Journal of Geophysical Research Space Physics
Supporting Information for
Formation and evolution of high plasma pressure region in the near-Earth plasma
sheet: Pre-cursor and post-cursor of substorm expansion onset
Y. Yao1, Y. Ebihara1, T. Tanaka2
1Research
Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto, Japan, 2Kyushu University,
Fukuoka, Japan
Contents of this file
Text S1
Text S2
Figures S1 to S3
Introduction
In the presented study, we carried out a comparison study on formation and evolution of
high-pressure region (HPR) in the near-Earth plasma sheet between THEMIS
observation and global MHD simulation.
We determined, by visual inspection, the closest position in the simulation domain, at
which both the THEMIS observations and simulation results show most similar temporal
variations in pressure, velocity, and magnetic field. In the manuscript, except for the
pressure, we did not show directly the comparison of the velocity and magnetic field. In
Text S1, we demonstrated the detailed comparison of the velocity and the magnetic field
at probes THE and THD between the observation and the simulation.
Before and after the substorm onset, the HPR propagates earthward and retreats
tailward, respectively. We used the ion pressure observed at multiple THEMIS probes to
determine the HPR propagation. In the presented study, we have the data from two
probes THE and THD, which were separated more in YGSM direction than that in XGSM
direction. In Text S2, we discussed the radial and azimuthal propagation of the HPR
before and after the onset.
Text S1.
Comparison of pressure, velocity, and magnetic field between THEMIS observation and
MHD simulation
1
1. At probe THE
In Figure S1 we plot both THEMIS observed and simulated pressure, bulk velocity, and
magnetic field at probe THE in GSM coordinate. It shows a good agreement of
simulated plasma pressure (Fig S1b) with observed ion pressure (Fig S1a), that is two
pressure peaks around substorm onset, except for the difference of time scale between
each other, which is discussed in [Yao et al., 2015]. Figures S1c and S1d show
observed ion velocity and bulk velocity of the MHD simulation in X, Y, and Z
components, referring to blue, dark green, and red lines (same format for magnetic
field), respectively. It is found that both Vx have two peaks structure. The difference is
seen during the time interval between two velocity peaks. The THEMIS observation (Fig
S1c) shows that there is a deep dip between the two peaks, however, there is no such
dip found in the MHD simulation (Fig S1d). It may be due to that the THEMIS probes did
not observe continued earthward fast flow. The simulated Vx at probe THE increases
continuously. For Vy, it is found that there is a quite large difference between the
observation and the simulation, that is observed Vy has a more complicated variation
compared to the simulated one, which may be considered as the real location of probe
THE that is located a little far away from noon-midnight meridional plane, where the fast
flow deflects duskward in the premidnight region. However, the coincident position in
the MHD domain is close to the noon-midnight plane, where the fast flow does not
mostly deflect duskward. In Figures S1e and S1f we demonstrate magnetic field of the
THEMIS observations and the MHD simulation. It is found that the simulation can
reproduce well what the THEMIS observed in Bx and Bz. There is a similar one step
jump of the Bx, and a similar two step jump of the Bz in both. For Y component, no
significant variation was found from a rough view. It seems that both By are almost
constant and closely around 0. On the other hand, we also found the difference that the
value of observed By is almost positive, however the value of simulated By is almost
negative, which may attribute to different magnetic structure at probe THE between the
real world (more complicated) and the global MHD simulation.
2. At probe THD
In Figure S2 we plot the comparison of pressure, bulk velocity, and magnetic field in the
same format as Figure S1 at probe THD. Result of the pressure also shows a good
agreement between the MHD simulation and the THEMIS observation. Two pressure
peaks structure around the substorm onset can be seen obviously. The bulk velocity of
the simulation and the observation is shown in Figures S2d and S2c, respectively. We
can still find similar two peaks structures in Vx to the case at probe THE. These two
velocity peaks seems to have a longer time duration than that observed at probe THE.
The observed Vy also demonstrates a complicated variation trend than the simulated
one. At probe THD, the simulated Vz has a resemblant evolution of the observed one,
which is a sharp decrease associated to the second Vx peak. We show the comparison
of the magnetic field in Figures S2e and S2f. It is found that the simulated Bz has a
similar variation pattern as the observed one. The highlight difference can be concluded
as the amplitude and time scale of the simulated Bz are larger and longer than those of
the observed one, respectively. For both By, it has the almost same situation as that
found at probe THE. The simulated Bx has a similar temporal variation as the observed
one. However, the magnitude of the simulated Bx is larger than the observed one. After
comparing the observed Bx at probes THD and THE, we can find that the average |Bx|
level is smaller at probe THD than that at probe THE. It may attribute to their relative
distance away from the magnetic equator during the observed substorm event.
However, in the MHD simulation the results show almost the similar magnitude in the Bx
2
at probe THD to that at probe THE, which may be due to the same ZGSM of the
coincident positions at probes THE and THD.
As a summary, we used pressure, velocity, and magnetic field to identify the coincident
position of THEMIS probe in the MHD domain. Primarily we look at pressure, Vx, and Bz
these 3 parameters by visual inspection with focusing on their variation pattern. It is
found that the results of the MHD simulation could demonstrate a good agreement with
that of the THEMIS observations. Qualitatively, the coincident positions that we
determined by the visual inspection in the MHD domain could respond to the real probe
ones.
Text S2.
Discussion on radial and azimuthal propagation of the HPR before and after the
substorm onset
Before and after the substorm onset, the HPR propagates earthward and retreats
tailward, respectively. We will discuss the problem separately within these two time
intervals. We used the ion pressure observed at multiple THEMIS probes to determine
the HPR propagation. In the presented study, we have the data from two probes THE
and THD, which were separated more in YGSM direction than that in XGSM direction.
Before the substorm onset, we found in MHD simulation (shown in Figures 6d and 6e in
the manuscript) that the convergence term  P Vx x in XGSM direction mainly
contributes to the plasma pressure enhancement, in other words the formation of the
HPR. The convergence term  P V y y in YGSM direction is almost equal to 0, which
does not contribute to the formation of the HPR. Then we might determine in the MHD
simulation that there is radial earthward propagation of the HPR in XGSM direction, and
there is no azimuthal propagation in YGSM direction. From the THEMIS observation, the
situation seems more complicated. In XGSM direction, Figure S3c shows that ion Vx at
probe THE is greater than that at probe THD, which meets the convergence condition
Vx x  0 leading to  P Vx x  0 the formation of the HPR. In YGSM direction
(shown in Figure S3e), we found the dawnward Vy associated to the ion pressure
enhancement, however, the Vy distribution at probes THE and THD might not contribute
to the HPR formation by simply calculating V y y : V y _ THE  V y _ THD  yTHE  yTHD  ,


since the dawnward Vy_THD is greater than the dawnward Vy_THE, which results in the
V y y  0 leading to  P V y y  0 . Then we might exclude the azimuthal
propagation of the HPR, since there is no HPR formation in YGSM direction.
After the substorm onset, the HPR will retreat tailward radially seen from both THEMIS
observation and MHD simulation [Yao et al., 2015]. The propagation of the HPR is
different from that before the onset. In the MHD simulation, we found that both subterms  P Vx x and  P V y y contribute to the HPR formation at coincident
position of probe THE shown in Figure 6e in the manuscript. The sub-term that in XGSM
direction is greater than that in YGSM direction. From THEMIS observation, positive
(duskward) Vy was found at both probes THE and THD, which is comparable to the Vx.
3
By a similar calculation V y y :
V
y_ THE
 Vy_ THD 
 yTHE  yTHD 
as that in XGSM
direction, we found that the Vy distribution at both probes (shown by green arrows in
Figure S3e) can result in V y y  0 leading to positive  P V y y , which implies
that we cannot exclude the azimuthal propagation of the HPR after the onset. In the
MHD simulation at both coincident position of probes THE and THD the Vy is small equal
to 0. The difference in the Vy between the THEMIS observation and the MHD simulation
might be due to the location of THEMIS probes in the HPR. Earthward plasma flow will
deflect duskward and dawnward when the flow is braked by sub HPR and encounter the
dipole magnetic field. The observed positive Vy at probes THE and THD associated to
the second pressure peak indicates that both probes were located in this deflection
region (dusk-side) that is far from the central HPR in YGSM direction. Figures S4a and
S4b show simulated value of sub-terms  P Vx x and  P V y y in XGSM-YGSM
plane, respectively. The spatial range is from −9 to −10 Re in XGSM direction with ∆x=
0.5 Re and from 3 to −3 Re in YGSM direction with ∆y= 1 Re. It is obviously that within
the given region  P V y y can contribute to the HPR formation at most locations.
However, the radial propagation of the HPR (shown in Figure S4a) is dominant one by
comparing both sub-terms. There is one notable position (−9.5, −3) away from the
central HPR around YGSM= 0 Re, at which  P V y y is comparable to  P Vx x .
It may suggest that sub-term  P V y y may play comparable role as sub-term
 P Vx x in the HPR propagation depending on the relative location in the HPR.
As a result, we discussed the radial and azimuthal propagation of the HPR before and
after the substorm onset. We found that before the onset there is only earthward radial
propagation of the HPR in XGSM direction, and no azimuthal propagation in YGSM
direction. However, after the onset we found that both radial and azimuthal propagation
of the HPR are available. By comparing both sub-terms  P Vx x and  P V y y
in the given region, the former one predominantly corresponds to the radial propagation
of the HPR, and the later one is comparable to the former one only at limited local
positions.
Reference
Yao, Y., Y. Ebihara, and T. Tanaka (2015), Sudden pressure enhancement and tailward
retreat in the near-Earth plasma sheet: THEMIS observation and MHD simulation, J.
Geophys. Res. Space Physics, 120, doi:10.1002/2014JA020482.
4
Figure S1. Comparison between THEMIS observations (left-hand) and MHD simulation
results (right-hand) at probe THE. Pressure, velocity, and magnetic field are shown from
top to bottom. Three components of the velocity, or magnetic field vector are plotted in
blue, dark green, and red lines, respectively. Observed velocity, and magnetic field are
averaged over a 15 sec-window.
5
Figure S2. Comparison between THEMIS observations (left-hand) and MHD simulation
results (right-hand) at probe THD with the same format as Figure S2.
6
Figure S3. Comparison between THEMIS observations (left-hand) and MHD simulation
results (right-hand) at probes THE in blue line and THD in red line. Pressure, Vx, and Vy
are shown from top to bottom. Observed velocity is averaged over a 15 sec-window.
7
Figure S4. (a) Convergence term in XGSM direction  P Vx x , and (b) that in YGSM
direction  P V y y in XGSM-YGSM plane at ZGSM= −0.5 Re associated to second
plasma pressure enhancement after the substorm onset in MHD simulation.
8