Patchy r econnection and evolution of multiple plasmoids in the Earth's magnetotail-

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. All, PAGES 25,011-25,020, NOVEMBER 1, 1999 Patchy r econnection and evolution of multiple plasmoids in the Earth's magnetotail- Effects on near-earth current system L. Rast//tter and M. Hesse NASA Goddard Space Flight Center, Greenbelt, Maryland Abstract. Reconnection during substorms in the near-earth magnetotail occurs in a complicated way. Local instabilities can trigger anomalous resistivity in several spatial regions, which may initially be well separated from each other. As time progresses, the resulting plasmoids grow larger until they reach the dimension of the entire system and start o interact with each other. Satellite observations show that this expansion occurs rapidly during the downtail travel after plasmoid development when -10 R > X SM > --30 R [leda et al., 1998]. In this paper we study the interaction of two and three plasmoids and their coalescence, as well as the current system seer,. near the Earth brought about by the reconnection regions. In the numerical experiments, resistivity is prescribed at localized patches which ara placed at different downtail locations. We compare the magnitude of the influence the reconnectiou sites have on the near-earth current system. We find that not only the relative position of the resistivity patches but also the absolute distance front the Earth play roles in the relative amplitude of the field-aligned currents associated with the ind' vidual reconnection events. 1. Introduction to magnetosphere-ionosphere coupling models as proposed by Kan [1993]. Large-scale plasmoids [see, e.g., Plasmoid formation occurs during substorms in the Slavin et al., 1998, and references therein] develop on magnetotail owing to current sheet thinning in the the tailward side of a reconnection region typically loplasma sheet and subsequent resistive instability. Satelcated between -20 and -30 RE downtail [Ieda et al., lite observations of current sheet thinning [Mitchell et 1998]. The plasmoids expand into the tail cross secal., 1990; Sergeev et al. 1993; Sanny et al., 1994; Pulkkition as they travel downtail, thus erasing any signs of nen and Nishida, 1994] are well explained by means small-scale initiation seen by the presence of bursty bulk of analytic studies [Hahm and Kulsrud, 1985; Wiegelflows in the inner magnetosphere [Slavin et al., 1997, mann and Schindler, 1995] and MHD and hybrid simu- 1998]. The links between the small-scale bursty bulk lations [Hesse et al., 1996; Hesse et al., 1997; Birn, et flows and the development of the plasmoids still remain al., 1998a], and, finally, in kinetic simulations [Pritchunclear, especially how initially small-scale structures ett and Coroniti, 1994; Pritchett and Coroniti, 1995]. in the near-earth magnetotail evolve into large-scale Recent Hall-MHD simulations [RastStter et al., 1999] structures in a relatively short time. found a good correspondence of Hall-MHD results with MHD and hybrid/particle simulations in the global pic- The effects of reconnection in the near-earth magneture of thin-current-sheet formation. totail on the magnetospheri current system were stud- Observations show that reconnection events occur in ied by Birn and Hesse [1996] for a single reconnection site. Birn and Hesse found that the maximum cross-tail the near-earth magnetotail mainly in the range of-20 RE to --30 RE in XCSM which result in highly localelectric field Ey is found earthward of the reconnection ized bursty bulk flows [Angelopoulos et al., 1992, 1996]. region as a consequence of earthward flow originating These flows carry reconnected magnetic flux toward the at the reconnection site being braked by the increasing Earth in narrow flow channels. Observations closer to magnetic pressure toward Earth and and thus facilitat- the Earth (near geosynchronous orbit) show coherent larger-scale dipolarization as flux is added to the nightside inner magnetosphere by earthward flows leading Copyright 1999 by the American Geophysical Union. Paper number 1999JA /99 / 1999JA $ ,011 ing the dipolarization of the magnetic field Bz. The convection electric field accelerates particles in geosynchronous orbit which then travel along magnetic field lines toward the Earth's polar ionosphere [Birn and Hesse, 1996; Birn, et al., 1998b]. The magnetic disturbances also generate the typical field-aligned cur- rent system (current wedge) signature in the near-earth magnetosphere.

2 25,012 RAST TTER AND HESSE' MULTIPLASMOID EVOLUTION IN THE MAGNET(3TAIL The effects of multiple reconnection sites have been studied for the dayside magnetopause by Otto [1995], and a recent simulation study addresses field-aligned current features emerging from a single magnetopause reconnection region [Ma and Lee, 1999]. A systematic study of simultaneous multiple reconnection in the near- Earth magnetotail has not been done although recent global MHD simulations of the Earth's magnetosphere show multiple reconnection events in the near tail during active times [see, e.g., Pulkkinen et al., 1998]. In this work we extend the study of Birn and Hesse [1996] to the occurrence of multiple reconnection sites in the near-earth magnetotail. We start from a presubstorm configuration with a thin current sheet and place resistivity patches in different positions into the current sheet region in three-dimensional MHD. We follow the development of the system of field-aligned currents near the Earth and analyze current amplitudes and distributions for different reconnection site locations in the tail. The paper is organized as follows: After a brief explanation of the model in section 2 we present a oneplasmoid simulation in section 3.1 to explain the current wedge signature. A three-plasmoid run in section 3.2 shows the effects of a typical plasmoid interaction. Section 3.3 is devoted to a controlled numerical experiment with varied locations of the resistivity patches triggering reconnection. The behaviors of the current system found in the series of simulations are analyzed and discussed. 2. Resistive MHD Model 2.1. MHD Equations We use resistive magnetohydrodynamics (MHD) in a three-dimensional Cartesian grid. Assuming the typical lobe magnetic field to be, say, B0 40 nt and the plasma to be a fully ionized proton plasma with particle density no cm -3 and mass density P kg/m 3 the velocity is normalized to the Alfv n velocity VA - Bo/v/lUopo km/s (with / 0 = Vs/Am). We normalize the pressure to Po - Bo2/l o -' 1.3 npa. The polytropic index for the isotropic pressure is chosen as? - 5/3 for absence of heat flux. With a length scale of L = 1RE 6000 km the current density normalization is Jo - Bo/l ol " 50 na/m 2. Finally, the time t is measured in Alfv n time units -A- L/V 4 6 s. The dimensionless MHD equations are given by op/ot = -V.(pV) pov/ t - -p (V. V) V - VP + J x B (2) OP/Ot = -V. (PV) - (7-1)P(V.V) (3) OB/Ot = -Vx[-VxB+r/J] (4) J = V xb. (5) with the resistivity 1 in equation (4) described in section 2.3. The coordinates x,y, and z correspond to XGSM, YGSM, and ZGSM and run from-5 to-80 along the tail in x, -10 to 10 in y, and 0 to 10 in z. The MHD equations are integrated by means of the leapfrog method, a finite difference method of second order accuracy in space and time [Potter, 1973; Birn, 1980]. Hall effects as well as electron pressure effects are neglected in this fundamental large-scale study. On the semiglobal scale considered, the effects of these terms remain small enough to conserve the qualitative features of plasmoid evolutior_ found in this study [RastStter et al., 1999]. The system is assumed to be symmetric, so only the upper half of the tail (z > 0) needs to be computed. The simulations are carried out on a nonequidistant grid with grid size of (NX, NY, NZ) = (107, 73,53) for the spatial region-5 > x > -80, -10 < y < 10 (run with three reconnection sites: -20 < y < 20 with NY = 113), and 0 < z < 10. The finest grid resolution is Ax = 0.2 at x = -18, Ay = 0.2 for -2.4 < y < 2.4, and Az = 0.1 at z = 0. The boundaries are closed to inflows and outflows at all boundaries, and tangential flows along all boundaries are permitted except for x0 = -5 where all components are zero and x = -80 where outflow is permitted. The rigid boundary condition (V = 0) at x = -5 can be justified by the assumption that magnetic fields in the inner magnetosphere are strong enough to prevent large-scale flows and that the conductivity of the ionosphere is large. The difference between an ideally conducting ionosphere and a ionosphere with finite resistivity was found to be negligible in previous magnetotail simulations [Birn and Hesse, 1996]. The magnetic field parallel components have zero normal derivative (O/On = 0) at all boundaries and V-B = 0 determines the respective normal component. At z = 0, mirror symmetry is assumed (Bx is antisymmetric and By and B are symmetric). The explicit time integration scheme requires that information may only be carried to an adjacent grid point in a ti ne step At, thus limiting At to A/Vrn x, with Vm x being the fastest phase velocity found in the MHD system and A being the smallest grid space in any direction [see, e.g., Potter, 1973]. We chose a time step of 2, determined by the fast-mode velocity VF ---- V/(fP + B2)/p for the chosen grid resolution Initial setup As initial condition we use the result of a two-dimensional MHD compression as described by RastStter et al., [1999]. The magnetic and current structure is invariant in the y direction and models a presubstorm configuration containing a thin current sheet within the wider plasma sheet. The thin current sheet results from the compression of the tail lobes during the presubstorm phase and is computed from an initial tail equilibrium model by applying plasma inflows at the near-earth boundary (x = -5) and the tail lobe boundary (z - 10) [Birn, et al., 1998a]. Although monotonically decreas-

3 RAST*TTER AND HESSE: M(]'LTIPLASMOID EVOLUTION IN THE MAGNETOTAIL 25, ,50-60 X Figure 1. Initial magnetic field and current. The magnetic field structure and the cross-tail current density ds contain a thin current sheet and are two dimensional (y independent). ing along the length of the tail, the compression generates a localized current enhancement in the middle of the tail on the x axis. Figure i shows the magnetic field lines and the associated cross-tail current. The current has its maximum between -13 and -22 in x in a thin sheet within the plasma sheet current. The near-earth magnetosphere contains a dipole-like field structure Resistivity Model To initiate reconnection, patches of localized resistivity are introduced in the plasma sheet in different locations xp,yp, zp. The patches are characterized by their resistivity amplitude /p and the patch radius r. The value /p is variable but is 1 for most runs. In all cases, zp - 0 is fixed as well as r The localized resistivity has the form ]patch- ]pcosh-2 (a: a:p) cosh-2 ( / /P) (6) x 1 [1- tanh (t- t to )]. The patches are added to a background of r/0-01 and exist for a time interval 0 _< to _< to - 15 and decay afterward on a timescale At The resistivity amplitudes of the patches are rm - (1, 05, 15) for the three-plasmoid run for x - (-20,-17,-23), all +18 Figure 2. Single plasmoid run (xp - -15, yp - 0). The magnetic field Bz is shown at z = 0 and t = 20. The reconnected flux Bz < 0, enclosed by the line Bz = 0, is clearly seen as well as a region of enhanced Bz earthward of the reconnection site. "'" 0 ' -18 respectively. The two-plasmoid runs in section 3.3 have xp : (i2+i, 15+i) with varying i (0,2,4,6,8), y = --(2.5, 2.5), and constant /p = (1, 1). The localized resistivity chosen in our model reproduces the observed timescales of reconnection and plasmoid formation (several minutes). As long as the reconnection electric field is represented correctly the global dynamics of the tail substorm and plasmoid formation are modeled in a realistic way [Birn, 1980; Birn and Hesse, 1996]. The large amplitude of the resistivity offsets the lack of spatial resolution and proper representation of the microphysics associated with small scales found in the magnetotail current sheet during substorm onset [Birn, et al., 1998a]. Recent particle-incell (PIC) simulations (Hesse et al., 1999, Collisionless Magnetic Reconnection: Electron Processes and Transport Modeling, submitted to Journal of Geophysical Research) of reconnection in very thin magnetotail current sheets yield an even lower effective Lundquist number of S = 10 compared to S = 100 used here ß --. ::{;. -?:: i{{ i-::--'. -'.:- ::{::: :"-'.'"'J:-.-"'::::{ - i. -!A;'.-": :-:.-i ';".... :.:... -lo -20 ii :::'e... '::1:i '... '.; '"""'"-'-"-': : !i:::::.& i -. ß ::'....:' x Figure 3. Cross-tail current at t - 20 and 40. The initially smooth current distribution becomes highly variable with concentrations at, or near the reconnection site which travel downtail with the plasmoid. dy o.'::': Uy -50 o.' '"'

4 25,014 RAST i. TTER AND HESSE: MIILTIPLASMOID EVOLUTION IN THE MAGNETOTAIL 3. Results 3.1. One Plasmoid as a Reference To show the effects of a single reconnection site and the associated plasma flows and changes of the magnetic geometry on the near-earth current system, we present a run with a single resistivity patch, located at xp - -15, yp - 0 with - 1. The earthward part of the plasmoid associated with the reconnection site is characterized by the reconnected magnetic flux (region with Bz < 0) shown in Figure 2. For time t - 20 in Figure 2 this region of negative Bz is surrounded by the line B - 0 which consists of the reconnection X line on the earthward side and the O line in the tail side. The O line is in the center for the plasmoid traveling tailward. Additionally, a region of enhanced B is found earthward of the reconnection site generated by strong earthward flows from the reconnection. Figure 3, in the upper diagram, shows the distribution of the cross-tail current density Jy at the same time 5 +O. lo6 (t - 20) in the plane z - 0. The plasmoid which initially formed around x travels downtail (lower 10 "' : --' diagram: t- 40) and takes with it the intensification x of the current density that is associated with the recon- Figure 5. Magnetic field B at z - 0 and t - 20, 40, nection process. Figure 4 shows a cross section through and 60. (top) In the early stage of plasmoid formation the current wedge at x - -5 (earthward boundary of (t = 20), the individual plasmoids are well separated the simulation). The current wedge is formed by field- from each other. The reconnected fluxes ß (enclosed by aligned currents JIi - (J' b)b (with b - B/B being the lines denoting Bz - 0) are -0.25,-0.17 and -0.22, the unit vector in the direction of B) and shows the respectively. (middle and bottom) Later the plasmoids characteristic region i and region 2 current structures merge during the downtail travel (t - 40 and 60, respectively). A complex current system is associated with [McPherron, 1979; Scholer and Otto, 1991] in each of this configuration which should show on the near-earth the quadra.nts (symmetric above and below z - 0 and signature of JII (Figure 7). 'with opposite sign for the regions y < 0 and y > 0) Three P asmoids The three-plasmoid run demonstrates a typical case of multiple patchy reconnection in the near-earth magnetotail. The patches of resistivity x - (-20, -17, -23) and y = (-5, 0, +5) have the respective amplitudes of r/p = (1, 05, 15). The three diagrams of Figure 5 show the magnetic field component B in the z = 0 plane for t = 20, 40, and 60. The relative strength of the reconnec- 0 - i t) q ii ½ J:½'.'--; ' - "'"... tion rates in the three reconnection regions can be determined by the reconnected flux of the plasmoids - f <0 BzdXdy - (-0.25,-0.17,-0.22), which is enclosed by the line Bz - 0 for each plasmoid (t - 20, upper diagram). The middle and bottom diagrams show Bz at later times (t - 40 and 60). The plasmoids have grown, and two of them have merged with each o -15 -lo ¾ Figure 4. Cross-tail cut at x - -5 through the current wedge for t = 40. The characteristic two-layer structures can be seen in each quadrant. The field-aligned current system is symmetric with respect to z - 0 and antisymmetric with respect to y = J>, 7.6 Figure 6. Current density J in the plane z - 0 at t The current sheet has been disrupted, but the distinct current intensifications that formed at the indi- vidual X lines can still be seen in the cross-tail current Jy at this time.

5 .... RAST TTER AND HESSE: MULTIPLASMOID EVOLUTION IN THE MAGNETOTAIL 25, all +045.:,:.w--:. :: all all +33 other to form a large structure that is moving downtail. Note that the enhancement region of B earthward of the reconnection site of the central reconnection site (yp - 0) approaches the boundary x = -5, while the others stay well away from that boundary. The cross-tail current density in Figure 6 shows the cross-tail current density Jy in the plasma sheet for t = 60. The thin current sheet is initially located in the region -13 > x > -20, and current enhancement structures associated with the individual reconnection regions are clearly visible. At t - 60 the strongest current intensification is found in the central region (at x 0-22, y = 0). -52 Figure 7 shows the field-aligned current JII in the plane x - -5 for this case. Although the prescribed resistivity in the resistivity patch nearest to the left boundary (at xp - -17, yp - 0) is the weakest and the reconnected flux is the lowest of all plasmoids, the fieldaligned currents strongly resembles the pattern found for a single reconnection site (Figure 4, z > 0). The current systems of the other reconnection sites are also present; however, they fade compared to the central current system during the time evolution (Figure 7). The current system at x - -5 reflects the effects of the patch of enhanced B near this cross-section plane associated with the plasmoid closesto this plane (Figure 5). This result is surprising because the reconnection in each of the other reconnection sites at yp - -5 and 5 is much stronger than in the central reconnection site at yp = 0 (Figure 5, upper diagram for t = 20). The two plasmoids at the tail flanks were expected to inhibit the growth of the plasmoid in the center and thus should contribute more to the near-earth current system. It is seen from the lower diagram of Figure 5 (t = 60) that the plasma flows associated with the central plasmoid sweep both the regions of enhanced B and the regions Figure 7. Field-aligned current JII at x and times t = 20, 40, and 60. Though the magnetic field B and the current in the plane z - 0 show many fine structures (Figures 5 and' 6), the signature of the field- of reconnected flux (B < 0) of the other plasmoids aligned current looks largely similar to the signature into the tailward direction. This effectively suppresses associated with a single reconnection region (Figure 4). any impact those plasmoids can have on the near-earth Note that the range of the gray scale in the JII plots current system. grows in time (over tenfold) while the scale for the B plots (e.g., Figure 5) remains fixed. The pattern of plasmoid interaction in this general case is complicated. Thus further study is needed through a more controlled experiment which is carried out in the next section to find what determines the dom- inance of a particular reconnection process in the near- Earth current signature Two Plasmoids in Varied Locations The numerical experiment is performed with two resistive patches at yp - (-2.5,2.5) and fixed resistivity amplitude /t= - 1. The patches are separated in x and are located at xp = (-10,-13) in the first run. Then the patches are moved tailward in steps of Axp in the subsequent runs up to xp = (-20,-23). Thus the patches are placed throughout the region with enhanced current density, and the Table 1. Runs With Two Reconnection Sites. Run x. (t = 0) ß (t = 20) yi==-2.5 yi==2.5 yi==-2.5 yi==2.5 yi==-2.5 y,=2.5 Winner Figures I , I 10, I 12, 13 Quantities listed include current density Jr, reconnected flux (I,, and reconnection site dominating the current system (winner: 0, no dominance; 1, site closer to Earth dominates; 2, site farther downtail dominates). The resistivity patch sites have resistivity amplitude r/, = 1.

6 ... :...: 25,016 RASTJiTTER AND HESSE: MULTIPLASMOID EVOLUTION IN THE MAGNETOTAIL x Figure 8. Time series of Bz at z - 0 (t - 20, 40, and 60) for run I (xp = -10,-13). The reconnected flux (Bz < 0) is enclosed by the solid lines (Bz: 0). As the plasmoids grow the patches of reconnected flux grow and move tailward. Eventually they merge to form a single large structure. Earthward flows create patches of enhanced Bz near the Earth boundary. z the same associated field-aligned currents at the near- Earth boundary (for t - 20 in the upper diagram; the signatures centered at both yp and 2.5 are similar in amplitude). In contrast to most cases, eventually, the plasmoid farther downtail, generated at xp - -13, starts to dominate the whole structure at later times (middle and lower diagrams). For xp and-17 (run 3), Figure 10 shows Bz at z - 0, similar to Figure 8. The time evolution shows that the two reconnection sites generate plasmoids with almost equal reconnected flux. Both developing plasmoids have equal reconnection tates and finally merge into one large structure. The field-aligned currents at x - -5 in Figure 11 show a dominance of the nearer reconnection site (xp - -14, yp ). The current system associated with the reconnection site farther downtail (at xp - -17, centered at y- +2.5) is strongly suppressed. The case of rather distant reconnection (xp and -23, run 6), is shown in Figure 12 by the magnetic field Bz 0. Here the reconnection closer to the Earth is stronger than the process farther downtail, in contrast to the preceding runs. This happens because the current density Jy decreases downtail of x The overall field-aligned currents shown in Figure 13 are much weaker than in the previous cases (Figures 9 and 11). Note that the center of the current system double layers remains at slightly larger z compared to the previous cases (here z _ 1, as opposed to Figure 9), reflecting the field line mapping to the current generation zones which are farther downtail in this case. relative strength of the reconnection process between the reconnection sites changes with the varying current density. Table I summarizes the parameters of the runs and the results obtained. For the two y positions of the resistivity patches (in the second row) in each of the six simulation runs, x p is listed in the second column, initial electric current density Jy(t - 0) in the third, and reconnected flux at t - 20, ß (t=20)- fbz<o dx dy, in the fourth. The fifth column lists the number of the plasmoid dominating the current system at x = -5 for t = 60: 0, no clear dominance; 1, plasmoid at ye = -2.5; 2, plasmoid at ye = 2.5. The last column lists the figures associated with some of the runs. For run I of Table 1, Figure 8 shows the magnetic field Bz in the equatorial plane and demonstrates the progress of reconnection and the growth of the two plasmoids. In this case the plasmoid generated at xe = -13 dominates the reconnection process. The plasmoid generated at x e = -10 eventually ceases to grow and eventually is almost swallowed by ambient background reconnection in later times (t - 40 and 60). The region of enhanced Bz of the plasmoid farther downtail moves toward the left boundary and surpasses in magnitude the more earthward reconnection site. Figure 9 shows the parallel currents at x = -5 for run 1. Initially, both plasmoids s. :ow approximately '::'/o ': "... :. ' '? : : :.... ".0 ii i :.,..:, ' -...,...:.. ::...!:... ::. ½ :":":.' :::::.':...:':':.:?;."'....i....:.w.j.'..::'.'.-.;..... '... 0 ß '-, a-.' ',,.,',,,.*,' ' :.-: : ;i:'.'i ' ::'::'...: ;.:? `...::... :`:::.::.::: :.::`:? :..:: : :... ::.::;::...``: ;:::.n :... :, -:.: -: :-:-: :, :::::::-.'. ::...:::::--::::.:-: ß ::::.':' ::::.i: ;:._:::- --, ½ :: "'""' -" :-;.."" ""' "" '... "' '" ' '" "'"'": '.....':i:.'... ; +o.2 :: ;-. ::.: '::; :i:::;:?-.::...-:'2 i:? 71! i?.:.':::...,:: - ""- ' :.c....?. '"":- :...-, -5 i :- i;; o ß.-, %.,.. :. :.,...,..... %:...:...::... :....:.....,., :.:.: : :....,...,.. ::,, : JH y -o. 17 Figure 9. JII at x- -5 and t- 20, 40, and 60 for run 1 (xe = -10,-13 and ye = -2.5, 2.5; see Table 1). Shown is the upper half of the current system (z 0, compare to Figures 4 and 7) for a current system of two plasmoids. In this case the current systems of both plasmoids are of equal strength in the beginning, and finally the plasmoid at y dominates the system.

7 RAST TTER AND HESSE- MULTIPLASMOID EVOLUTION IN THE MAGNETOTAIL 25,017 : : : - :, :;: ::. : : : :...:?..: : :.:::: ";:-":; -'?-" '.i... :! "':i :: :i....:..::: :.:.-i?.. } i' :i ::! :::i:. :' -, :....:: : ': - :?..?:.:,.... : ::. ;::,:..: : : ;;:: ß o.o o.o Figure 10. Bz at z = 0, z > 0, and t = 20, 40, and 60 Figure 12. Bz at z- 0, z > 0, and t- 20, 40, and 60 for run 3 (x[, = -14,-17; see Table 1). Both reconnec- for run 6 (x[, - -20,-23; see Table 1). Reconnection tion events are equally strong, but the enhancement of is stronger in the patch closer to the Earth in this case. Bz generated closer to the Earth is of stronger influence The entire reconnection structure farther downtail is (Figure 11). accelerated into the downtail direction. Although the reconnection rate decreases with the current density in the downtail direction for this setup, as opposed to Figures 9 and 11 where the current increases or remains constant along the downtail direction ' ' "" " ' ' :- --, ---- J... ' : : : : : * '"'"'" ' ' '::' '.-.'... '"' ½*" : ' : :... ' +09 -lo -5 o 5 lo - 2 Jl ';:;' " o +0.2D -lo,....-5,... o,... 5,... lo, ' ': ': 0 -o. g y -O.08g Figure 11. JII at x--5, z>0, andt- 20, 40, and 60 for run 3 (xe - -14,-17; see Table 1 and Figure 10). The reconnection site at ye clearly dominates the current system. J between the reconnection patches), the influence of the plasmoid developing farther downtail still remains visible (similar to the previous case of Figure 11). Similar to the three-plasmoid case, the plasmoid closer to the Earth causes the entire magnetic structure (regions of Bz < 0 and Bz > 0) of the plasmoid farther downtail to move only into the tail direction. The difference in xe, however, is relatively smaller, which allows for the current system of the more distant reconnection site still to be visible in the near-earth current system together with the dominating feature of the nearer reconnection site. Figure 14 shows the comparison between the time evolution of the reconnected flux ß - f.<0 B=dxdy and the minimum and maximum of the field-aligned current JII for a single patch location xe and ye The amount of reconnected flux ß rises lin- early until the resistivity patch expires at t = 15, then stays constant until it grows farther owing to reconnection in the background resistivity. The parallel current remains zero for a certain time until the field-aligned current signal reaches the boundary x = -5. The min- imum in this case follows the reconnected flux with a clearly visible delay, but the maximum rises continuously. This time delay found (e.g., in the minimum of the parallel current) can become significant for quanti- tative comparisons in systems which evolve rapidly on the timescale of the delay.

8 ß ß. 25,018 RAST TTER AND HESSE: MULTIPLASMOID EVOLUTION IN THE MAGNETOTAIL ,,.-':. '"-"-'-... -','... ß.- j!i.! Jll ,0015 d d Figure 13. JII at x - -5, z > 0, and t - 20, 40, and 60 for run 6 (xp = -20,-23). Note that the current system of these plasmoids farther away from x = -5 than in Figures 9 and 11 is very weak. The reconnection at y dominates, similar to Figure 11. To quantify the signal transport time and separate the time delay effects from the highly dynamic evolution of the reconnection, a series of ideal perturbation runs have been performed. A small pressure enhancement in the spatial shape of a resistivity patch (equation (6)) with amplitude 5P = 0.2 (equilibrium pressure: I at x and 0.7 at x - -35) was introduced in ideal MHD (no reconnection is permitted). Figure 15 shows the time evolution of the integrated positive field-aligned current I = fo (JII,x) JII,x dy dz at x = -5 (with O (JIl, ) = I for JIl, > 0, 0 otherwise), after a pressure perturbation was introduced at different xp between -10 and -35 in the center of the plasma sheet " h - ( x (j,,) , o.oo---<-:zt-- --:::..-:.:... o ":::' '"'- "-:... min(j,) -2 '" ' flux i ,,,, time Figure 14. Time evolution of reconnected flux and parallel current amplitudes for a reconnection site at xp and yp The reconnected flux grows instantly and linearly until the resistivity patch expires at t = 15. The minimum and maximum of JII at x = -5 rises from zero later because the current system needs time to build up. 20 -'""\ t I t ' '\.: :.t[ ',. i ' }. i //5/ ",, -/ / N...; ', v'', W o.o o / i i X'?-. ' /", o i "..... /. ß ' ',.. -. / i... i..,-, i... i,,, time Figure 1E. Time evolution of fo (Jil, )JIl, dy dz at x - -5 for ideal MHD test runs after a pressure perturbation was introduced at the x positions x (run - ½un 2), (un (run 4), x (run 5), and x (run 6). The delays obtained from these tests are listed in Table 2. (yp -- 0, zp -- 0). The time evolution of I shows the different times that are needed for J II to reach the observer at x With increasing distance of the perturbation site x p to x - -5, the response arrives later, consistent with signal transport with the fast-mode velocity VF = V/("/P + B2)/P. Table 2 summarizes these results. The peak amplitudes of the field-aligned currents remain fairly constant over the range of x p investigated (runs 1-4, xp = -10,-15,-20, and-25) and eventually decrease for perturbations farther downtail (runs 5 and 6 with xp = -30 and-35, respectively). Figure 16 shows the field-aligned currents associated with the individual reconnection sites of the runs listed in Table 1, normalized by their size, which is measured by the reconnected flux ß at time t = 20. For reconnec- tion occurring at yp = -2.5, max (JII) is taken for the region y < -2.5; for yp = 2.5, I min (JII)l is taken in the region y > 2.5 as the representative value. The analysis of the currents only in the tail flanks ensures that the interference of the current system from the other reconnection site is minimal. The value r is the time after a signal reaches the boundary x As determined from test runs, this time difference is 1.3 for xp = 10, 3.6 for xp - 15, 6.0 for xp - 20, and 8.9 for xp - 25 (Table 2). These times are interpolated for the given reconnection patch positions and used to find the values of the parallel currents at the correctime. Although the current density varies in the region considered and has a maximum at x - -16, the normalized effects of the plasmoids are monotonous, showing that dividing by the respective reconnected flux eliminates the effect of the different growth rates of the plasmoids on the current system evolution. The decay of the amplitude of the field-aligned current density for reconnection sites, displaced farther into the tail, effectively reduces the visibility of the cur-

9 RASTJiTTER AND HESSE: MULTIPLASMOID EVOLUTION IN THE MAGNETOTAIL 25,019 range of tail locations xp of the perturbation and found only decay for larger distances xp _<-30). The maximum (or minimum) of the field-aligned current density, however, is more strongly affected by the distance at which the reconnection (or ideal perturba- 100 tion) takes place. This can be attributed to a wider spread of the current system in the tail cross section 0 which is associated with smaller current density amplitudes. The results of the numerical reconnection expero iment show that the effect of magnetic reconnection on field-aligned currents generally decreases with downtail X Figure 16. Distance effect on parallel current amplidistance. Thus a large tailward increase of the reconnection rate (e.g., in a localized thin current sheet) is tude Jll' At t - 20 for all the reconnection sites of Table necessary to offset the sharp decline of current ampli- 1, the maximum of IJll(t + -)/ (t)l is plotted against tude (per unit of reconnected flux) IJll/ l to allow the -xp for each plasmoid. The delays r listod in Table 2 reconnection site farther downtail to have a dominant were used for interpolation. effect on the appearance of the near-earth current sys- rent system of a reconnection event farther downtail in comparison with a site closer to the Earth. Only in the case where the cross-tail current density (and reconnection rate) rises in tailward direction can a plasmoid dominate the current system observed near the Earth although it is farther away. This effect may be enhanced by a current-driven resistivity. In conclusion, the location of the thin current sheet is a preferred location of reconnection that can develop with the largest impact on the current system observed in the near-earth magnetotail and in the ionosphere. 4. Discussion We studied the formation of plasmoids in the near- Earth magnetotail using a MHD model with a thin current sheet, obtained by tail compression. The thin current sheet is located between x and x = -20 RE downtail. After prescribing a resistivity model in several localized regions in the tail plasma sheet, reconnection occurs, and plasmoids develop. As time progresses, these flows associated with the reconnection in- fluence the electric current system at the near-earth boundary(x = -5) of the simulation box. The amount of current and the current density amplitudes found in that plane were studied in this work. We found that generally a large-scale system of field-aligned currents appears on the cross-tail plane and that the signature of a single reconnection site dominates in many cases. To find the reason of the dominance, a numerical exper-. iment was carried out to study the interaction of two plasmoids which are generated in different places in the magnetotail. Because of the rapid time evolution of the reconnection we used a perturbation in idealmhd to find the delays associated with the current system buildup far from the reconnection sites. These delay times agreed with propagation at the fast-mode speed. We found that the peak of the total current through the near- Earth plane remains fairly constant over a considerable tem. Signal travel timings have to be taken into account to compare the current amplitudes per unit of reconnected flux in the fast-evolving systems. Delays found in the current system buildup are in good agreement with fastmode or Alfv nic transmission along the magnetic field lines. In the case when the reconnection at the site closer to the Earth is strong compared to the site located farther downtail both flows and Bz enhancements generated by the reconnection site located farther tailward start to move downtail, and thus earthward flows from this site cannot contribute significantly to magnetic field dipolarization and field-aligned currents in the near-earth magnetotail. This case was found in two different cir- cumstances: (1) on the tailward side of the thin current sheet region where the current density and the reconnection rate diminish with larger downtail distance and (2) very close to the Earth where even comparable reconnection rates have considerably different effects owing to the sharp decline of the amplitude of field-aligned currents with larger downtail distance Ax = IxP -x01 of the reconnection sites from the near-earth cross- sectional plane. If both competing reconnection events have comparable reconnection rates because of constant current density tailward of the thin current sheet region, both field-aligned current signatures become comparable again because of the weak dependence of the current amplitudes on Ax at those distances. Table 2. Signal Delays From Figure 15 and Parallel Currents. Run x p r to max [JII(t)] I- f o (JII,x)JII,x dy dz is the integrated positive par- allel current through the plane x = -5; r is the time delay found in Figure 15 for each run.

10 25,020 RAST TTER AND HESSE: MULTIPLASMO!D EVOLUTION IN THE MAGNETOTAIL A thin current sheet in the presubstorm magnetotail plasma sheet is the preferred location of a reconnection event with largest impact on inner magnetospheric and ionospheric current systems. In future work the threedimensional distribution of reconnection onsets has to be modeled self-consistently. It is to be expected that current-driven instabilities as well as reconnection cer- tainly emphasize the region of presubstorm current intensifications even more than these MHD simulations with a prescribed resistivity model. Our model predicts that multiple reconnection sites in the magnetotail generate systems of field-aligned currents which overlap and form one global-scale current system. In most cases, one of those reconnection sites dominates this current system. This means that al- though one current system (current wedge) is observed, there may exist more than one active reconnection region in the near-earth magnetotail. Under these circumstances the attempt to determine the location of every single active region requires observations with a ill-represented by statistical (averaged) magnetic field models. Acknowledgments. This work was funded by NASA Supporting Research and Technology and Space Physics Theory Programs. One of us (L.R.) gratefully acknowledges the support by the National Research Council's Research Associateship Program. Janet G. Luhmann thanks David Sibeck and Ferdinand Coroniti for their assistance in evaluating this paper. References Angelopoulos, V., W. Baumjohann, C. F. Kennel, F. V. Coroniti, M. G. Kivelson, R. Pellat, R. J. Walker, H. Liihr, and G. Paschmann, Bursty bulk flow in the inner central plasma sheet, J. Geophys. 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Geoelectr., , Hesse, M., D. W nske, and J. Birn, On the ion scale structure of thin current sheets in the magnetc;ail, Phys. Scr., TTJ, 63, Ieda, A, S. Machida, T. Mukai, Y. Saito, T. Yamamoto, A. Nishida, T. Terasawa, and S. Kokubun, Statistical analysis of the plasmoid evolution with GEOTAIL observations, J. Geophys. Res., 103, 4453, Kan, J.R., A Global magnetosphere-ionosphere coupling model of substorms, J. Geophys. Res., 98, 17,263, Ma, Z. W., and L. C. Lee, A simulation study of generation of field-aligned currents and Alfv6n waves by threedimensional magnetic reconnection, J. Geophys. Res., 104, 10,177, McPherron, R.L., Magnetospheric Substorms, Rev. Geophys., 17, 657, Mitchell, D. G., D. J. Williams, C. Y. Huang, L. A Frank, and C. T. Russell, Current carriers in the near-earth cross-tail current sheet during substorm growth phase, Geophys. Res. Lett., 17, 583, Otto, A., Forced three-dimensional reconnection due to linkage of flux tubes in the dayside magnetopause, J. Geophys. 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Goodrich, and R. E. Lopez, Pseudobreakup and substorm onset: Observations and MHD simulations compared, J. Geophys. Res., 103, 14,847, Rastiitter, L., M. Hesse, and K. Schindler, Hall-MHD modeling of near-earth magnetotail current sheet thinning and evolution, J. Geophys. Res., 104, 12,301, Sanny, J., R. L. McPherron, C. T. Russell, D.N. Baker, T. I. Pulkkinen, and A. Nishida, Growth-phase thinning of the near-earth current sheet during the CDAW 6 substorm, J. Geophys. Res.,!)9, 5805, Scholer, M., and A. Otto, Magnetotail reconnection: Cur- ent diversion and field-aligned currents, Geophys. Res. Lett., 18, 733, Sergeev, V. A., D. G. Mitchell, C. T. Russell, and D. J. Williams, Structure of the tail plasma/current sheet at - 11 Rs and its changes in the course of a substorm, J. (Yeophys. Res., 98, 17,345, Slavin, J. A., et al., WIND, Geotail, and GOES 9 observations of magnetic field dipolarization and bursty bulk flows in the near-tail, Geophys. Res. Lett., 2, 971, Slavin, J. A., et al., ISTP observations of plasmoid ejection: IMP 8 and Geotail, J. Geophys. Res., 103, 119, Wiegelmann, T., and K. Schindler, Formation of thin current sheets in a quasistatic magnetotail model, Geophys. Res. Lett., 22, 2057, M. Hesse and L. Rastiitter, Code 696, NASA Goddard Space Flight Center, Greenbelt, MD (michael.hesse@gsfc. nasa.gov; lr@waipio.gsfc.nasa.gov) (Received June 22, 1999; revised August 18, 1999; accepted August 18, 1999.)