This paper presents THEMIS measurements of two substorm events to show how the substorm current wedge (SCW) is generated. In the late growth phase when an earthward flow burst in the near-Earth magnetotail brakes and is diverted azimuthally, pressure gradients in the X- and Y-directions are observed to increase in the pileup and diverting regions of the flow. The enhanced pressure gradient in the Y-direction is dawnward (duskward) on the dawnside (duskside) where a clockwise (counter-clockwise) vortex forms. This dawn-dusk pressure gradient drives downward (upward) field-aligned current (FAC) on the dawnside (duskside) of the flow, which, when combined with the FACs generated by the clockwise (counter-clockwise) vortex, forms the SCW. Substorm auroral onset occurs when the vortices appear, Near-Earth dipolarization onset is observed by the THEMIS spacecraft (probes) when a rapid jump in the Y-component of pressure gradient is detected. The total FACs from the vortex and the azimuthal pressure gradient are found to be comparable to the DP-1 current in a typical substorm.
 The substorm current wedge (SCW) is an essential feature of the substorm expansion. A dynamical process in the near-Earth magnetotail associated with expansion onset causes cross-tail current to be diverted into the ionosphere, forming a SCW, consisting of downward (upward) field-aligned currents (FACs) on the dawnside (duskside) of the wedge and a westward auroral electrojet in the ionosphere [McPherron et al., 1973]. Substorm current wedge is closely related to near-Earth cross-tail current disruption (NECD) and leads to magnetic field dipolarization at substorm expansion onset [Lui, 1996].
 Substorm current wedge creation has been attributed to development of instabilities in the NECD region [e.g., Lui, 1996, and references therein] and to the slowdown/diversion of earthward flow and the shear at the edges of the flow [e.g., Birn et al., 1999] and references therein). Generation of FACs can be formulated in an expression consisting of three source terms in the magnetosphere [Hasegawa and Sato, 1980; Sato and Iijima, 1979]:
where j∥,i is the total FAC in the ionosphere, represents the magnetospheric current perpendicular to the magnetic field, ρ is the mass density, and Ω = · ∇ × /B refers to the field-aligned component of vorticity. For isotropic plasmas
and represent diamagnetic and inertial current, respectively. In equation (1)j∥,i(1) comes from the magnetic gradient in the direction of the magnetospheric current; j∥,i(2) is associated with a time-dependence of a twist in the magnetic field caused by vortical flow; and j∥,i(3) arises from density inhomogeneities in the direction of the inertial current, because is considerably less than [Birn et al., 1999], it is commonly ignored [Keiling et al., 2009; Lui et al., 2010]. Using force balance ∇P = j × B and by neglecting the contribution to from , Vasyliunas  obtained
Which is a well-known relation between the divergence of the plasma sheet perpendicular current and field-aligned currents for an isotropic plasma [Lyons et al., 2009], where denotes the flux tube volume of one unit magnetic flux; P is the plasma pressure; and Beq and Bi represents the magnitude of magnetic field at the equator and in the ionosphere, respectively. Therefore, FACs can be generated by build up of an azimuthal pressure gradient in the magnetosphere in the presence of a tailward gradient of flux tube volume [Xing et al., 2011].
Keiling et al.  showed that a clockwise (counter-clockwise) magnetospheric vortex corresponds to downward (upward) FACs and the related j∥,i(2) contributes a significant part of the FAC at beginning of a substorm expansion phase. Xing et al.  showed that enhancement of a duskward pressure gradient is associated with enhanced upward FAC during the late growth phase and leads to intensification of the onset auroral arc before breakup.
 In this paper, measurements from three of the five THEMIS [Angelopoulos, 2008] probes (THA-E) that directly detected the azimuthal pressure gradient in the near-Earth magnetotail are used to infer the SCW formation mechanism. Two substorm events are presented. The aurora images obtained from the THEMIS ASI array [Mende et al., 2008] are in the auxiliary material. GSM coordinates are used throughout this study.
2. Case Studies
 In this section, two substorm events will be investigated using measurements from three THEMIS probes that were near the equatorial plane in a triangular configuration with separations of ∼1–2 RE. Figure 1 shows their projected locations on the X-Y plane. The earthward moving and azimuthally-diverted flows and the directions of the observed pressure gradient are also indicated there.
2.1.1. Equatorial Pressure Gradient Estimation
 Assuming that plasma pressure is isotropic and the plasma sheet is symmetric across the neutral sheet and in approximate force balance, Xing et al. [2009, 2011] showed that vertical pressure balance holds near the equatorial plane so that equatorial plasma pressure can be estimated from:
where plasma pressure P, Bx2 and By2 are from in situ measurements, and Peq is the pressure at the vertical projection point in the equatorial plane. Assuming that within the probe equatorial projection region Peq varies linearly with a constant 2D gradient ∇Peq = (∇xPeq, ∇yPeq), one has
where ΔX21, ΔX31, ΔY21, ΔY31 are the separations between the three probes' equatorial projections. By solving (4) we can approximately estimate ∇Peq based on measurements from the three probes.
2.1.2. FAC Calculations
 A key step in applying equation (2) for j∥,i(1) is to obtain ∇V = ∇ as accurately as possible. For this purpose, we adopt the advanced Time-Dependent Magnetic Field Model with a thin current sheet (AM03) [Kubyshkina et al., 2011] which was developed to reconstruct the time-varying magnetotail configuration (with 1 min resolution) based on multi-spacecraft measurements. This model is the only magnetic field model that can adequately represent the stretching of the tail magnetic field during a substorm based on observations. For a moderately disturbed configuration in small /moderate substorms, AM03 provides a magnetic field value close to that observed near the spacecraft, with a least squared deviation of about 1–5 nT. This gives a possibility to calculate the model ∇V in the vicinity of probes, as the measured magnetic field is well reproduced there. Even so, to avoid the time variability we do not use the model at the exact time of breakup, but before and after it. To get j∥,i(2) using (1) we assume a uniform, incompressible plasma and solid-body rotation for the vortex, following the simplified expression given by Keiling et al.  and Lui et al. .
2.2. Case 1
 The first event studied is a substorm on 19 February 2008. The positions of THA, D and THE (see Figure 1a) allow us to calculate ∇Peq. Overview observations of the three probes are plotted in Figure 2. From top to bottom plotted are the AL index from THEMIS mid-latitude ground magnetic observations, Peq, ∇xPeq and ∇yPeq; and three components of the bulk flow velocity and magnetic field measured by THA, D and THE, respectively. The estimate of Peq should be reliable since the probes were all close to the neutral sheet (β ∼ 102). Auroral substorm onset is identified at 05:24:48UT from ASIs at FSIM. The black and red vertical lines indicate auroral substorm onset and dipolarization, respectively, at THD. Both the auroral substorm onset and dipolarization at THD were observed during the first rapid drop in the AL index.
 An eastward flow was observed simultaneously by THA (∼200 km/s), THD (∼150 km/s) and THE (∼50 km/s) within ∼1 min of auroral substorm onset. About 1 min later, a clockwise flow vortex formed in/near the probes region. (Conjugate ionospheric vortices and downward FACs were observed and studied in detail in Keiling et al. ).
 An eastward ∇yPeq appeared and increased as the eastward flow was detected by the three probes. It is of interest that a magnetic dipolarization was observed by THE just as the first rapid jump in eastward ∇yPeq was seen. Along with the enhancement in eastward ∇yPeq from almost 0 to ∼0.3 nPa/RE, earthward ∇xPeq increased from about 0.1 nPa/RE to ∼0.3 nPa/RE. Based on (2)
AM03 modeling gives ∇xVeq ∼ −0.1 nT−1 and ∇yVeq ∼ −0.01 nT−1. Adopting, ∇xPeq ∼ 0.3 nPa/RE, ∇yPeq ∼ −0.3 nPa/RE and Beq = 20 nT from observations, we obtain a downward FAC j∥,i(1) ≈ 16 μA/m2 that lasted for about 8 min after dipolarization.
where vfinal is the rotational vortex speed averaged over three satellites, τ is the time scale of vorticity change, L is the plasma sheet thickness and r is the length scale of the flow vorticity. Using Bi = 6 × 104 nT, L ≈ 1.5 RE, n ≈ 0.7/cm3, vfinal ≈ 500 km/s, τ ≈ 60 s, Beq,start = 10 nT (approximately the value of the equatorial magnetic field averaged over the three satellites around the beginning of vortex formation), and Beq,end = 20 nT (after expansion phase onset), we find that the clockwise magnetospheric vortex may generate a downward j∥,i(2) ∼ 12 μA/m2 at the auroral substorm onset and ∼3 μA/m2 after dipolarization. It is noteworthy that more than one flow burst was observed by the probes by the time the pressure gradient had subsided.
2.3. Case 2
 The second event studied is a substorm on 12 April 2009. Equatorial projections from THB, THC, and THD are plotted in Figure 1b. Figure 3 is an overview of their measurements in the same format as in Figure 2. The westward flow observed by the westernmost probe (THD) starting at ∼07:20 can be attributed to diamagnetic drift, since ∇xPeq already had a high value of ∼0.25 nPa/RE. Considerable increases in vy (∼100–200 km/s) were observed by THC and THD at about 07:25UT, and then by THB at about 07:26UT. A counter-clockwise flow vortex was then seen to form at about 07:26:30UT. Auroral breakup can be identified at 07:25:06UT from ASIs at FSMI. Note that the active aurora propagated from the east across the edge of the field of view. Onset might have started slightly prior to 07:25:06 UT. Clear dipolarization was observed at THC at ∼07:26 UT, when both ∇yPeq and ∇xPeq increased dramatically. Within about half a minute, ∇xPeq increased from ∼0.2 nPa/RE to ∼0.4 nPa/RE, and ∇yPeq from ∼0 to ∼0.25 nPa/RE. Note that the rapid drop in the AL index started within about half a minute of the observation of magnetic dipolarization. The enhanced pressure gradients persisted for about 5 min; the flow vortex lasted only for less than 1 min. Note also that more than one flow was observed in the event.
 AM03 modeling gives ∇xVeq ∼ −0.11 nT−1 and ∇YVeq ∼ 0.02 nT−1; from in situ measurements ∇xPeq ∼ 0.4 nPa/RE, ∇yPeq ∼ 0.25 nPa/RE and Beq ≈ 20 nT. We then find j∥,i(1) ≈ 17 μA/m2 which is almost the same as in case 1. On the other hand, by taking Bi = 6 × 104 nT, L ≈ 1.5 RE, r = 1.5 RE, n = 0.5/cc, vfinal = 200 km/s, τ ≈ 60 s and Beq,0 = 20 nT, we find j∥,i(2) ≈ 0.8 μA/m2 which is much smaller than that in Case 1.
3. Substorm Current Wedge Formation
 We have shown that in Case 1 (2), a clockwise (counter-clockwise) flow vortex formed at aurora expansion onset, and immediately at and after dipolarization, a dawnward (duskward) pressure gradient appeared and was enhanced substantially. Vortices and azimuthal pressure gradients in Cases 1 and 2 were closely related to eastward and westward diversion of earthward flow, with THEMIS probes being on the eastward and westward side of the flow, respectively. The dawnward (duskward) pressure gradient and the clockwise (counter-clockwise) flow vortex are an effective source of downward (upward) FACs. Our observations were possible thanks to the fortuitous location of the THEMIS probes in or near the eastward and westward edges of the substorm current wedge in Cases 1 and 2, respectively. Assume the equatorial cross-section of the downward/upward FACs is ∼2 × 2 RE2. For case 1, the integrated intensity of the downward FAC from the pressure gradient at dipolarization is J∥(1) ≈ 8.7 × 105A; the integrated FAC from vorticity is J∥(2) ≈ 3.2 × 105A at auroral substorm onset, and J∥(2) ≈ 1.6 × 105A after onset. Hence the total downward FAC around onset time is J∥ ∼ (1.0 − 1.2) × 106A. The sum of the two current types for Case 2 are J∥(1) ≈ 9.3 × 105A at dipolarization time, and J∥(2) ≈ 0.4 × 105A at or after auroral breakup. Therefore, the total upward FAC would be J∥ ∼ 1.0 × 106A. It is noteworthy that substorms 1 and 2 are both moderate with the peak of AL reaching −450 and −650 nT, respectively. According to Kamide and Baumjohann , the total current in such events should be about 106A, which is in agreement with the above results obtained from local pressure gradient and flow vortex estimations. Our result suggests that both pressure gradient and vorticity changes contribute to SCW formation in substorms, with the former being dominant near the dipolarization time/region.
Figure 4 illustrates an observationally-derived scenario of substorm current wedge formation. During the growth phase, the cross tail current enhances, corresponding to enhancement of ∇xPeq in the near-Earth tail. In the late growth phase, pressure-depleted earthward flowing plasma slows down, and is diverted dawnward and duskward. Two vortices appear, and a bow-shaped high-pressure gradient forms. This pressure gradient originalates as follows: High pressure piles up ahead of the diverting flow [Zhou et al., 2011, Li et al., 2011], then the pressure drops upon arrival of pressure-depleted fast flow or bubble [Yang et al., 2011]. As a consequence, a diverging pressure gradient pattern is created in ahead of the flow (plasma bubble), namely, dawnward (duskward) ∇yPeq appears in the flow's dawnside (duskside) edge, and a SCW is thus formed. Satellites at the dawnside (duskside) may observe the dipolarization and FAC within one or several minutes after the start of flow braking/diversion. Xing et al. [2009, 2011] studied the pressure gradient ahead of a dipolarization front associated with growth phase auroral arc intensification. In their cases, a converging pressure pattern is seen. Our study focuses on the pressure gradient during the expansion phase and displays a diverging pressure gradient pattern ahead of the earthward flow. Yang et al.  showed that the two different pressure gradient patterns co-exist in the flow burst interaction process.
 Our study is consistent with the observation that substorm auroral onset occurs on a thin arc associated with a large pressure gradient in the near-Earth plasma sheet, when a new streamer reaches near the pre-existing arc [Nishimura et al., 2011]. Numerous flow channels may contribute multiple intensifications during the expansion phase [Lyons et al., 2012]. According to Friedrich et al. , the inner edge of the plasma sheet becomes unstable to the shear flow ballooning instability, which may also generate a significant part of FACs at the onset of the expansion phase, but we did not specifically address that mechanism in the present study.
 This work is supported by NSFC grants (40974095, 41031065, 41011120250, 40731056, 40904043, 41004072) and the Chinese Major Research Project (2011CB811404). THEMIS work in the U.S. was supported by NASA NAS5-02099. The fluxgate magnetometer team was supported by the Deutsches Zentrum für Luft- und Raumfahrt under grant 50QP0402. We acknowledge the Canadian Space Agency for support in fielding and data retrieval from the THEMIS GBO stations and for provision of data by the CARISMA network.
 The Editor thanks an anonymous reviewer for assisting in the evaluation of this paper.