Onset of magnetic reconnection in the presence of a normal magnetic field: Realistic ion to electron mass ratio

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010ja015371, 2010 Onset of magnetic reconnection in the presence of a normal magnetic field: Realistic ion to electron mass ratio P. L. Pritchett 1 Received 18 February 2010; revised 5 July 2010; accepted 7 July 2010; published 6 October [1] Two dimensional particle in cell simulations with a realistic ion to electron mass ratio are used to investigate the impact of an externally applied convection electric field on the stability of a moderately thick (1.6c/w pi ) current sheet configuration containing a nonzero B z. The imposition of the electric field produces a thinning of the current sheet associated with the formation of an embedded electron current layer and a reduction in the normal magnetic field component. The time scale for these processes is found to be nearly independent of the electron mass. Once k x r en becomes of order unity (k x is the wave number for the maximally growing tearing mode, and r en is the electron gyroradius in the normal field), fluctuations drive B z southward over a subion inertia length scale region; further driving then leads to a conventional reconnection process featuring B z pulses (dipolarization fronts) propagating away from the X line. Consistent with earlier results with heavier electrons, strong parallel electric fields and an electron current layer form on scales of about an ion inertia length in the outflow direction, while electron outflow jets extend over much larger distances downstream from the X line. Citation: Pritchett, P. L. (2010), Onset of magnetic reconnection in the presence of a normal magnetic field: Realistic ion to electron mass ratio, J. Geophys. Res., 115,, doi: /2010ja Introduction [2] A recurring theme for more than 40 years in the theoretical investigation of the relation between magnetic reconnection and the expansion phase of substorms in the terrestrial magnetotail is the possibility that the collisionless tearing instability could serve as the substorm trigger mechanism (for a review, see, e.g., Pritchett [2007]). Very early in this history it was realized [Galeev and Zelenyi, 1976] that the electron tearing instability [Coppi et al., 1966] is not a viable mechanism since the cyclotron motion of electrons in even a very weak normal field B z removes the electron Landau resonance that provides the free energy for the collisionless tearing instability. Thus most attention has been focused on the ion tearing instability [Schindler, 1974]. Here, the consensus is that, due to the effects of electron stabilization in the normal field [Lembège and Pellat, 1982; Pellat et al., 1991; Quest et al., 1996; Schindler, 2007], the spontaneous ion tearing instability cannot exist in the transition region between dipole and tail magnetic fields where significant disruptions associated with substorm onset occur. The situation further down the tail is less clear [Sitnov et al., 2002]. [3] Despite this long history, it is by no means clear that the spontaneous tearing instability is the relevant process for explaining substorm onset. Considerable attention has also been paid to the possibility that substorms could be triggered 1 Department of Physics and Astronomy, University of California, Los Angeles, California, USA. Copyright 2010 by the American Geophysical Union /10/2010JA by external perturbations [Caan et al., 1975; Rostoker et al., 1983; Lyons, 1995, 1996]. It appears that a substantial fraction ( 60%) of substorm onsets can be associated with northward turnings of the IMF [Hsu and McPherron, 2003]. Prior to onset, a southward IMF imposes an enhanced convection electric field on the magnetotail. A number of MHD and Hall MHD studies [Birn and Hesse, 1996; Rastätter et al., 1999; Birn et al., 1999] have shown that reconnection can be initiated in regions of finite resistivity by such an externally imposed convection electric field, and a 2D particle in cell (PIC) simulation [Pritchett and Coroniti, 1995] showed that the local B z field could be readily driven through zero during the convection process, resulting in the tailward expulsion of a plasmoid. A possible limitation of this latter study was that the ion to electron mass ratio was only m i /m e = 16. [4] In the present study we revisit the question of how an externally applied convection electric field can trigger reconnection in a collisionless plasma sheet configuration containing a finite normal magnetic field component. Due to the dramatic increases in massively parallel supercomputer power in recent years, it is now possible to use a realistic value of m i /m e = 1600 in explicit PIC simulations (at least in 2D). This permits use of an initial configuration where the electron stabilization condition k x r en <1[Pellat et al., 1991] is strongly satisfied with k x r en 0.08, where k x is the wave number for the maximally growing tearing mode and r en is the electron gyroradius in the normal field B z. This represents a reduction by more than an order of magnitude in the value of k x r en as compared to early PIC simulations [Pritchett, 1994; Dreher et al., 1996]. The driving electric field in the present work is taken to be peaked on scales of a few ion inertia 1of9

2 lengths in x. As this field penetrates into the plasma sheet, it causes a depression in the normal field profile as a function of x over a similar multi inertia length scale and induces an embedded electron current layer at the center of the sheet. As the B z profile is further depressed, fluctuations drive B z through zero in a localized region with a size of 5 10 electron inertia lengths. Once this southward B z region is formed, the electron stabilization effect is removed, and reconnection ensues. The southward minimum in the profile then continues to deepen, and the spatial limits of the southward region initially expand faster in the earthward direction than in the tailward direction. During this initial period, the density in the southward B z region is hardly changed. As the reconnection proceeds further, the more familiar pattern [Pritchett, 2001a; Sitnov et al., 2009] featuring pulses of B z propagating away from the X line in both directions and a hollowing out of the density near the X line begins to be established. These pulses strongly resemble the dipolarization fronts identified by Sitnov et al. [2009] in which the ions dominate the dissipation and which have been observed to propagate nearly undisturbed over distances of 10R E in the magnetotail [Runov et al., 2009]. [5] The outline of the paper is as follows. Section 2 describes the simulation model. In section 3 we compare the onset process of reconnection as the mass ratio is varied from 25 to 1600 and show that the resulting reconnection rate is nearly independent of the electron mass. Section 4 illustrates for the case of m i /m e = 1600 the spatial extent of various bulk flow velocities, electric field components, and potentials in the electron dissipation region. Section 5 contains the summary and discussion. 2. Simulation Model [6] The simulation configuration is the same as in our previous studies of externally driven magnetic reconnection [Pritchett, 2005, 2006]. A plasma current sheet of initial halfthickness w = 1.6c/w pi and containing a 2D (x, z) magnetic field structure with normal field component at the center of the sheet B 0z (x, 0) = 0.04B 0 independent of x is subjected to a driving electric field E y (x, t) applied at the z boundaries. The form of the driving field is E y ðx; tþ ¼ fðþe t 0y sech 2 ðx=d x Þ: ð1þ This field is turned on over roughly one ion cyclotron time W i0 1 and then is maintained at a constant value of ce 0y /v A B 0 = 0.2. Here, B 0 is the asymptotic value of the lobe field at x =0, the Alfvén speed v A = B 0 /(4pn 0 m i ) 1/2, n 0 is the peak value of the Harris density distribution at x =0,w pi =(4pn 0 e 2 /m i ) 1/2, and the scale length D x = 3.2c/w pi. There is also a uniform background component with density n b /n 0 = 0.2, the temperature ratio is T i /T e = 5 for both the plasma sheet and background species, and T i = (5/12)m i v A 2. The system size is L x L z = 25.6d i 12.8d i where d i c/w pi, and the ratio w pe /W ce = 2. In order to balance the J y B z /c stress, the initial plasma density and pressure are monotonically decreasing as a function of x at the center of the current sheet. Thus we shall refer to negative x directions (toward the high density) as earthward directed and positive x directions (toward the low density) as tailward directed. The presence of this density gradient introduces asymmetries with respect to the X line in many of the reconnection fields and current densities despite the reconnection flows being approximately symmetric. [7] Four different simulation runs have been performed with values of the ion to electron mass ratio = 25, 100, 400, and Each quadrupling of m i /m e increases the computational cost by a factor of 16 [Pritchett, 2000]. For the m i /m e = 1600 run, the grid dimensions are N x N z = , so that c/w pi =80D, where D is the grid spacing, and the speed of light is c/v A = 80. The total number of particles in this run is 1.7 billion, corresponding to a reference density of n 0 = 845 particles per species per cell. The time step in the simulation is W e0 Dt = 0.1. [8] The simulations employ open boundary conditions at the x boundaries in which magnetic flux is free to cross the boundaries. This is achieved by requiring that the perturbed field db z 0 at these boundaries. The x boundaries are taken to be open for the particles as well: particles crossing such a boundary are removed from the system, and new particles are injected at a constant rate based on a thermal Maxwellian distribution. At the z boundaries, ambient particles striking the boundary are reintroduced on the corresponding field line in the opposite half z plane with v x = v x and v z = v z. 3. Reconnection Onset [9] Figure 1a shows the time history of the reconnection flux y for the four simulation runs with values of m i /m e between 25 and y is defined as the difference between the maximum and minimum values of the perturbed vector potential da y (x, z = 0) on the axis z = 0. There is very little variation in the behavior of y as m i /m e is varied. A similar lack of dependence of reconnection rate on m i /m e for the case of no initial normal magnetic field has been observed previously [Shay and Drake, 1998; Hesse et al., 1999;Pritchett, 2001a; Shay et al., 2007]. There is a relatively long development period of W i0 t 25 during which y grows slowly as the perturbation fields propagate in from the boundary. As shown in Figure 1b, the half width of the current layer, defined as the value w J where B x (0,w J ) = tanh(1)b 0 = 0.76B 0, decreases during this period from its initial value of 1.6d i to a minimum of 0.4d i. During this same period the peak number density on axis increases by just 20%. Thus the increased current density on axis is due primarily to the formation of an embedded thin electron current layer [Pritchett and Coroniti, 1995; Hesse and Birn, 2000; Pritchett, 2005; Karimabadi et al., 2007; Shay et al., 2007]. [10] Beginning at W i0 t 25 30, there is a much more rapid increase in the flux function y. The peak slope corresponds to a reconnection field ce y /v A B , which is more than twice as large as the driving field at the boundary. Thus the reconnection has not reached a steady state during this time interval. The peak slope for the m i /m e = 25 case is slightly smaller, but the other three cases have essentially the same value. Thus the mechanism that breaks the frozen in condition and enables reconnection is not sensitive to the value of m i /m e. To compare with determinations of the reconnection rate in nondriven simulations [e.g., Daughton et al., 2006; Cassak and Shay, 2007], we normalize to the conditions upstream of the ion diffusion region where the inflow field is B B 0 and the inflow density is n n 0. This yields a renormalized reconnection rate of ~E R Thus the 2of9

3 and Schindler [2001] in a PIC simulation with m i /m e = 100 in which the lobe driving electric field was ramped up to the maximum and then decreased back to zero well before the B z field on axis reached zero. In addition, the driving amplitude at the boundary as a function of x was monotonically decreasing; this is in sharp contrast to the peaked nature of Figure 1. Time histories of (a) the reconnected flux y and (b) the current sheet half thickness w in 2D PIC simulations with mass ratio m i /m e = 1600 (red curves), 400 (blue curves), 100 (green curves), and 25 (black curves). driven reconnection proceeds at a faster rate than the canonical value for spontaneous reconnection of [11] Figure 2a shows a sequence of plots for the normal field profile on axis B z (x,0)/b 0 for the m i /m e = 1600 simulation. During the development phase, the B z value is increased for x < 3d i and decreased for x > 3d i. The minimum in the B z profile occurs for x 2d i.byw i0 t 22, the value of B z has been reduced to 0.01B 0 over a range of several d i near x = 2d i, and the current sheet half thickness has been reduced to about 0.5d i. The corresponding value of k x r en is then 1, which marks the stabilization criterion limit. This reduction in the B z profile is a direct consequence of the driving electric field and the accompanying formation of the embedded electron current layer. The reduction in the B z field is necessary to preserve pressure balance in the presence of the increased current density J y. [12] Figure 2b shows a localized region of the B z profile near x =2d i for several times in the interval 22.5 < W i0 t < 25. At W i0 t = 22.5, there are localized fluctuations in which B z is as small as 0.004B 0 at x/d i = 1.2, 2.3, and 3.1. By W i0 t = 23.1, only that at 3.1 has deepened through zero. This has occurred in a region of size 10d e, which is more than an order of magnitude smaller than the half width of the driving field on the boundary. The reversal in B z results in the formation of an X line O line pair. A similar localized reduction of the B z profile through zero was observed by Hesse Figure 2. Profiles for the magnetic field B z (x,0) for the simulation with m i /m e = 1600 for (a) times in the range 2.5 < W i0 t < 25, (b) for a restricted x range near the X line for times in the range 22.5 < W i0 t < 25, and (c) for later times in the range 27 < W i0 t < 39. 3of9

4 Figure 3. Structure at time W i0 t = 39 for the simulation with m i /m e = 1600 for the energy dissipation J E: (a) electron contribution and (b) ion contribution. the driving field in the present simulation. The fact that the response of the B z field on axis was so similar for two such different driving scenarios suggests that the precise form of the driving field is not critical, but this should clearly be checked in additional simulations. Once the B z field reversal occurs, the electron stabilization effect is removed, and reconnection ensues. The southward minimum in the profile then continues to deepen, and the spatial limits of the southward region initially expand faster in the earthward direction than in the tailward direction. By W i0 t = 25, the familiar reconnection pattern [Pritchett, 2001a; Sitnov et al., 2009] has begun to emerge with roughly equal positive and negative magnitudes for B z on either side of the X line at x 2d i. Meanwhile, the O line moves tailward. [13] At later times, the expanding B z pulses behave similarly to the dipolarization fronts identified by Sitnov et al. [2009]. In particular, the magnitudes of B z at the head of the fronts reach levels of the order of 0.5B 0, as is demonstrated in Figure 2c. In addition, as shown in Figure 3, the dissipation J E at the center of the pulses is strongly dominated by the ions. This dissipation is stronger in the earthward moving pulse, which is a reflection of the asymmetry associated with the stronger current density on the earthward side of the X line. Near the X line itself, the dissipation is dominated by the thin electron current layer (see the discussion in section 4). Interestingly, there are also positive contributions from the ions along the separatrices and both positive and negative contributions from the electrons. The positive ion dissipation is an electrostatic effect associated with the existence of a large scale electrostatic potential across the separatrices that diverts and accelerates the incoming ion flow (see the discussion in section 4). The negative electron dissipation at z 0 and x 0.3d i and x 2d i arises from J ex E x and is associated with the slowing down of the electron outflow jets, while the positive electron dissipation just inside the separatrices arises from J ey E y and J ez E z. The propagation speed of the B z fronts is about 0.6v A on the earthward side and 0.5v A on the tailward side. This is somewhat smaller than the value of v A observed by Sitnov et al. [2009] in 2D PIC simulations with no initial normal magnetic field component in the equilibrium, but it is reasonably consistent with the propagation speed of about 350 km/s for the fronts in the THEMIS observations [Runov et al., 2009] which corresponds to 0.4v A based on B 0 30 nt and n cm Structure Near the X Line [14] Figure 4a shows the profile U ey (z) (red curve) through the X line at time W i0 t = 39, where U ey is the y component of the bulk electron flow velocity. The spatial scale for z is the ion inertia length d i based on the initial density n 0. The electron drift reaches a peak value of 25v A at the center of the sheet. The blue curve shows the profile of c(e B) y /B 2. 4of9

5 Figure 4. Spatial profiles at time W i0 t = 39 for the simulation with m i /m e = 1600 for (a) the electron bulk flow velocity U ey (red curve) and the drift c(e B) y /B 2 (blue curve) as a function of z at x/d i = 1.1; (b) the electron bulk flow velocities U ex (red curve) and U ey (black curve), the ion bulk flow velocity U ix (green curve), and the drift c(e B) x /B 2 (blue curve) as a function of x at z = 0; and (c) the electron bulk flow velocity U ex (red curve) and ion bulk flow velocity U ix (green curve) as a function of x at z =0. The actual electron drift speed substantially exceeds this value for z ] 0.05d i =2d e. Noting that the local density is 0.16n 0, this range corresponds to z < 0.8d e loc. This then is a measure of the region where the electrons are demagnetized in the inflow direction, namely at about the local electron inertia length. [15] In Figure 4b the red and blue curves show, respectively, the x profiles at z = 0 at time W i0 t = 39 for U ex (x) and c (E B) x /B 2. Except in the immediate vicinity of x = d i, the actual electron outflow magnitude far exceeds the E B value, reaching a peak speed of 18v A. The red and blue curves rejoin each other only at a distance of d i away from the X line. The green curve shows the ion velocity profile U ix (x). Its magnitude is much smaller than that of U ex (x) in the region plotted. The black curve shows U ey (x). The full width at half maximum of this out of plane flow is 1.2d i. Figure 4c shows that U ix (x) and U ex (x) do not rejoin each other until a distance 5d i away from the X line. If the size of the simulation in the x direction were increased, it is likely that these outflow regions would become larger, as has been observed in lower mass ratio simulations without a normal field [Karimabadi et al., 2007; Shay et al., 2007]. [16] Figure 5 shows the structure of the electric field components near the X line region. E k (Figure 5a) has a strong quadrupolar structure located at z 0.05d i = 0.8d e loc as well as a weaker extended quadrupolar structure with the opposite parity [cf. Pritchett, 2001b]. The intense inner E k fields extend over a distance d i in x on either side of the X line. These inner fields are directed toward the X line, while the outer fields are directed away from the X line. The net E k structures result from significant cancellations among the separate E x B x, E y B y, and E z B z terms. The fields directed toward the X line have the sign determined by E z B z, while those directed away have the sign of E x B x. As the ratio m i /m e increases, the spatial extent of the inner E k decreases, and their magnitude increases. [17] The E x (Figure 5b) and E z (Figure 5d) fields are localized along the separatrices; E z also has a bipolar structure directed toward the center of the current sheet from above and below [Pritchett and Coroniti, 1995; Arzner and Scholer, 2001]. The opening half angle is 26 on the negative x side and 35 on the positive x side. Figure 6a shows the electrostatic potential F. The strength of the potential drop across the separatrices from upstream to downstream is edf/t e 10 or edf/t i 2. This potential drop accelerates the ions into the outflow direction. As a function of x at z = 0, the potential has a local maximum at the X line (Figure 6b). This serves to trap electrons near the X line as they are accelerated by the inductive electric field and eventually expelled by the J y B z /c Lorentz force. The potential difference between the X line and the potential minimum at x 1.5 is edf/t e 8. [18] Figure 5c shows the inductive field component E y. As noted before, the value at the X line is ce y /v A B For the present case of a 2D system with no y variation, the electron momentum equation in a two fluid model yields the result that E y ¼ 1 ð c U ezb x U ex B z Þ e xy en m ey þ U þ ey ez : This is the generalized Ohm s law for the electric field, where U e is the bulk electron flow velocity and P e is the electron pressure tensor. In the present configuration, the explicit time derivative term is negligibly small. The electric field can thus be supported by the convective term, the derivative of the off diagonal electron pressure tensor elements, and the convective derivative electron inertia terms. At the X line, the first and third of these terms must vanish, leaving only the pressure tensor terms. Figure 7 shows the profile E y (x, z =0) at time W i0 t = 39 (blue curve) in the vicinity of the X line. Also shown are the U ex B z (red curve), (m e /e)u ex U ey / x (green curve), (1/en e ) P e xy / x (magenta curve), and (1/en e ) P e yz / z (black curve) terms. Right at the X line, E y is supported almost entirely by the P e yz / z term [Hesse et al., 2004]. The convective term U ex B z /c vanishes at the X line itself and then way overshoots E y in magnitude [Pritchett, 2001a; Karimabadi et al., 2007; Shay et al., 2007]. This 5of9

6 Figure 5. Structure at time W i0 t = 39 for the simulation with m i /m e = 1600 for (a) the parallel electric field ce k /v A B 0, (b) the electric field ce x /v A B 0, (c) the electric field ce y /v A B 0, and (d) the electric field ce z /v A B 0. Figure 6. The electrostatic potential ef/t e at time W i0 t = 40 for the simulation with m i /m e = 1600 in (a) the x, z plane and (b) as a profile along x at z =0. 6of9

7 [19] Figure 8a shows the parallel potential F k computed from the field E k by the definition [Egedal et al., 2009] F k ðxþ ¼ Z 1 x E d ; ð3þ Figure 7. Profile of the electric field ce y (x)/v A B 0 at z =0 in the vicinity of the X line at time W i0 t =39(bluecurve). Also shown are the separate contributions to the right hand side of the generalized Ohm s law (equation (2)): U ex B z /c (red curve), (m e /e)u ex U ey / x (green curve), (1/en e ) P xy / x (magenta curve), and (1/en e ) P yz / z (black curve). overshoot is compensated by the pressure tensor and bulk inertia terms. The tendency of the E y field to increase in magnitude at increasing distances from the X line results from the increase in the convective term as flux propagates outward. where the integration is carried out from the point x along the magnetic field to the boundary of the simulation box. Note that F k contains contributions from both the electrostatic and inductive electric fields. F k has a peak value that exceeds 2.5kT e /e in the electron inflow region. Smaller values > kt e /e extend out along the separatrices and also occur in the outflow regions where the electron outflow speed exceeds the E B value. As shown in Figure 8b (note the change in spatial scales from Figure 8a), in the inflow region the ratio T ek /T e? is much greater than unity. Such enhanced parallel electron temperatures have been observed near reconnection sites in the magnetosphere [Egedal et al., 2005; Chen et al., 2008], and it has recently been shown through kinetic equations of state for the parallel and perpendicular pressures for magnetized electrons that such an anisotropy is mainly caused by the trapping of electrons in parallel electric fields [Le et al., 2009, 2010]. 5. Summary and Discussion [20] In this report previous particle in cell simulations of the onset of driven reconnection in a plasma sheet configuration Figure 8. Structure at time W i0 t =40forthesimulationwithm i /m e = 1600 for (a) the parallel potential ef k /T e and (b) the electron temperature anisotropy T ek /T e?. 7of9

8 containing a normal magnetic field component [Pritchett, 2005, 2006] were extended to the case of a realistic ion to electron mass ratio (m i /m e = 1600). With such a large mass ratio, it is possible to choose the simulation parameters such that k x r en 0.1, way below the stability criterion k x r en 1 for the spontaneous ion tearing instability [Pellat et al., 1991]. The imposition of a convection electric field at the lobe boundary produces a thinning of the current sheet associated with the formation of an embedded electron current layer and a reduction in the normal magnetic field component. These processes combined lead to an increase in the value of k x r en. Once k x r en 1, fluctuations in the system lead to the formation of a small scale ( 10d e ) region of southward B z. The southward B z minimum then continues to deepen, and the spatial extent in x increases faster on the earthward side than on the tailward side. This leads to the usual reconnection situation where a bipolar B z field is formed relative to an X line, and the system continues to reconnect. The B z pulses propagating away from the X line strongly resemble the dipolarization fronts identified by Sitnov et al. [2009] and observed by the THEMIS satellites to propagate over large distances in the magnetotail [Runov et al., 2009]. Since reconnection appears to be readily induced in a B z current sheet by an external perturbation, the long running arguments over whether the spontaneous ion tearing instability is possible in the magnetotail seem now to be mainly of academic interest. The driven reconnection process features dissipation based on both the ion and electron drifts at different locations. [21] The time scale for the onset of reconnection in response to the convection electric field, when expressed in terms of the ion cyclotron time, proves to be essentially independent of the electron mass over the range m e /m i = 1/25 to 1/1600. Thus, simulations with relatively heavy electrons appear to describe the reconnection onset process correctly. One possible caveat is that this result has been demonstrated only for 2D systems. It is known that the properties of the lower hybrid drift instability (LHDI, a finite k y mode), for example, are quite sensitive to the mass ratio [Daughton et al., 2004], at least for the case of ion scale current sheets. For the case of a realistic mass ratio, the nonlinear growth of the LHDI leads to an increase in the electron U ey flow velocity in the central part of the sheet, a strong bifurcation of the current density, and significant anisotropic heating of the electrons. This electron anisotropy can increase the growth of the tearing instability. Thus it is possible that the true 3D response of the current sheet could be more sensitive to the mass ratio. On the other hand, 3D PIC simulations with a reduced value of m i /m e = 100 [Pritchett, 2005] indicate that the LHDI is not excited in the presence of the normal magnetic field. The LHDI modes appear to be stabilized by the presence of finite k k [Gladd, 1976]. Also, the presence of a moderate nondrifting background plasma, as in the present simulation, reduces the effectiveness of the LHDI [Daughton, 2003]. Clearly, it is necessary to extend the 3D simulations to realistic mass ratios as well in order finally to resolve the response of a current sheet with a normal field to the imposition of a convection electric field. [22] Once the reconnection process is established, the results of the present simulations with a realistic mass ratio indicate that the properties of the electron dissipation region are similar to those seen in previous simulations with heavier electrons [Karimabadi et al., 2007; Shay et al., 2007; Le et al., 2010]. The parallel electric fields in the electron dissipation region and the electron out of plane current layer extend downstream over a distance of the order of the reference ion inertia length (or about twice the ion inertia length based on the local density). This is also the scale on which the electron outflow U ex exceeds the (E B) x flow. The electron outflow does not rejoin the ion value, however, until a much larger distance downstream of at least 5d i. The existence of a strong electron temperature anisotropy T ek /T e? 1 in the inflow region and a parallel potential ef k /T e > 1 are also confirmed. [23] Acknowledgments. The author would like to thank F. V. Coroniti for valuable discussions. This research was supported by NASA grants NNX08AM15G and NNX10AK98G. The computational resources supportingthisworkwereprovidedbythenasahigh EndComputing(HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. [24] Philippa Browning thanks the reviewers for their assistance in evaluating this paper. References Arzner, C. H., and M. Scholer (2001), Kinetic structure of the post plasmoid plasma sheet during magnetotail reconnection, J. Geophys. Res., 106, 3827, doi: /2000ja Birn, J., and M. Hesse (1996), Details of current disruption and diversion in simulations of magnetotail dynamics, J. Geophys. Res., 101, 15,345, doi: /96ja Birn, J., M. Hesse, G. Haerendel, W. Baumjohann, and K. Shiokawa (1999), Flow braking and the substorm current wedge, J. Geophys. Res., 104, 19,895, doi: /1999ja Caan, M. N., R. L. McPherron, and C. T. 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