Onset of reconnection in a tail-like equilibrium with a finite Bz magnetic field component is studied using 3-D explicit particle-in-cell simulations. Due to a region of a tailward Bz gradient the onset develops spontaneously as the magnetic flux release instability with dominant earthward ion flows. The instability drives the change of magnetic field topology internally, without any external forcing. The distinctive features of this regime are: previously unreported Hall magnetic field patterns; energy conversion near the dipolarization front prior to the X line formation; asymmetry of the energy conversion, plasma heating, and anisotropy relative to the X line, with regions of ion and electron heating out of phase both along and across the tail. These features distinguish the internally driven reconnection regime from similar processes in antiparallel magnetic field configurations as well as interchange and externally driven magnetotail reconnection regimes and can be used to identify the different regimes in upcoming Magnetospheric Multiscale (MMS) mission tail season observations.
- Magnetotail reconnection can be driven internally due to magnetic flux release instability
- New patterns of Hall magnetic field, plasma heating, anisotropy, and agyrotropy are demonstrated in this regime
- Energy dissipation at the dipolarization front precedes the topology change
In the present paper we consider another possible transition to magnetotail reconnection instability, which starts from macroscales and is controlled by the left-hand side of 1. Since the original work of Lembege and Pellat , the possibility of this transition was ruled out, because a seemingly obvious approximation of the flux tube volume V≈2Lz/Bz reduces the left-hand side of 1 to the WKB approximation in the stability theory (Cd=1), which requires that the wavelength of the perturbations should not exceed the inhomogeneity length of the tail. Recently, Sitnov and Schindler discovered that the original flux tube volume approximation is not universal, and for a class of 2-D current sheet equilibria with a region of a tailward Bz(x,z = 0) gradient, the destabilization parameter Cd>1. Then a potential for instability appears because the left-hand side of 1 describes only a section of the WKB region. The actual destabilization of the corresponding tail equilibria was shown later in simulations with open [Sitnov et al., 2013, 2014; Bessho and Bhattacharjee, 2014] and closed [Pritchett, 2015] boundaries. While the latter are more conservative and consistent with the energy principle used in the stability analysis, they may artificially limit the flux tube volume and hence the destabilization parameter Cd, block spontaneous generation of plasma flows generated by the reconnection instability, and as a result, require longer simulation boxes to reproduce reconnection regimes similar to those seen in simulations with open boundaries [Merkin and Sitnov, 2016]. In this respect, closed boundary conditions artificially modify the simulated magnetotail system from the real one, as do open boundaries, whose effects remain insufficiently understood. Thus, in either case, effects of boundary conditions need to be attenuated as much as possible. To this end, in this paper we perform fully 3-D simulations in a computationally challenging box that is several times longer compared to the previous simulations with open boundaries, yet retaining the important 2-D structure of the magnetotail equilibrium serving as the initial condition. Note that the reconnection onset regime to be considered does not require any external driving. As shown by Sitnov and Swisdak  and Sitnov et al. , reconnection in this regime arises spontaneously, as a result of the development of an instability similar to the long-sought ion tearing instability [Schindler, 1974]. Yet since the instability develops in the region with magnetized electrons and changes the original tail topology only in its nonlinear (finite-amplitude) phase, following Pritchett, we refer to this regime as internally driven (rather than spontaneous) reconnection or IDR.
2 Simulation Setup
Simulations have been conducted using an open boundary modification [Divin et al., 2007; Sitnov and Swisdak, 2011] of the explicit massively parallel PIC code P3D [Zeiler et al., 2002] in a 3-D box with dimensions Lx×Ly×Lz=60di×10di×20di, where di is the ion inertial scale. Note that compared with earlier simulations [Sitnov et al., 2014], the initial equilibrium does not impose an equilibrium X line in the center of the simulation domain. This allowed us to substantially increase its effective size, particularly tailward of the flux accumulation region. In the following we focus on the part of the simulation box with −36di<x < 0 and |z|<2.5di, where the most interesting phenomena take place. Further details of the simulation setup are provided in the supporting information (SI) file.
3 Internally Driven Reconnection
As seen from Figure 1, a distinctive feature of the IDR regime is that the tail activity starts from spontaneous generation of earthward ion flows (Figure 1c) and redistribution of magnetic flux (Figure 1a). These processes transform the initial Bz hump into a dipolarization front (DF) [Nakamura et al., 2002], whereas flux depletion behind the front causes the formation of a new X line. The transformation takes place mainly in the (x, z) plane and is governed by the same physical mechanism as conventional magnetic reconnection, namely, the mutual attraction of parallel current filaments [Galeev, 1984], even though it starts before the magnetic topology change.
The corresponding instability [Sitnov and Swisdak, 2011; Sitnov et al., 2013] termed the magnetic flux release (MFR) instability [Merkin and Sitnov, 2016] may start in ideal (MHD) regime when Lz≫di, and both species are magnetized, if the destabilization parameter Cd is sufficiently large (Cd>5/3) [Merkin et al., 2015]. This is the case in our simulations with . When the region with the enhanced dawn-dusk electric field Ey inside the plasma sheet (Figure 1d) reaches its earthward section, where , ions become unmagnetized and can be directly accelerated leading to ion Landau dissipation. At this point the MFR transforms into the ion tearing instability [Schindler, 1974] as long as electrons remain magnetized. By the time of their demagnetization ω0it≈27, the tail is already in a state of active dipolarization, which results in strong asymmetries along the tail discussed below.
The characteristic sequence of the IDR processes with fast earthward ion flows preceding the magnetic field topology change is qualitatively similar to the empirical picture inferred by Machida et al.  from a statistical visualization of the magnetotail around the substorm onset. However, a quantitative comparison will likely require simulations of thicker current sheets to match the corresponding time scales (currently, seconds in simulations versus minutes in observations).
In 3-D the MFR instability is accompanied by plasma waves with ky≠0 (Figure 1b). They include the lower hybrid drift waves ahead of the DF (panel ω0it = 21) and outside the current sheet (not shown here, but the effect is described in [Lui, 2016, Figure 1] using a similar simulation run), as well as a combination of flapping and buoyancy-driven motions at and behind the DF (panel ω0it = 31). These waves were extensively studied before for 1-D current sheet models [Harris, 1962] with superimposed X lines [Divin et al., 2015] as well as for 2-D models with equilibrium X lines [Sitnov et al., 2014; Lui, 2016]. Here we show for the first time that this wave activity may likewise precede any topology changes in the system in the absence of preexisting equilibrium X lines. The IDR regime should also be distinguished from reconnection regimes [Pritchett and Coroniti, 2011, 2013] driven by kinetic ballooning/interchange instabilities [Pritchett and Coroniti, 2010] whose distinctive feature is the localization of the X line regions behind earthward moving interchange fingers in the y direction consistent with the instability wavelength of a few di. Moreover, the ballooning/interchange instability generates necessarily bipolar earthward and tailward flows, which develop simultaneously with comparable intensities prior to reconnection onset. See, for instance, Figure 2c in Pritchett and Coroniti  and Figure 10e in Pritchett and Coroniti , where the tailward flow magnitude is typically 50–70% of the earthward flow. In contrast, prior to the topology change, the IDR is distinguished by earthward ion and electron flows (though different in amplitudes and localization as discussed in the next section), whereas the X line forming in the flux starvation region is rather global (see panel ω0it = 31 in Figure 1b). Note here that the limited y dimension of the present simulation (Ly=10di) may prevent observing the full interchange spectrum. Pritchett et al. [2014, Figure 2c] found that the strongest mode occurred at a wavelength of about 20di. At the same time, no signatures of such waves were found in simulations with open x boundaries and Ly=20di [Sitnov et al., 2014], where instead pronounced flapping motions were detected. Hence, the role of longer-wavelength y modes requires further study in larger 3-D simulations.
4 New Hall Patterns
Collisionless regimes of magnetic reconnection are often identified using the characteristic quadrupole pattern of the “out-of-plane” magnetic field, which appears due to different motions of ion and electron species and the resulting Hall currents arising in the absence of collisions and on the scales comparable to the thermal ion gyroradius ρ0i [Sonnerup, 1979; Uzdensky and Kulsrud, 2006]. The quadrupole Hall pattern in antiparallel reconnection was confirmed later in simulations [Shay et al., 1998] and is often used to reveal regimes of collisionless reconnection in space [Runov et al., 2003; Eastwood et al., 2010] and laboratory plasmas [Ren et al., 2005]. (The addition of a guide field breaks the quadrupole symmetry, although a signal is still present [Rogers et al., 2003; Ricci et al., 2004; Huba, 2005].) Here we show that in addition to the classical quadrupole pattern of the By magnetic field, which indeed appears at later stages of the IDR (patterns marked by the green frame in Figure 2), this regime of magnetotail reconnection has two new characteristic Hall current signatures. First, prior to the X line formation, different motions of ions (Figure 1c) and electrons (SI, Figure S2) behind the DF form a dipole By pattern D1, which transforms later into the earthward half of the quadrupole pattern. It is marked by the red frame in Figure 2 (left column) and is also seen in 2-D simulations with closed boundaries [Pritchett, 2015] (Figure 2, right column). An additional dipole pattern D2 with the polarity opposite to that of D1 was reported in simulations with open boundaries [Sitnov et al., 2014]. There it might be confused, however, with the effect of the secondary reconnection, which started ahead of the DF and could be interpreted as a boundary defect. The present extended simulations show that it arises rather due to different motions of ions and electrons ahead of the DF, and it is not related to any additional X lines. The dipole pattern similar to D2 is also seen in simulations with closed boundaries (Figure 2, right column), where, however, it is substantially attenuated, presumably, due to the blockage of the ion and electron flows in the x direction by the closed left boundary.
5 Energy Conversion and Plasma Heating Features
Distributions of the energy conversion parameters before and after the X line formation (Figure 3) show that the dissipation (regions of the positive Joule heating rate parameter, where j = ji+je, , ji,e are the ion/electron currents in the laboratory frame of reference and vi is the ion bulk flow velocity) caused by kinetic effects starts prior to the topology change in the tail and it is focused in the DF region. Consistent with observations [Runov et al., 2011, Figure 8a], it peaks in the region of the strongest tailward Bz gradient, and its magnitude averaged over the y direction constitutes a substantial portion of the total energy conversion rate, close to partial contributions from each plasma species. Due to eigenmodes with ky≠0, the energy conversion parameters are highly structured in the dawn-dusk direction. Moreover, the comparison of the equatorial distributions of the parameters ji,e·E(x,y) shows that the energy conversion peaks are higher for electrons than for ions and they are more localized on the scales well below di. In contrast, their localization along the tail exceeds di resulting in a set of characteristic stripes.
After the topology change, the energy conversion picture changes due to the formation of the electron diffusion region, but it is still drastically different from similar pictures in 1-D models [e.g., Lapenta et al., 2014] because of the asymmetry along the tail relative to the X line. Both the total energy conversion and Joule heating distributions are concentrated earthward of the X line. This is true even for the electron diffusion region, where the asymmetry is best seen in the equatorial (x,y) distributions of the parameters je·E and which reveal another set of stripes on the left of the X line. Similar stripes with much larger amplitudes and different signs of values are formed near the DF Bz peak region. However, their values averaged over the y coordinate are relatively small and do not exceed the dissipation near the X line. The latter in its turn contributes much less ( 25%) to the total energy conversion, which is concentrated near the DF with the main contribution from ions. This picture resembles regimes of magnetic reconnection in 2-D MHD simulations with a localized ad hoc resistivity region as well as 2-D PIC simulations of the externally driven reconnection regime [Birn and Hesse, 2014], because the energy conversion is mainly determined by the bulk flows of plasma in the reconnection exhaust 〈j·vi×B/c〉. The important distinctions of the IDR regime are, however, that the dissipation is not limited to the X line vicinity and that all energy conversion distributions, including and 〈je·E〉y, are strongly asymmetric relative to the X line.
The resulting plasma heating in the IDR regime is also unusual and challenging for future observations and theoretical interpretations. First, according to Figures 4a–4d, both before and after the topology change plasma is mainly heated near the DF. Ions are heated ahead of the front (Figures 4a and 4b), while electrons near the Bz peak or behind the DF, in the flux pileup region (Figures 4c and 4d). These features as well as the specific peak heating factors ( and ) are consistent with THEMIS observations [Runov et al., 2011, Figures 5g and 5f]. They can be used to differentiate the IDR from interchange-driven reconnection, for which the predicted heating factors are an order of magnitude larger [Pritchett and Coroniti, 2013, Figure 13]. As seen from Figure 4d, electron temperature variations along the DF correlate with buoyancy (Bz variations) and flapping motions (the latter is seen from the meridional plane panel). The IDR also develops significant plasma anisotropy and agyrotropy. The distributions of the corresponding invariant parameters [Swisdak, 2016] (see SI Figures S3 and S4 and accompanying text) exhibit strong day-night asymmetry and strong correlation with the DF.
6 Discussion and Conclusion
Reconnection in the magnetotail has important distinctive features caused primarily by the finite Bz component of the magnetic field that is sharply stretched in the antisunward direction rather than antiparallel, as is assumed in many models. In this paper we considered one of the new regimes of reconnection allowed by the Bz effects. It differs both from the antiparallel reconnection and from other regimes possible in the tail when the reconnection processes are driven externally or by nonreconnection plasma instabilities. In the regime reported here and denoted IDR the topology change is caused internally, but the instability causing it has the same physical mechanism as magnetic reconnection, and its properties are similar to those of the ion tearing instability [Schindler, 1974]. Yet we call this reconnection internally driven rather than spontaneous to emphasize that the topology change, which was always considered as the defining feature of the reconnection phenomenon, is not the primary effect in this regime. The IDR starts from the spontaneous generation of earthward plasma flows and the redistribution of magnetic flux, while the new X line arises as a consequence, in the process similar to the bubble-blob formation in some models [Yang et al., 2011; Hu et al., 2011]. Yet an important distinction of the IDR regime from those models and similar kinetic models of interchange-driven reconnection [Pritchett and Coroniti, 2013] is that the X line formation is caused not by plasma buoyancy, but by the same reconnection mechanism, which works in an antiparallel case. As a result, the IDR provides the formation of a global X line rather than localized magnetic islands whose extension in the dawn-dusk direction is limited to the corresponding interchange wavelength. Note that in 3-D simulations reported here the new X line appears earlier (ω0it≈27) compared to 2-D simulations (ω0it > 40) [Sitnov et al., 2013; Bessho and Bhattacharjee, 2014]. In view of the similar results obtained earlier in shorter 3-D simulation boxes [Sitnov et al., 2014] to those presented here, a likely reason is the contribution to the collisionless resistivity from instabilities with ky≠0.
One of the most interesting distinctive features of the IDR is a new set of Hall magnetic fields that form around the DF prior to the X line formation. The By pattern around the DF represents an inversion of the classical quadrupole magnetic field pattern near the X line with an additional distinction that the plasma flows have no reversal at the DF. These features might be an interesting target for the Magnetospheric Multiscale mission during its tail season [Burch et al., 2016]. Other features include the substantial plasma dissipation preceding the topology change in the magnetotail with residual asymmetry along the tail relative to the X line after its formation and characteristic modulation in the dawn-dusk direction both near the DF and earthward of the X line. The IDR dissipation may be localized on the scales well below the ion inertial length. Plasma heating, anisotropy, and agyrotropy in the IDR are mainly determined by the DF formation and dynamics, although the dissipation at X line, when it forms, is significant. While some of these features, such as temperature and anisotropy profiles along the tail already match the present multiprobe observations, others, such as anticorrelation of the temperature variations between ion and electron species, anisotropy modulation in the dawn-dusk direction, and the agyrotropy variations, remain to be checked with observations.
Whether magnetotail reconnection is indeed spontaneous, that is, driven internally by the ion tearing instability, remains an interesting open question. The answer depends on the solar wind loading rate and may be different at different distances from the Earth [Nagai et al., 2005]. The formation of the Bz pileup region, which is necessary for this IDR regime may be determined by various global factors, such as earthward convection flows [Goodrich et al., 2007] or flux depletion in the near-Earth tail [Hsieh and Otto, 2015]. At the same time, continued solar wind loading may prevent formation of the new X line by preventing flux starvation from occurring. However, the accompanying processes of the current sheet thinning to proton scales necessary to provide collisionless dissipation involve kinetic effects. As a result, even the description of the initial states in PIC simulations of the global magnetotail requires new classes of tail current sheet equilibria taking into account plasma anisotropy and agyrotropy [Sitnov and Merkin, 2016].
The authors thank A. Artemyev, J. P. Eastwood, Y.-H. Liu, T. Motoba, A. Otto, A. Runov, and C.-P. Wang for useful discussions. The work on this paper also benefited greatly from the discussions at the ISSI workshop on “Explosive Processes in the Magnetotail: Reconnection Onset and Associated Plasma Instabilities” held in Bern, Switzerland on 17–21 October 2016. This research was supported by the NASA HSR and LWS programs and by the NSF GEM program. The data used to produce figures in the paper are available upon request. Simulations were made possible by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center as well as NCAR's Yellowstone supercomputer supported by the NSF.
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