, the number of points maximizes inside of 6R E , is relatively low in a region up to 15R E , and lowest  between 15 and 30R E distance from the Earth.Note that the last panel showing all spacecraft shows the number of points in logarithmic scale to increase readability of the plot.
Due to the near-equatorial nature of the spacecraft orbits, the data coverage is highest near the equatorial region.As the plasma data are not always available, we have not set limitations based on for example, plasma beta to explicitly ensure that the measurements are made within the plasma sheet.This may mean that in some instances, the spacecraft will be close to the plasma sheet boundary where the B X becomes the dominant field component.However, even in those cases, the magnetic field B Z weakenings due to tail stretching and increases due to field dipolarizations would be seen in a similar manner than within the central plasma sheet.

Superposed Epoch Analysis of Substorms in the Magnetotail
Superposed epoch analysis is a numerical technique often used to search for periodicities or recurring responses in time series data.This method requires a continuous, evenly sampled data set (such as the observed magnetic field timeseries) and a list of epoch times (such as the substorm onset/peak/end times).Data from the time-series are extracted from fixed time windows around the epoch times.The extracted data for all epochs are then averaged to reveal an average behavior around the epoch time.expansion phase time of almost 40 min (time from onset to peak value) and about 80-min recovery phase (from peak of SML to return of median values to above 100 nT).The median values prior to substorm onset do not indicate a clear growth phase behavior (slow enhancement of the SML index).However, the mean values (being more dominated by large events) show a signature of recovery from previous activity until start of the new onset.
We note that the difference between the mean and median values arises from the non-Gaussian distribution of the data: Most of the SML index data are concentrated between 200 and 0 nT with a long tail in the negative direction.Thus, the median will always be smaller than the mean in these distributions.
The middle panel centered around the peak value shows the recovery time scale to be about 60 min (time from peak to values above 100 nT).Note that this time scale is shorter than the recovery time from peak to 100 nT in the superposed epoch centered around onset, which is a consequence of the varying lengths of the expansion phase in the data sets.As most previous analyses have chosen the substorm onset as the epoch time, the cited recovery phase lengths are longer than those obtained here (Pulkkinen et al., 1994).
The right panel shows the result of superposed epoch analysis of SML considering zero epoch at the end time of the substorm.The recovery phase can be seen clearly to end when SML (mean and median) reaches above 100 nT.Beyond the recovery end, the mean curves show the growth phase of the next substorm.Centered around the substorm end gives a recovery time (from the mean peak to the end) to be about 50 min.
The average duration of the expansion and recovery phases can also be calculated for each event independently using the onset, peak and recovery values; this yields a mean 38 min (median 45 min) for the expansion phase and mean 64 min (median 73 min) for the recovery phase, consistent with the superposed epoch results.
We combined all satellite measurements of magnetic fields from RBSP THEMIS, and MMS for a statistical analysis of the inner magnetosphere and magnetotail magnetic field variations during substorms.Figure 4 shows superposed epoch analysis of the ΔB Z , with International Geomagnetic Reference Field (IGRF) subtracted from the observed values, for epoch times at substorm onset (left), at substorm peak (middle) and at substorm end (right).Similarly to Figure 3, the vertical dotted lines, black and red dashed curves, and blue shading show the epoch time, onset, peak, recovery end, median and mean, and the interquartile range, respectively.A clear magnetic field recovery is not seen in Figure 4j, therefore green dotted line is not plotted in this figure .To examine the temporal evolution of the magnetic field in different parts of the magnetotail, we divided the observations into different bins based on the spacecraft distance along the tail as indicated in the lower left part of each left panel.Focusing on the center of the tail, we limit the study to events with spacecraft located in the range 5 < Y < 8R E (noting earlier results that substorms tend to occur in the premidnight sector), and examine four distinct bins in X, 4 to 7R E , 7 to 10R E , 10 to 15R E , and 15 to 25R E .We considered a time window from 180 to 180 min around each epoch time.
Figures 4a-4c show superposed epoch analysis of ΔB Z in the closest bin ( 4 < X < 7R E ).Due to reduction of data after restricting the analysis to periods when the spacecraft locations fell within the given X Y range, we were left with 3,426 out of the total 5,077 substorms.The following panels show the observations in consecutively more tailward bins with 2,489 substorms included in the superposed epoch analysis between 10 < X < 7R E (Figures 4d-4f), 1,779 substorms in the bin 15 < X < 10R E (Figures 4g-4i), and 495 substorms in the bin 25 < X < 15R E (Figures 4j-4l).
The three bins outside geosynchronous orbit show very consistent results, while the innermost bin data show no clear tendencies and the mean and median are somewhat apart.The left panels of Figure 4 show that the tail magnetic field stretches during the substorm growth phase prior to onset, which is caused by increasing magnetotail current tailward of the spacecraft.The left panels of Figure 4 also show that the field dipolarization is seen very near to the ground-based onset recorded by the SML index.The magnetotail onset signatures are seen within a few minutes of each other, near-simultaneously to the accuracy of the superposed epoch results.However, we note that the two middle bins, the inner ( 10 < X < 7R E ) and outer ( 15 < X < 10R E ) transition regions, show the onset signatures slightly prior to the ground onset.This indicates that statistically, the onset signatures are seen near-simultaneously throughout the magnetotail out to about 25R E .
Following the dipolarization, ΔB Z reaches a maximum statistically first closer to the Earth and later further away from the Earth (blue dotted lines in the left panels of Figure 4).Return of the field to pre-onset value occurs also statistically earliest near the Earth and statistically later in the more distant magnetotail; the 180-min window is not sufficiently long for the midtail field to fully recover.
The middle panels of Figure 4 show the superposition centered around the ground substorm maximum (peak SML value).That peak coincides with the field maximum in the outer transition region ( 15 < X < 10R E ), while the peak is observed somewhat later both further Earthward and further tailward.Thus, we interpret that reaching the maximum substorm intensity as measured by the ground magnetometers is associated to reaching the field dipolarization peak in the outer transition region.
The right panels show superposition centered around the end time of substorms.The only clear signature in these superposed results is the outer transition region, where the substorm end as measured by SML is coincident with the field recover to the pre-substorm value.This further supports our conclusion about the association of the auroral electrojet activity with the outer transition region.
The timing differences between the tail bins are of the order of a few minutes around the substorm onset times.To the accuracy of the analysis, the onset signatures are near-simultaneous throughout the tail beyond geostationary orbit.This is likely a signature of the rapid reconfiguration that expands over a substantial portion of the tail at substorm onset.In the magnetotail (roughly in the region between |Y| < 8R E and 15 < X < 6R E ), the pre-onset field is strongly negative, caused by the strong magnetotail currents prior to the substorm onset.The largest values are observed in the inner part of the nightside magnetosphere, the field inside the nightside geostationary orbit reaches as high as 40 nT, while the field stretching extends out to the outer boundary of the coverage of the observations.The stretching is limited to |Y| < ∼10R E , with the most intense stretching occurring even closer to the sun-Earth line than that, within about |Y| < ∼5R E .

Spatial Distribution of Substorm Signatures in the Magnetotail
Around the substorm peak time (Figures 5b and 5c), the magnetotail field is dipolarized near the local midnight, as the field depression gets smaller beyond geostationary orbit indicating weakening currents in the magnetotail.On the other hand, the ΔB Z changes at the dawn and dusk edges of the current sheet continue to grow more negative, indicated by the widening and flattening of the cyan "donut" shaped contour which shows field depression region much clearly in the magnetotail from pre-onset to pre-peak and post-peak.This can be interpreted to be caused by the field aligned currents associated with the substorm current wedge.Furthermore, there is a slight dawn-dusk asymmetry in the field that develops in the transition region magnetotail.By the end of the recovery phase, the field depression has resumed a more circular shape (cyan and blue curves) and expanded back to further out in the magnetotail, indicating recovery of the tail currents, while the tail remains less stretched than the pre-onset situation that includes the growth phase associated thin current sheet.
Figures 6a and 6b show difference maps indicating the changes from substorm onset to substorm peak (Pre-peak-Pre-onset), and from the substorm peak to end of the recovery phase (Pre-end-Post-peak).Similarly to Figure 5, each phase is calculated as a 5-min average prior to (pre-onset, pre-peak, pre-end) or after (post peak) the time of interest.Figure 6a clearly demonstrates the field dipolarization at the center of the tail ( 10 < Y < 10R E ) and between geostationary orbit and X = 15R E .The innermost portion of the tail inside geostationary orbit shows a field decrease, which may be associated with the field aligned currents above and below the current sheet associated with the auroral precipitation within the auroral bulge (Gjerloev, 2012).
Figure 6b showing the difference map from peak to recovery end reveals a strong decrease of the pre-midnight sector magnetotail field indicating rebuilding of the tail current.Note that also this process is limited to the center part of the tail.The peak to end values also show different behavior inside and outside geostationary orbit, with positive change in the innermost region and negative change in the outer magnetotail.

Effects of IMF B Y and B Z
The substorm processes are driven by the solar wind and IMF, and therefore their characteristics contain a substantial component that is controlled by the external driver.Moreover, the magnetic field inside the magnetosphere as well as the substorm onset locations are potentially affected by the IMF B Y component.
We identify each substorm with a mean value of IMF B Y and B Z .This is accomplished by calculating the mean IMF B Z (all values of IMF B Y ) and mean IMF B Y (all values of IMF B Z ) over the entire duration of a substorm, spanning from the onset of the substorm to the end of the recovery phase.We investigate the influence of the IMF B Z and B Y on the location and time scales of expansion and recovery phases by separating the substorm events to those with average IMF northward (〈B Z 〉 > 0 nT) and southward (〈B Z 〉 < 0 nT) independent of B Y , as well as to those with average IMF B Y duskward (IMF 〈B Y 〉 > 0) and dawnward (IMF 〈B Y 〉 < 0) independent of the IMF B Z orientation.The time duration of expansion phase is nearly 50 min (Figure 7a) for substorms during southward IMF, which is somewhat longer than the expansion phase for substorms during northward IMF.For southward IMF, substorms are stronger (higher amplitude) and their recovery time scale is much longer (Figures 7a and 7b) than for substorms during northward IMF.However, the pre-onset behavior during the growth phase shows no differences for northward and southward IMF B Z .Figure 7c shows that substorms recover independent of IMF orientation, but the southward IMF curves show a decrease following the end indicating that often the substorm is immediately followed by the next one.
Both the expansion and recovery phases are longer under southward IMF when the external driving continues throughout the substorm evolution.We thus conclude that the recovery phase timing is a combination of internal processes and external driver effects.
Similarly to Figure 3, the lower left panel of Figure 7, distinguishing duskward and dawnward IMF cases, shows average duration of expansion phase to be about 40 min and for the field recovery it is about 80 min (from the peak of SML to above 100 nT).The behavior of mean and median curve prior to the onset shows no clear effect of IMF B Y .The median and mean curves centered around the peak (middle panel of Figure 7) also reveals a negligibly small effect of IMF B Y on amplitude and almost no effect on the time scale of recovery phases, which is about 60 min from the peak to the SML value above 100 nT.
Figure 8 shows the superposed epoch analysis of the external magnetotail field (ΔB Z with IGRF subtracted), for epoch time at onset (left), at substorm peak (middle) and at substorm end (right) for average IMF 〈B Y 〉 > 0 and 〈B Y 〉 < 0 nT.Similarly to Figure 7, the black, (blue) and red (maroon) dotted curves represent the median and  While limiting to a subset of the events makes the data more ragged, the basic features remain the same as for the full data set.The growth and onset are now most clearly seen in the outer transition region (Figure 8g), with no marked differences between positive and negative B Y .The peak magnetic field values are similar (to Figure 8h) and reached at the same time relative to the ground substorm peak time.The field dipolarization region or onset timings are not affected by the IMF B Y .
Figure 9 displays the result of superposed epoch analysis of IGRF subtracted (external field) ΔB Z , considering epoch time at onset (left), at substorm peak (middle) and at substorm end (right) for average IMF 〈B Z 〉 > 0 and 〈B Z 〉 < 0 nT.The black, (blue) and red (maroon) dotted curves represent the median and mean of ΔB Z , respectively and are similar to those discussed in Figure 8.The vertical dotted lines (black, blue and green) represent epoch time, time of substorm peak (min SML) and time of recovery end, respectively.Similar to Figure 8, this figure does not show any significant effect of the sign of the IMF on the evolution of ΔB Z at different locations in the magnetotail during onset/peak timing of substoms.The main characteristics of the substorm processes are the same as shown in Figure 8, that is, the peak of the substorm still appears first in the outer transition region (Figure 9h) and few minutes later in the inner transition region and down the tail.The field dipolarization region (in the left panels) are not affected by the IMF orientation.
In Figure 10, we investigate asymmetric responses in the magnetotail currents under different IMF B Y orientations.The left (right) panels show color-coded maps displaying average magnetic field ΔB Z in 2R E × 2R E bins in X and Y during the different substorm phases for duskward (dawnward) IMF B Y .Each panel shows 5 min averages of ΔB Z before substorm onset (Pre-onset), after the peak (Post peak) and before the substorm end (Pre-end),   Figures 12a and 12b depict difference maps illustrating changes in tail magnetic field configuration at various phases of substorm activity, specifically during the expansion phase (Pre-peak -Pre-onset) and from the substorm peak to the end of the recovery phase (Pre-end -Post-peak) during IMF B Y > 0. These maps are generated using 5min data of ΔB Z before and after substorm timing (onset, peak, end).Notably, Figure 12a clearly demonstrates the magnetic field changes from pre-peak to onset, during the expansion phase, particularly in the vicinity of the tail center during duskward IMF.
In Figure 12b, the difference map from peak to the end of the recovery phase displays a decrease (blue) in the magnetotail field, with a more pronounced effect observed on the duskside.Figures 12c and 12d present difference maps from substorm onset to end during IMF B Y < 0. Each phase is calculated in a manner similar to Figures 12a and 12b.The field configuration in the expansion phase, and in the recovery phase seems to resemble that in Figures 12a and 12b.However, the influence of a dawnward IMF appears to be more substantial compared to the impact of a duskward IMF.
Figure 13 depicts difference maps similar to Figure 12 but under the conditions of a positive IMF B Z (a b) and a negative IMF B Z (c d).These maps are also constructed using 5-min data of ΔB Z before and after each substorm phase (onset, peak, end).The field configuration during the expansion phase and in the recovery phase appears to be similar for both northward and southward IMF.However, the influence of a southward IMF seems to have a more significant impact compared to a northward IMF as the building up of positive (red during expansion phase) and negative (blue during recovery phase) field around the center of magnetotail is bit stronger and somewhat duskward (recovery phase) for southward IMF.
Figures 12 and 13 present almost similar results to those depicted in Figure 6, albeit with a reduced number of data points resulting from a filter based on IMF B Y and B Z , respectively.They represent the negligible impact of IMF components B Y and B Z on the evolution of the tail magnetic field.

Discussion and Conclusions
Substorms are transient phenomena in the Earth's magnetosphere that release solar wind energy stored in the magnetotail injecting part of it into the ionosphere and inner magnetosphere (D.N. Baker et al., 1996).In order to examine substorm evolution in detail, one needs to first identify the substorm onset, peak and end timings that delimit the expansion and recovery phases.
Substorm onsets are often identified from ground magnetic records, for example, as rapid decrease of the ground magnetic field H component in the auroral region, growth of ULF wave power, or positive deflections of the midlatitude magnetic records in the night sector.The AL index has frequently been used to time substorm onsets (Hsu & McPherron, 2012;Juusola et al., 2011), as has their SuperMAG counterpart, the SML index (Forsyth et al., 2014;Partamies et al., 2013).Chu et al. (2015) identified substorms as the intervals during which a midlatitude positive bay peaked above 25 nT.Based on magnetic ULF wave power, Murphy et al. (2009) and Milling et al. (2008) established a model for identifying substorm onsets.Several authors have used auroral observations to time substorm onsets: Liou et al. (2001) determined substorm onsets from a space-based auroral imager, while Rae et al. (2009) used auroral all-sky cameras.Substorms have also been timed using magnetotail observations, inner magnetosphere field dipolarizations (D. Baker & Pulkkinen, 1991;Nagai, 1982) or the magnetic reconnection signatures in the mid-magnetotail (D.N. Baker et al., 1996;Baumjohann et al., 1989).However, due to the sensitivity of the obtained timings to the location of the spacecraft relative to the tail instability, these timings contain much larger uncertainties than those based on ionospheric measurements.In this study, we used the Ohtani and Gjerloev (2020), substorm data set identified using the SML index.We focus on a subset of 5,077 substorms (Figure 1) that occurred during the period 2016-2020.We examine the average time scale of the substorm phases as well as the tail magnetic field changes during the expansion and recovery phases using combined magnetic measurements from THEMIS-A, D, E, RBSP-A, B, and MMS-1 spacecraft.We identify the peak time as the time of lowest value of SML between two onsets and substorm end as the time when the SML recovers to values greater than 100 nT after the peak.The duration of the expansion phases vary from 10 minutes (limit value in the Gjerloev (2012) identification) to hours, and the same is true for the recovery phase (Tanskanen, 2009), dependent on the orientation of the IMF B Z and season (Chua, 2004).From this data set, we obtained average duration of the expansion phase of 45 min and the recovery phase of 73 min.
Superposed epoch analysis of the SML index (Figure 3) and of the ΔB Z (IGRF field subtracted; Figure 4) from the magnetotail were used to further examine the characteristic time scales of the substorm expansion and recovery phases at different radial distances along the magnetotail.Performing three superposed epoch analyses using epoch times at substorm onset, at peak intensity and at the substorm end, the expansion phase duration obtained was ∼40 (Figure 3a) and the field recovery time scale was ∼60 min (Figure 3b).
The choice of the substorm recovery phase timing based on recovery to 100 nT is somewhat arbitrary, but is based on the analysis in Gjerloev (2012).It is expected that by the time the SML index reaches values smaller than that, the substorm current wedge associated currents have decayed, signifying the end of the substorm process (D.N. Baker et al., 1996).This conclusion is further supported by the superposed epoch analysis of Weimer (1994), who shows that at the recovery time when the AL index is equal in magnitude to the AU index the activity level is very close to 100 nT.
Using the spacecraft ephemeris data, we examine the magnetotail response in four bins, defined as inner magnetosphere ( 4 to 7R E ), inner transition region ( 7 to 10R E ), outer transition region ( 10 to 15R E ), and midtail ( 15 to 25R E ).In all regions, we focus only on the central part of the magnetotail ( 5 < Y < 8R E ), justified by the 2D maps in Figure 6, which show that the main changes occur within this region.The superposed epoch analysis on ΔB Z shows that the onset signatures are near-simultaneous at all distances tailward of geostationary orbit, with the transition region beyond 7R E onset preceding the others by a few minutes (within the accuracy of the superposed epoch analysis, which can range from a few min up to 10 min, Figure 4).However, these results are consistent with the (Angelopoulos et al., 2008) study, who point out that the substorm signatures are usually seen within ∼2 min around substorm onset timing.On the other hand, the peak value following the onset is obtained first in the inner transition region ∼50 min after the onset, in the outer transition region after about one hour, and in the midtail the peak is very broad and the peak is reached after about 80 min.
If the superposition is centered around the peak time, the peak coincides with the field maximum in the outer transition region, while obtained 10-20 min later in the inner transition region and midtail.This would suggest a causal relationship between the outer transition region magnetic field variations and the intensity of the auroral electrojet currents, consistent with mapping of auroral structures and location of the current sheet breakup obtained from an empirical model (Pulkkinen et al., 1992).The end of the tail magnetic reconfiguration in the outer transition region seems to end the substorm expansion phase (as measured by SML) in the ionosphere, which would then caused by the subsiding of the field-aligned currents generated by the tail field reconfiguration.
After the substorm peak, the field recovers fastest in the inner transition region (∼90 min), somewhat slower in the outer transition region (∼120 min) and slowest in the mid-tail (∼150 min).This ordering of time scales along the tail is different from that obtained in Pulkkinen et al. (1994), who asserted using 13 events that the inner magnetosphere was the slowest to recover.While the innermost bin in our superposed epoch series is challenging to interpret, as the field shows a different tendency around epoch time (onset/peak), and the mean and median do not have similar temporal trends when the epoch time is centered around the substorm peak intensity, it supports the above conclusions.Similar timescales of the field recovery have been reported in earlier studies, about 30 min to 1 hr near geosynchronous orbit, and those have been associated with the development of the ring current (D.N. Baker et al., 1981;R. McPherron et al., 1993).Jayachandran and MacDougall (2007) used polar cap convection measurements to study substorm phases, and determined the average growth, expansion, and recovery phase times scales to be 31.6,22.4, and 38.8 min, respectively.They further conclude that the expansion phase time scale (22 min) is much longer than the time scale obtained from geosynchronous measurements when the expansion phase in space was defined as the initial rapid dipolarization following the dipolarization.Baumjohann et al. (1989) analyzed Geotail flow and magnetic field data, and conclude that the near-Earth neutral line forms somewhere between 20 and 25R E in the tail.They propose a time scale for the expansion phase based on the dipolarization front propagation from the transition region tailward, and meeting the NENL after about 45 min, which is close to the results obtained in our superposed epoch analysis.Juusola et al. (2011) developed an automated method for determining substorm phases from a time series of the global AL index and IMF B Z .They found the length of growth phase, expansion phase and recovery phase to be 31, 12, and 31 min, respectively.Later, Partamies et al. (2013) used same routine and reported a typical length of a substorm of 74 min.On the other hand, using auroral data from the Polar spacecraft, Kullen (2004) conclude that the duration of expansion and recovery phases vary from about 80 to 140 min, depending on auroral oval conditions, roughly consistent with Tanskanen (2009) study using IMAGE magnetometer data, which found that the average duration of a substorm is about 180 min.Our results are more in line with the latter two studies.We note that the averages are sensitive to the solar cycle phase affecting the substorm size and duration (Pulkkinen et al., 2011;Tanskanen, 2009) as well as the exact definition of the substorm phases, which may cause artificial differences between the analyses.
We examined the magnetotail statistics around the onset, peak and end of substorm (Figure 5).The pre-onset panel during the late growth phase shows the tail has a strongly negative ΔB Z representing a highly stretched field in the magnetotail out to almost 15R E , implying a strong cross-tail current in the midnight sector magnetotail.During the SML peak intensity, the field is dipolarized, and at the end of the substorm, the tail field is stretched again to pre-substorm state due to enhancing cross-tail current.While the (Juusola et al., 2011) study used slightly different binning of their data, they basically show similar concentration of the magnetic field changes to within 10R E from the tail center, as well as limiting of the field dipolarization to outside geostationary orbit.These changes are even more clearly seen in the difference images showing the difference from pre-onset to peak and from peak to substorm end.
While the field dipolarizes in the tail transition region following substorm onset, the field continues to be in a stretched configuration at the dawn and dusk sectors.This may be associated with the field-aligned currents within the substorm current wedge, which cause further decrease in the field outside the current wedge.Ohtani and Gjerloev (2020) study of the substorm characteristics using the full SuperMAG network of stations concluded that the substorm current system is globally coherent, evolving and increasing in size post-onset, consistent with the magnetotail configuration obtained here.Our results would indicate that the substorm current wedge reaches roughly 20 MLT in the evening sector and 04 MLT in the morning sector.
We also investigate the effect of dawn-dusk IMF B Y (regardless of the orientation of IMF B Z ) and the effect of northward-southward IMF (with all dawn-dusk IMF) on the amplitude and time scale of substorm phases and magnetotail magnetic field.We qualitatively observe almost no effect of positive/negative IMF B Y on the amplitude of superposed epoch median and mean of ΔB Z .
We also notice that the duration of expansion and recovery phase is unaffected by the dawn-dusk IMF component.While some authors have suggested seasonal variation of the B Y effect (Holappa et al., 2021;M. V. Kubyshkina et al., 2023), our data set does not allow separation of the events by season due to the annual rotation of the satellite orbits.
We found noticeable effect of IMF B Z orientation on the amplitude and time scale of substorm phases as measured by the ionospheric SML index.The substorms during southward IMF are stronger and have a longer recovery time than those during northward IMF.The duration of expansion phase is few minutes longer for southward IMF.On the other hand, in the magnetotail, the size of the dipolarization (change in B Z from pre-onset to peak) was not dependent on IMF orientation.
However, the effect of the IMF B Y and B Z orientation is negligible on the magnetotail configuration particularly its rotation around Sun-Earth line.We observe a slight asymmetry in the dusk/dawn sector during both the positive/ negative IMF B Y and B Z , which can be seen as a preferentially more stretched magnetic configuration in the postmidnight sector for positive (negative) B Y and B Z during expansion and early recovery phases.Recently, Pitkänen et al. (2021) statistically investigated the influence of non-zero IMF B Y on the rotation of neutral sheet in the Earth's magnetotail between 30R E to 15R E .They found that the direction of rotation is opposite for IMF B Y > 0 and IMF B Y < 0, which is not in accordance with the results presented in this study.Furthermore, using multi-spacecraft data, Xiao et al. (2016) studied the position and shape of neutral sheet and deduced that the angle of rotation was slightly greater for negative IMF B Y for a small dipole tilt angle and for IMF |B Y | between 3 and 8 nT.They also observed a noticeable difference in rotation angle for positive and negative IMF B Y during northward and southward IMF.
The results shown here allow us to connect the magnetotail field changes with the intensity of the auroral electrojet currents.We show that the tail field dipolarization signatures span a wide region along the tail almost simultaneously, but the auroral electrojet enhancement is most closely associated with the inner transition region field dipolarization, pointing to an original and strongest source of field aligned currents from that distance.
Centering the activity at the substorm electrojet peak shows that it is simultaneous with the peak dipolarization in the magnetotail outer transition region, indicating outward motion of the FAC source.This sequence would be consistent with a scenario where the field-aligned currents are mostly drawn from the outer transition region during the peak of the substorm.
In summary, we use a large data set of substorm observations to show that 1.The superposed epoch results give the expansion, and recovery phase durations of about 40 and 60 min, respectively.
2. The superposed epoch analysis suggests that substorm onset is near simultaneous (to within a few minutes) from inner magnetosphere out to midtail.The onset is observed first at the inner transition region ( 10 < X < 7R E ), which precedes the ground onset time.3. The peak SML time coincides with the peak magnetic field B Z in the outer transition region ( 15 < X < 10R E ), while the peak values are obtained later both further in and further out in the magnetotail.This suggests that it is this region that feeds the field-aligned currents into the ionosphere that drive the auroral electrojet currents.4. The substorm recovery is fastest in the inner transition region ( 10 < X < 7R E ) and lasts longer further out.
This behavior is different from earlier studies using more limited data sets in the magnetotail (Pulkkinen et al., 1994).5.The magnetotail current intensification associated with substorms is limited to the center of the tail within |Y| = 10R E .The dipolarization is faster in the dusk sector, while it continues after the substorm peak in the morning sector.The current intensification and dipolarization are largely limited to within 15R E distance down the tail with very small changes in the mid-magnetotail.6. Duration of substorm expansion and recovery phases are not affected by the sign of IMF B Y .Sorting the data by average IMF B Y did not reveal any significant asymmetries in the substorm process.7.During southward IMF substorms are stronger and have longer expansion and recovery phases than those during northward IMF.However, the size of dipolarization (onset to peak value) is independent of IMF B Z orientation.A slight down-dusk asymmetry in the tail magnetic field is observed during expansion and recovery phases during southward IMF.

Figure 1 .
Figure 1.(Top panel) Annual number of substorms in the Ohtani and Gjerloev (2020) database.(Bottom panels) Sample substorm events.The shaded region shows the substorm interval, the dashed lines indicate the substorm onset, peak, and end times.

Figure 2 .
Figure 2. Number of observations in 1R E × 1R E bins from (a) RBSP-A and RBSP-B inside geostationary orbit, (b) THEMIS-A, THEMIS-D, and THEMIS-E, inside ∼15R E (c) MMS-1, and (d) all spacecraft inside ∼30 R E in the Y Z plane.

Figure 3 .
Figure 3. Superposed epoch analysis of the SuperMAG AL (SML) index.The black curves indicate the median, the dashed red curves indicate the mean, vertical dotted black, blue, green lines indicate epoch, SML peak, and recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.The three panels show superposed epoch analysis centered around the substorm onset, peak, and end times.

Figure 3
Figure 3 shows the superposed epoch analysis of the SML index with 240 min time window before and after the epoch.The vertical black dotted lines mark the onset (left panel), peak (middle panel) and substorm end (right panel) times, which were used as epoch times.The vertical blue dotted lines in the left and right panels denote the activity peak (min SML) and vertical green dotted lines in the left and middle panels indicate the time when the superposed SML median reaches a relatively quiet value above 100 nT.The figure shows the superposed epoch median and mean (black and red dashed lines, respectively).The blue shading indicates the interquartile range.The left panel showing the onset as epoch time reveals the rapid decrease of the SML index at onset, a mean

Figure 4 .
Figure 4. Superposed epoch study of the external magnetic field ΔB Z in the magnetotail in the ranges of (a, b and c) 7R E < X < 4R E , (d, e, and f) 10R E < X < 7R E , (g, h and i) 15R E < X < 10R E , and (j, k, and l) 25R E < X < 15R E , all limited to central section of the tail between 5R E < Y < 8R E .The black curves indicate the median, the dashed red curves indicate the mean, vertical dotted black, blue, green lines indicate epoch, peak, and recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.

Figure 5
Figure5shows color-coded magnetic field ΔB Z (observed field with IGRF field subtracted) averaged for 2R E × 2R E bins in X and Y during different substorm phases.Each panel shows ΔB Z from all spacecraft for the five years.

Figure 5 .
Figure 5. Average magnetic field ΔB Z in the equatorial magnetosphere.The field shown has the IGRF field subtracted to display the range of values in the same image.The four panels show the averages during 5 min prior to onset (pre-onset), during 5 min prior to the substorm peak as measured by the SuperMAG AL index (pre-peak), during 5 min after the substorm peak (post-peak), and during the last 5 min of the recovery phase (recovery end).Contour curves representing variations in ΔB Z are graphed, featuring distinctive colors corresponding to specific values: 30, 20, 10, and 5 nT of ΔB Z .The color scheme assigns yellow, light green, cyan, and deepskyblue to the respective values.

Figure 6 .
Figure 6.Difference maps showing the change from pre-onset to pre-peak and from post-peak to recovery end.Each panel shows the difference of a 5-min averages color coded such that positive values (field increases) are shown in red and negative values (field decreases) are shown in blue colors.

Figure 7
Figure 7 displays the results of the superposed epoch analysis of the SML separately for northward, southward, duskward and dawnward IMF, considering epoch time at onset (left panel) and substorm peak (center panel), and substorm end (right panel).The black (blue) curve represents the superposed epoch median for positive (negative)

Figure 7 .
Figure 7. Superposed epoch analysis of the SuperMAG AL (SML) index under northward/southward (top panels) and duskward/dawnward (bottom panels) IMF.The average of IMF B Z (B Y ) is calculated for each substorm period from onset through recovery end.The black (blue) curve indicates the median for IMF 〈B Y,Z 〉 > 0 nT (〈B Y, Z 〉 < 0 nT), the dashed red (maroon) curve indicates the mean for IMF 〈B Y,Z 〉 > 0 nT (〈B Y,Z 〉 < 0 nT).The vertical dotted black, blue, green lines indicate epoch, SML peak, and recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.

Figure 8 .
Figure 8. Superposed epoch study of the external magnetic field ΔB Z for dawn-dusk IMF B Y in the magnetotail in the ranges of (a-c) 7R E < X < 4R E , (d-f) 10R E < X < 7R E , (g-i) 15R E < X < 10R E , and (j-l) 25R E < X < 15R E ,all limited to central section of the tail between 5R E < Y < 8R E .The black (blue) curve indicates the median for IMF 〈B Y 〉 > 0 (IMF 〈B Y 〉 < 0) nT, the dashed red (maroon) curve indicates the mean for IMF 〈B Y 〉 > 0 (IMF 〈B Y 〉 < 0) nT, the vertical dotted black, blue, and green lines indicate epoch, peak, recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.
Figure 8. Superposed epoch study of the external magnetic field ΔB Z for dawn-dusk IMF B Y in the magnetotail in the ranges of (a-c) 7R E < X < 4R E , (d-f) 10R E < X < 7R E , (g-i) 15R E < X < 10R E , and (j-l) 25R E < X < 15R E ,all limited to central section of the tail between 5R E < Y < 8R E .The black (blue) curve indicates the median for IMF 〈B Y 〉 > 0 (IMF 〈B Y 〉 < 0) nT, the dashed red (maroon) curve indicates the mean for IMF 〈B Y 〉 > 0 (IMF 〈B Y 〉 < 0) nT, the vertical dotted black, blue, and green lines indicate epoch, peak, recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.

Figure 9 .
Figure 9. Superposed epoch study of IGRF subtracted magnetic field ΔB Z for northward-southward IMF in the magnetotail in the ranges of (a-c) 7R E < X < 4R E , (df) 10R E < X < 7R E , (g-i) 15R E < X < 10R E ,and (j-l) 25R E < X < 15R E , all limited to the central section of the tail between 5R E < Y < 8R E .Similar to Figure8, the black (blue) curve indicates the median for IMF 〈B Z 〉 > 0 (IMF 〈B Z 〉 < 0) nT, the dashed red (maroon) curve indicates the mean for IMF 〈B Z 〉 > 0 (IMF 〈B Z 〉 < 0) nT, the vertical dotted black, blue, and green lines indicate epoch, peak, recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.
Figure 9. Superposed epoch study of IGRF subtracted magnetic field ΔB Z for northward-southward IMF in the magnetotail in the ranges of (a-c) 7R E < X < 4R E , (df) 10R E < X < 7R E , (g-i) 15R E < X < 10R E ,and (j-l) 25R E < X < 15R E , all limited to the central section of the tail between 5R E < Y < 8R E .Similar to Figure8, the black (blue) curve indicates the median for IMF 〈B Z 〉 > 0 (IMF 〈B Z 〉 < 0) nT, the dashed red (maroon) curve indicates the mean for IMF 〈B Z 〉 > 0 (IMF 〈B Z 〉 < 0) nT, the vertical dotted black, blue, and green lines indicate epoch, peak, recovery end, respectively and the shaded region shows the interquartile range between 25% and 75%.

Figure 10 .
Figure 10.Average magnetic field ΔB Z in the equatorial magnetosphere for (left panels) IMF B Y > 0 and (right panels) IMF B Y < 0. The IGRF field has been subtracted to reduce the range of values shown.The three rows show evolution of average ΔB Z from the pre-onset, to post-peak, and pre-end (recovery end).The inner magnetosphere field depression is decreased during the post-peak (following dipolarization), and recovers back by the substorm end.The effect of B Y is shown as slightly higher field depression in the dusk sector magnetotail for positive and negative B Y .Contours depicting changes in ΔB Z have been plotted, with each contour line distinguished by specific colors corresponding to distinct values: 30, 20, and 10 nT.The color scheme designates yellow, light green, and cyan to represent these respective magnetic field values.

Figure 11 .
Figure 11.The binned average magnetic field ΔB Z in the X Y plane of magnetosphere for IMF B Z > 0 (left) and B Z < 0 (right).The field shown has the IGRF field subtracted to display the range of values in the same image.The three panels on the left and right side show the evolution of average ΔB Z for the pre-onset, post-peak, and pre-end (recovery end).The graph displays contours illustrating variations in ΔB Z , where each contour line is differentiated by specific colors corresponding to distinct values: 30, 20, and 10 nT.The color scheme assigns yellow, light green, and cyan to represent their respective values.

Figure 12 .
Figure 12.Differential maps illustrate changes in average magnetic fields from before the onset to before the peak, and from after the peak to the recovery end phase under the condition of IMF B Y > 0 (a-b) and IMF B Y < 0 (c-d).In each panel, a colorcoded representation is used to indicate differences in 5-min data of average ΔB Z , with red denoting positive values (indicating field increases) and blue representing negative values (indicating field decreases).

Figure 13 .
Figure13.Differential maps visually depict changes in the average magnetic fields occurring during various phases: from the pre-onset to the pre-peak phase and from after the peak to the recovery end phase, all while the condition of IMF B Z > 0 (a-b) and IMF B Z < 0 (c-d) are met.Each panel employs a color-coded scheme to convey disparities in 5-min average data for ΔB Z .In this scheme, red signifies positive values (field increases), while blue corresponds to negative values (field decreases).