Large-scale flow vortices following a magnetospheric sudden impulse

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 3 364, doi:1.12/jgra.329, 213 Large-scale flow vortices following a magnetospheric sudden impulse A. A. Samsonov 1 and D. G. Sibeck 2 Received 22 February 213; revised 24 April 213; accepted 9 May 213; published 7 June 213. [1] Global MHD simulations predict the generation of flow vortices on the magnetospheric flanks near the equatorial plane after the impact of solar wind dynamic pressure pulses on the magnetosphere. These vortices are associated with field-aligned currents, having similar senses to those responsible for the main impulse, i.e., the second impulse of the well-known sudden impulse variations at high geomagnetic latitudes. We investigate the evolution of the vortices and show that they result from the interaction of a fast MHD wave and the inner (near-earth) boundary of numerical models. Near the inner boundary, the Ampere force decelerates plasma flow resulting in two closely related phenomena: the generation of flow vortices and the launch of a reflected fast wave moving sunward. The vortices propagate antisunward and split into several parts during several minutes. The reflected wave interacts with the magnetopause and bow shock and changes its velocity. The interaction between the reflected wave and bow shock results in two new discontinuities moving earthward through the magnetosheath. The first is either a very weak fast rarefaction wave or a weak fast shock, and the second is either a tangential discontinuity or a compound discontinuity with a decrease of the density and magnetic field and an increase of the temperature. We speculate that the inner boundary in simulations may correspond to either the plasmasphere or ionosphere. Citation: Samsonov, A. A., and D. G. Sibeck (213), Large-scale flow vortices following a magnetospheric sudden impulse, J. Geophys. Res. Space Physics, 118, 3 364, doi:1.12/jgra Introduction [2] As early as the nineteenth century, it was established that magnetic storms begin with a sudden increase of the horizontal (H) magnetic field component called the storm sudden commencement. Later, it was realized that not all increases in the H component are followed by storms, therefore, the term sudden commencement was replaced by the more common name, sudden impulse (SI). In the twentieth century, space observations showed that positive sudden impulses are connected with magnetospheric compressions caused by interplanetary shocks (IS) and tangential discontinuities with density increases. The solar wind dynamic pressure increases across interplanetary shocks, the magnetopause moves earthward after the shock impact, and a fast compressional wave or magnetospheric sudden impulse propagates through the magnetosphere. To be more exact, this is not compressional wave, but a weak fast shock [Grib et al., 1979] with the fast Mach number only slightly more than unity, at least near the magnetopause. However, the difference is mainly terminological and we will call both earthward- and sunward-propagating magnetospheric disturbances waves, because compressional fronts in the magnetosphere are much smoother than in the solar wind. 1 Department of Earth Physics, Physical Faculty, Saint-Petersburg State University, St. Petersburg, Russia. 2 NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. Corresponding author: A. A. Samsonov, Department of Earth Physics, Physical Faculty, Saint-Petersburg State University, St. Petersburg 1984, Russia. (andre.samsonov@gmail.com) 213. American Geophysical Union. All Rights Reserved /13/1.12/jgra.329 Observations in the magnetosphere show that the velocity of the compressional wave is approximately equal to the fast mode magnetosonic velocity (in the dayside magnetosphere it nearly coincides with the Alfvén velocity) [Nishida and Cahill, 1964; Patel, 1968; Sugiura et al., 1968; Wilken et al., 1982; Andréeová et al., 28; Keika et al., 28], which is usually greater than the IS velocity in the solar wind. [3] In addition to the global magnetospheric compression, ground magnetic observations (in particular, those made close to the auroral region) demonstrate that variations of the H component during sudden impulses usually consist of two pulses with opposite polarities. The pulses are supposed to be connected with two magnetospheric-ionospheric current systems, with the current flowing downward into the ionosphere on the evening side and upward on the morning side during the first stage (preliminary impulse) and the direction of the currents reversing in the second stage (main impulse) [see Araki, 1994, and references therein]. As noted in several papers [e.g., Wilson and Sugiura, 1961; Tamao, 1964a], fast compressional waves propagating through the magnetosphere excite converted Alfvén waves even in uniform cold plasmas. The resonance mode coupling occurs in regions with strong gradients of the Alfvén velocity, in particular, at the plasmapause [Tamao, 196]. According to Tamao [1964b], the converted Alfvén wave in the magnetosphere is accompanied by a field-aligned current (FAC). This current is the source of the magnetic field variations in the preliminary impulse. The second electric current system responsible for the main impulse can be explained in terms of azimuthal viscous stresses applied by the solar wind stream to the outer magnetospheric boundary. According to Araki s qualitative model [Araki, 1994], the polarization current flowing along the 3

2 compressional front transforms into the FAC and ionospheric currents of the preliminary impulse, while the FAC and ionospheric currents during the main impulse are generated by a duskward electric field connected to enhanced magnetospheric convection in the compressed magnetosphere. [4] Global MHD models simulate magnetospheric processes and ionospheric currents in a self-consistent way. In most simulations, the solar wind disturbance has been imposed as an isolated density pulse without variations of other parameters [Slinker et al., 1999; Chen et al., 2; Keller et al., 22; Fujita et al., 23a, 23b; Kataoka et al., 24], i.e., differently from the fast shock jump conditions, which also include changes of the magnetic field and velocity. Interactions of idealized and observed interplanetary shocks with the magnetosphere were simulated by Ridley et al. [26], Samsonov et al. [27, 21], and Andréeová et al. [211]. The results show that both fast shocks and density pulses produce similar magnetosphericionospheric variations. The numerical simulations predict that two electric current systems with oppositely oriented FACs successively form in the ionosphere, and the sequence of the current systems in time agrees with that inferred from the magnetic field variations during the preliminary and main impulses of SI. The impact of the pressure pulse on the magnetopause results in fast plasma flows in the magnetosphere. In the equatorial plane, these streams move from the dayside magnetosphere toward the magnetospheric flanks where large-scale vortices form. The flow rotation in the vortices is counterclockwise on the evening flank and clockwise on the morning flank when viewed from the north. This sense of rotation coincides with the sense of rotation in the global magnetospheric convection pattern. The corresponding FAC flows downward (upward) in the morning (evening) side, and the polarity of the ground magnetic variations coincides with the polarity observed in the main impulse. Both the ionospheric and magnetospheric vortices move tailward through the terminator plane and gradually weaken. [] However, different scenarios have been suggested to explain the magnetospheric generation of the two ionospheric current systems [e.g., Keller et al., 22; Fujita et al., 23a, 23b; Ridley et al., 26; Samsonov et al., 21, and references therein]. Recently, Samsonov et al. [21] simulated the interaction of an interplanetary shock with the magnetosphere in an artificial case with a northward interplanetary magnetic field (IMF). Intensification of the two ionospheric current systems (similar to the preliminary and main impulse currents) coincides in time with intensification of two corresponding magnetospheric dynamos. According to Samsonov et al. [21], the magnetospheric dynamo responsible for the preliminary impulse is located at the inner edge of the magnetopause reconnection site, i.e., tailward of the cusp in the northward IMF case. The dynamo responsible for the main impulse is connected to the aforementioned flow vortices in the equatorial plane. The tailward motion of the magnetospheric vortices agrees with the ionospheric current convection toward the midnight meridian. [6] Another prediction of the global MHD simulation was made by Samsonov et al. [27]. Using numerical results along the Sun-Earth line, they found that the fast MHD wave reflects from the inner numerical boundary; and the reflected fast wave propagates sunward through the magnetosphere and magnetosheath. The interaction between the reflected wave and magnetopause (bow shock) stops the inward motion of the magnetopause (bow shock) and results in secondary waves or discontinuities in the magnetosphere and magnetosheath. In this paper, we discuss all waves/discontinuities predicted by the MHD simulations in the magnetosheath after the IS shock impact. However, the main purpose of this paper is to explain the mechanism by which flow vortices form in the equatorial plane and show that the vortices and the reflection of the compressional wave from the inner boundary are two parts of a single process. 2. Numerical Models and Boundary Conditions [7] We simulate the interaction of an interplanetary shock with the Earth s magnetosphere using the Block Adaptive Tree Solar-wind Roe Upwind Scheme (BATS-R-US) [Powell et al., 1999; Tóth et al., 212]. This global code solves the single fluid, ideal MHD equations on a three-dimensional Cartesian grid to simulate the interaction between the solar wind, magnetosphere, and ionosphere. The finest resolution ( R 3 E ) is used throughout most of the magnetosphere (for x > 1 R E ) and in the dayside magnetosheath, which are the main objects in the study. Checking that our predictions do not depend on any particular numerical code, we have made runs with the same or similar boundary conditions using two other global MHD codes, the Open Geospace General Circulation Model (OpenGGCM) [Raeder et al., 21], and the Lyon-Fedder-Mobarry global code (LFM) [Lyon et al., 24; Merkin and Lyon, 21] and get similar results. [8] The global models contain no plasmasphere: the average magnetospheric density on the Sun-Earth line is about.1,.2, and 2 cm 3 in the LFM, OpenGGCM, and BATS-R-US models, respectively. The low magnetospheric densities in the LFM and OpenGGCM codes result in high Alfvén speed, which exceeds 1 4 km/s for x < 7 R E in the subsolar region, therefore, the codes use the Boris correction [Gombosi et al., 23]. At the inner boundary near 3 R E, the magnetospheric MHD codes couple the ionospheric models. Field-aligned currents are calculated and mapped along dipole field lines to the ionosphere where they are used as the source term for the height-integrated potential equation. The calculated potential is then mapped back out to the MHD inner boundary where it is used to determine boundary conditions for the tangential velocity. Since no mass flux flows through the inner boundary, the radial component of the velocity is equal to zero at this location. [9] An artificial forward fast shock is imposed in the upstream solar wind with the same jump conditions as in our previous paper [see Samsonov et al., 21, Table 1]. In particular, the density varies from to 13.7 cm 3, V x from 4 to 27 km/s, B z from 4.7 to 13.4 nt, and B x is constant and equal to 1.71 nt. We keep constant solar wind conditions corresponding to the parameters before IS for the first 2 h of the simulation, and then, at 2:: UT (here and below the time format is hh:mm:ss), the jumps through the shock are imposed. The duration of the shock at the solar wind boundary is only 1 s. Such a strong shock with sharp changes through the front results in a clearly visible magnetospheric response. 36

3 2:4: UT 2:: UT ::3 UT 2:6: UT :6:3 UT 2:7: UT :7:3 UT 2:8: UT Figure 1. Results of BATS-R-US global simulation in equatorial plane in different times (the time format hh:mm:ss). Colors and arrows show the magnitude and direction of flow velocity. Area where the velocity exceeds the upper limit of the color bar 3 km/s is painted pink. Thick white line marks the magnetopause position. 3. Flow Vortices in Equatorial Plane [1] To begin, we show the evolution of plasma flow in the magnetosphere after the propagation of the sudden impulse obtained in numerical simulations using the BATS-R-US model. In Figure 1, the magnitude and direction of the velocity in the equatorial plane are presented. We restrict our attention to a dawnside magnetospheric region with x varying from 1 to +12 R E and y from 12 to R E. Since there is neither a V y or B y in the solar wind nor any dipole tilt, the flow is symmetric with respect to the noon-midnight plane. [11] The magnetopause position is shown by a thick gray curve. The IS moves from the solar wind boundary (at x =33R E ) to the subsolar magnetopause during about 4 min. In the top left panel in Figure 1, at 2:4: UT, the shock front is in the magnetosheath, but has not yet reached the subsolar magnetopause. The shock front is at x =1R E for y = 12 R E, but comes only to x =11R E for y =. The concave shape of the IS front in the magnetosheath was previously obtained in simulations and observations [Koval et al., 2, 26; Samsonov et al., 26] and explained by a smaller flow velocity in the dayside magnetosheath than in the supersonic solar wind. In the undisturbed magnetosheath (before the IS arrival), the velocity increases from the subsolar region toward the flanks. The velocity in the dayside magnetosphere at 2:4: UT does not exceed several kilometers per second. [12] When the shock front touches the magnetopause, the magnetopause starts moving inward and this results in compressional wave (or more precisely in a weak fast shock with the Mach number close to unity) propagation into the magnetosphere. At 2:: UT, the compressional wave reaches x =R E in the subsolar magnetosphere. In contrast to the propagation in the magnetosheath, the compressional front in the magnetosphere is convex, because the fast mode velocity in the magnetosphere is higher than that in the magnetosheath. According to the numerical prediction, the plasma moves earthward with velocity of about 1 km/s near the noon geosynchronous point downstream of the front, which corresponds to the dawnward electric field of about 1 mv/m. 37

4 SAMSONOV AND SIBECK: FLOW VORTICES FOLLOWING A SUDDEN IMPULSE 2:9: UT 2:1: UT :11: UT 3 2:12: UT Figure 2. Next set of times after those in Figure 1. [13] The curvature of the compressional front changes further in next 3 s (at 2::3 UT). The velocity slightly decreases in the inner magnetosphere near the Sun-Earth line; however, the front moves forward through the flank. At 2:6: UT, velocities decrease in the subsolar magnetosphere, but the front continues moving through the flank and passes the terminator plane x =. The deceleration of the flow along the Sun-Earth line was thoroughly studied using the global MHD simulation by Samsonov et al. [27], and it was explained in terms of shock reflection from the inner numerical boundary. [14] Another interesting, although weak, feature which begins to be observed at 2:6: UT is an eastward flow stream at radial distance near RE. The strength of this stream grows, so that it becomes clearly visible later, at 2:6:3 and 2:7: UT. At the same time, plasma moves westward at distances farther from the Earth, thereby forming a flow vortex. Zooming in on this vortex, we find that it begins with a tiny eastward stream at 2::3 UT in the inner magnetosphere at 1 2 RE from the Sun-Earth line. We discuss the physical reasons for the vortex generation in the next section. [1] Although the vortex forms in the inner subsolar region, it then extends tailward and its center approaches the magnetopause. At the same time, the compressional front moves through the nightside magnetosphere forming a circle of high-speed stream around the Earth. Throughout most of the magnetosphere, the velocity varies from several to 1 km/s, the region with a higher velocity appears close to the magnetopause and convects from the late morning to early morning sector (a similar region forms in the evening magnetosphere symmetrically with respect to the noon-midnight plane). The simulated electric field exceeds 1 mv/m both in the flank high-speed region (where V > 1 km/s) and in the eastward stream in the vortex. In the last panel of Figure 1, the center of the vortex is near (x,y) = (, 8) RE, but the eastward flow still exists in the dayside magnetosphere making another vortex near the dayside magnetopause. [16] Figure 2 shows numerical results for the same run at four subsequent times. The high-speed region continues growing and moving tailward through the nightside magnetosphere. The maximal velocity in the center of the region near ( 7, 9) RE at 2:9: UT exceeds 3 km/s. Since the flow is symmetric with respect to the noon-midnight plane, two streams flowing westward (eastward) from the morning (evening) side meet each other at the midnight plane. At 2:11: (2:12:) UT, a stagnation point appears on the Sun-Earth line at x = 13 (x = 16) RE from which two opposite streams accelerate in the antisunward and sunward directions. The high-speed region is followed by vortices. The center of the main vortex in the nightside magnetosphere moves from x = 3 RE at 2:9: UT to x = 8 RE at 2:12: UT, while the vortex gradually extends toward the Sun-Earth line, and a smaller vortex detaches from it closer to the magnetopause between x = 6 and 1 RE and y = 1 RE in the last two times. As mentioned above, the eastward stream inside the magnetopause and the westward stream outside the magnetopause form a third vortex. This last vortex stretches along the magnetopause and also moves tailward. Finally, the flow in the magnetotail becomes turbulent and new vortices form later (not shown). [17] We have considered in detail the case for a northward IMF when background magnetospheric convection is almost absent, but we have also determined that similar magnetospheric vortices appear for other IMF orientations. For illustration, we show numerical results of another run of the BATS-R-US model in which all solar wind parameters remain the same, except that the sign of Bz is negative before and after the IS. The velocity magnitude and direction in the equatorial plane in this run are shown in Figure 3. Before the beginning of the magnetospheric compression, at 2:4: UT, there was already a strong eastward flow in the outer magnetosphere as part of the magnetospheric convection. However, the picture changes significantly after the IS impact. Two streams, eastward- and westward-directed, impinge upon each other at 2:: and 2:6: UT; and finally, at 2:7: UT, a new vortex extends along the magnetopause from x = RE to the subsolar point. As in the northward IMF case, the vortex is formed by an eastward stream inside the magnetopause and a westward stream outside the magnetopause. The velocity disturbance gradually propagates tailward and finally may change the magnetic reconnection rate in the magnetotail. 38

5 2:4: UT 2:: UT :6: UT 2:7: UT Figure 3. Simulated velocity in equatorial plane for a run with southward IMF. [18] We have investigated variations of the magnetopause position in time in the northward IMF run. In Figure 4, the magnetopause position is shown every minute from 2:4: UT (black line) to 2:1: UT (red). The magnetopause compression begins in the subsolar region and then extends toward the magnetotail. Since the compressional wave moves faster through the magnetosphere than in the magnetosheath, Nishida [1978] suggested that magnetopause compressions are preceded by transient magnetopause expansions. However, this effect is very weak or absent in the MHD simulation. Another effect seen in the global MHD simulation by Samsonov et al. [27] is an outward magnetopause motion in the dayside region following the initial compression. The magnetopause near the Sun-Earth line is slightly closer to the Earth at 2:8: (green line) than at 2:1: UT (red). However, the outward magnetopause motion may continue, and the total sunward displacement after compression exceeds. R E as shown in Figure of Samsonov et al. [27]. According to Samsonov et al. [27], the outward magnetopause motion is related to the reflection of the compressional wave at the inner numerical boundary. 4. Mechanism of Vortex Generation [19] Although similar vortices in the equatorial plane have been obtained in previous simulations, the mechanism of the vortex generation has not yet been established. In the isotropic MHD approach, the equation of motion contains two forces: the Ampere force J B and the thermal pressure gradient. We determine which of the forces is responsible for the vortex generation using the same numerical results in the northward IMF case. We have found that in the dayside magnetosphere (in the area where the vortices initially appear), the magnitude of the Ampere force is at least one order greater than the magnitude of the pressure gradient. The plasma beta in this region is less than unity and decreases rapidly from the magnetopause toward the Earth. [2] Figure compares the Ampere force (left column) and the velocity (right column) at four times separated by only 1 s, during the interval from 2:: to 2::4 UT when the compressional wave moves through the dayside magnetosphere, contacts the inner numerical boundary, and reflects from that boundary. At 2:: UT, the compressional front is clearly observed in the dayside magnetosphere at x =~R E as a maximum of the Ampere force coinciding with an increase of the westward electric current at the front. There is a strong gradient of the flow velocity across the front. The Ampere force accelerates plasma antisunward at the compressional front. At 2::1 UT, the picture is significantly different. The compressional front interacts with the dayside inner boundary (at r =~3R E ). The Ampere force at the inner boundary (x =2, y = 2 R E ) is directed toward the subsolar line, while along the subsolar line in the inner magnetosphere (x =3 4 R E ), it is directed toward the Sun. These Ampere forces create the vortex shown in the previous section. The direction of the Ampere force at the compressional front in the inner magnetosphere also changes. In the area around (x =4,y 4) R E, it is directed earthward along the compressional front, rather than tailward perpendicular to the front as in the remaining part. This feature is probably related to the same disturbance at the dayside inner boundary, which results in the vortex formation. At 2::3 UT, two Figure 4. Magnetopause positions fixed every minute from 2:4: UT to 2:1: UT in equatorial plane in the northward IMF case. 39

6 Figure. The Ampere force J B (left column) and the velocity (right column) in equatorial plane in the northward IMF case. separated regions with a large Ampere force occur. One region coincides with the compressional front in the outer magnetosphere, while the other remains in the subsolar magnetosphere where the Ampere force is directed partly toward the subsolar line, partly sunward, and partly away from the subsolar line. Such complicated variations of the Ampere force direction continue the formation of the vortex. At 2::4 UT, the picture looks similar, but the compressional front moves further tailward and the vortex generation area in the dayside magnetosphere shifts outward and extends toward the flank. We can conclude from these results that the inner boundary is an essential element which is necessary for the vortex generation. [21] The subsequent evolution of the (J B) disturbance regions from 2:6: to 2:9: UT is shown in Figure 6. The figure includes both the morning and evening flanks to demonstrate that the solution is symmetric. The x interval is extended to cover from 2 to +12 R E, including both the near magnetotail on the nightside and the magnetopause, magnetosheath, and bow shock on the dayside. At the dayside magnetopause and bow shock, the Ampere force is always directed sunward and decelerates the solar wind plasma. At 2:6: UT, the Ampere force region in the subsolar magnetosphere (x ~6R E ) coincides with the reflected wave discussed in the next section. The Ampere force at the reflected wave is also directed sunward. From 2:7: to 2:9: UT, (J B) 36

7 1 1 2:6: UT 1 2:7: UT JxB[fN/m 3 ] JxB[fN/m 3 ] :8: UT 1 2:9: UT JxB[fN/m 3 ] JxB[fN/m 3 ] Figure 6. The Ampere force J B for the next set of times. regions move through the magnetosheath following at first the motion of the sunward propagating reflected wave and then another earthward propagating discontinuity resulted from the interaction between the reflected wave and bow shock (see explanation in the next section). [22] Two symmetrical (morning and evening) (J B) regions in the magnetosphere, which we identify as the generators of the flow vortices, move tailward through the magnetospheric flanks similar to the motion of vortices in Figures 1 and 2. Although the size of these regions grows, the magnitude of (J B) within them decreases with time. As noted in the previous section, beginning from 2:9: UT, two high-speed streams from the morning and evening sides meet each other near the midnight plane. However, the numerical simulation does not predict any significant increase of the Ampere force or pressure gradient in the region of the collision. The magnitude of (J B) in the magnetospheric disturbance region continues decreasing after 2:9: UT (not shown).. Secondary Waves and Discontinuities in Magnetosheath [23] As noted above, the interaction of the compressional wave with the inner boundary results in both vortex generation in the magnetosphere and the appearance of a reflected fast wave moving sunward. The simulations generate both reflected waves and vortices for all IMF orientations. Samsonov et al. [27] discussed the reflected compressional wave (or a weak fast shock) in the dayside magnetosphere. Here we discuss the signatures of this wave in the magnetosheath. Figure 7 shows time variations of four parameters along the Sun-Earth line. In the quasi-stationary solution at 2:: UT, the magnetopause and bow shock are at x =~11 and ~14R E, respectively. The magnetopause and bow shock positions and the motion of waves and discontinuities in the magnetosheath and magnetosphere can be traced using the electric current density J. In agreement with previous results, the bow shock and magnetopause move earthward after the interaction with the interplanetary shock at ~2:3: and 2:4: UT. The compressional fast wave clearly observed in the B 1 panel propagates earthward through the magnetosphere, encountering the inner boundary at x =~3R E at nearly 2::1 UT. We trace the motion of the initial compressional wave in the magnetosphere and reflected waves in the magnetosphere and magnetosheath using red lines. Beginning from 2::1 UT, the reflected fast wave propagates sunward through the magnetosphere and magnetosheath, interacts with the magnetopause and bow shock, and changes the velocities of their motion. According to Samsonov et al. [27] (see Figure ), these interactions result in secondary waves moving earthward. The secondary wave in the magnetosphere interacts again with the inner boundary, reflects back and goes to the magnetopause. The final magnetopause position is determined by the interaction with the secondary waves. [24] The reflected fast wave propagates sunward through the magnetosheath approximately between 2:6: and 2:7: UT. As shown in Figure 7, the reflected wave enhances the magnetic field magnitude, density, and temperature. The interaction of this wave with the bow shock launches another wave propagating earthward through the magnetosheath. The magnetic field and density decrease through this wave, but the temperature increases. A very similar discontinuity which moves earthward through the magnetosheath has been observed in Cluster data by Pallocchia et al. [21] and Pallocchia [212] and simulated using the local 3-D magnetosheath model [Pallocchia et al., 21]. According to the observations, this discontinuity propagates with the local flow velocity, similar to a tangential discontinuity. 361

8 Figure 7. Temporal variations of the electric current density, the magnetic field magnitude (B 1 is the difference between the total magnetic field and the Earth s dipole field), the density, and the temperature at the Sun-Earth line. [2] Figure 8 shows the perturbations associated with the same waves/discontinuities in the magnetosheath as time variations at a fixed point x =9.R E on the Sun-Earth line. At the beginning of the 8 min interval, the artificial spacecraft is in the magnetosphere where it observes the compressional wave (or shock) arrival at 2:4:1 UT. Less than 1 min later, the model predicts an outward magnetopause crossing (first vertical line) after which the following changes are observed in the magnetosheath. The second vertical line (~2:: UT) corresponds to the compound discontinuity which appears as a result of the interaction between the interplanetary shock and bow shock [Samsonov et al., 26; Šafránková et al., 27; Zhang et al., 212]. This discontinuity is characterized by an increase in density, a small increase of the magnetic field magnitude, and a decrease of temperature. It propagates nearly with the flow velocity. Note that the total pressure (the sum of magnetic and thermal pressures) does not change through the magnetopause or through the compound discontinuity. [26] The next vertical line (~2:6:4 UT) marks the arrival of the reflected compressional wave. As noted above, the density, temperature, and magnetic field magnitude (and accordingly the total pressure) increase through the compressional wave. As opposed to other discontinuities, this discontinuity propagates outward and reaches the bow shock. Its interaction with the bow shock results in another discontinuity (last vertical line), which is observed 1 min after the reflected wave. [27] We have made 1-D test MHD runs to simulate the interaction of two fast shocks moving in the same direction using initial parameters similar to those obtained in the global MHD simulation for this case. We find that the bow shock moves outward after this interaction and two discontinuities propagate through the magnetosheath. The first is either a very weak fast rarefaction wave or a weak fast shock, and the second is either a tangential discontinuity or a compound discontinuity with a decrease of the density and magnetic field and an increase of the temperature. The last discontinuity propagates with the local flow velocity and the total pressure does not change through its front. The compound discontinuity consists of a slow shock, contact discontinuity, and reversed slow rarefaction wave. Thus, the 1-D results predict the similar variations as obtained in the global simulations, but allow us to identify the nature of the discontinuities. Figure 8. Temporal variations of the density, total pressure, temperature, and field magnitude at point (9. R E,,). Dashed vertical lines at t = 2::, 2::, 2:6:4, and 2:7:4 UT mark magnetopause crossing and three discontinuities in the magnetosheath (see explanation in text). 362

9 6. Discussion and Conclusions [28] We use the results of global MHD simulations to explore processes in the magnetosphere following the impact of an interplanetary shock. Both the antisunward motion of flow vortices through the magnetospheric flanks in the equatorial plane and the shock reflection in the subsolar inner magnetosphere have been seen previously in MHD simulations [e.g., Slinker et al., 1999; Samsonov et al., 27]. Now, we show that both phenomena are two parts of the same process, which includes an interaction of the compressional wave (magnetospheric sudden impulse) with the inner boundary of the numerical model. When the compressional front reaches the dayside inner boundary, an Ampere force directed toward the subsolar line and sunward appears near the boundary. Since the Alfvén velocity is very high in the inner magnetosphere, the process is very fast. In 1 min, two vortices form in the dayside magnetosphere in the equatorial plane symmetrically with respect to the Sun-Earth line at the same time as the compressional front passes through the magnetospheric flanks. In the next several minutes, the vortices expand and move outward and tailward. Then they split into several parts and the flow becomes turbulent. The vortices in the equatorial plane are related to field-aligned currents with orientations similar to those of the Region 1 currents (downward in prenoon hours and upward in postnoon), which are responsible for the main impulse in SI variations [Samsonov et al., 21]. [29] Thus, effects at the inner boundary play a major role in generating the flow vortices and field-aligned currents. However, there is no physical boundary in the magnetosphere at a radial distance of 3 R E. Nevertheless, similar vortices have been observed in the equatorial plane at dayside geosynchronous orbit [Baumjohann et al., 1984], on the magnetospheric flanks [Samsonov et al., 211], and in the nightside plasma sheet [Shi et al., 213]. Besides, there are multiple observations of antisunward-moving convection vortices in the ionosphere caused by solar wind dynamic pressure variations [e.g., Friis- Christensen et al., 1988; Sibeck, 199]. Samsonov et al. [211] compare results of global MHD simulations with Polar observations and show that the first period of oscillations is successfully predicted by the model. [3] As noted by Samsonov et al. [27], two physical boundaries can reflect compressional waves and correspondingly can result in vortex generation. These boundaries are the plasmapause and ionosphere. Certainly, the plasmapause partly reflects the compressional wave, and the outer magnetosphere is the most probable region where the vortices can be observed. However, numerical estimations [Samsonov et al., 27] show that at least part of the wave energy can enter into the plasmasphere. Following many previous authors [Nishida, 1978], we believe that the compressional wave can reach the ionosphere, modify the ionospheric currents, and cause sudden impulse variations at the Earth s surface. However, without careful data analysis, we cannot speculate about generation of similar vortices in the plasmasphere. [31] In this paper, we also show changes of the magnetopause position during transient processes and enumerate waves and discontinuities predicted by the numerical MHD model in the magnetosheath. The magnetopause shifts earthward following the motion of the IS front, but the model does not predict magnetospheric expansion before the compression, as previously suggested by Nishida [1978]. The model predicts a slight magnetospheric expansion in the subsolar region after the compression, which results from the interaction of a reflected compressional wave with the magnetopause. In the magnetosheath near the Sun-Earth line several waves and discontinuities follow the IS. The first of these is the compound discontinuity (i.e., the combination of forward slow expansion wave, contact discontinuity, and reversed slow shock) discussed by Samsonov et al. [26]. The second is the reflected compressional wave moving sunward. The third is a discontinuity moving earthward, which results from the interaction between the reflected wave and bow shock. Using results of 1-D MHD simulations, we obtain that the interaction of two fast shocks moving sunward (i.e., the bow shock and reflected fast shock) launches a weak rarefaction wave (or weak fast shock) and tangential or compound discontinuity (or compound discontinuity) propagating earthward through the magnetosheath. The observed changes of parameters are determined mainly variations through the tangential or compound discontinuity. This numerical prediction is confirmed by recent observations [Pallocchia et al., 21; Pallocchia, 212]. [32] Finally, we note that the vortex generation in the magnetosphere is a general magnetospheric response to any solar wind dynamic pressure variation, which does not depend on the IMF orientation. Observations in previous papers agree with the model predictions, but we need to continue the data analysis in order to understand the role of magnetospheric boundaries (in particular, the plasmapause) in generating the magnetospheric response to solar wind shocks and tangential discontinuities. [33] Acknowledgments. This work was partly supported by NASA s Guest Investigator program. Simulation results have been provided by the Community Coordinated Modeling Center ( at Goddard Space Flight Center. 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