On the 3-D structure and dissipation of reconnection-driven flow bursts

The structure of magnetic reconnection-driven outflows and their dissipation are explored with 3-D particle-in-cell simulations. Outflow jets resulting from 3-D reconnection with a finite length x-line form fronts as they propagate into the downstream medium. A large pressure increase ahead of this “reconnection jet front” (RJF) due to reflected ions slows the front so that its velocity is well below that of the ambient ions in the core of the jet. As a result, the RJF slows and diverts the high-speed flow into the direction perpendicular to the reconnection plane. The RJF therefore acts as a thermalization site for the ion bulk flow and contributes significantly to the dissipation of magnetic energy during reconnection even though the outflow jet is subsonic. This behavior has no counterpart in 2-D reconnection. A simple analytic model predicts the front velocity and the fraction of the ion bulk flow energy that is dissipated. Magnetic reconnection is the dominant mechanism for dissipating magnetic energy in large-scale plasma systems and is the driver of explosive events such as flares in astrophysical systems and flow bursts in the Earth’s magnetosphere. Most of the energy released during reconnection takes place not at the x-line but downstream in the exhaust where newly reconnected field lines relax their magnetic tension. In the MHD description the Petschek shocks that bound the exhaust both drive the Alfvénic exhaust and heat the upstream plasma entering the exhaust [Petschek, 1964; Lin and Lee, 1995]. In the nearly collisionless environment of many systems, while the exhaust outflow is close to the MHD prediction [Sonnerup et al., 1981], the exhaust heating results from counterstreaming ions [Hoshino et al., 1998; Gosling et al., 2005] rather than Petschek shocks. The kinetic energy of the bulk flow driven during reconnection is a substantial fraction of the released magnetic energy, and in natural systems this energy is ultimately dissipated. However, the dominant processes that control the dissipation of these flows and their universality have not yet been established. During solar flares the termination shock that has been observed at the low-altitude edge of coronal reconnection exhausts [Masuda et al., 1994] is a possible mechanism for the dissipation of the energy in the bulk flow. Supra-arcade downflows (SADs) [McKenzie and Hudson, 1999], which are believed to be driven by reconnection, are observed to slow during their downward trajectory toward the solar surface. In the Earth’s magnetotail a key observational discovery was the formation of narrow boundary layers or fronts at the interface of the high-speed reconnection jets and the essentially stationary ambient plasma downstream. At the front the amplitude of the magnetic field normal to the initial current layer (Bz in the magnetotail) increases abruptly [Ohtani et al., 2004; Runov et al., 2009, 2011a]. Initially, such fronts (dubbed “dipolarization fronts”) were believed to result from the slowing of the reconnection outflow as it impacted the strong dipole field of the Earth, similar to coronal termination shocks. However, the measured propagation of these fronts over large distances both earthward and tailward of the reconnection site [Ohtani et al., 2004; Angelopoulos et al., 2013] is strong evidence that these fronts are generically associated with the development of reconnection in natural systems and are not specific to the geometry of a particular system. The role that reconnection jet fronts (RJFs) play is, however, unclear. It has been suggested that RJFs may be important sites for energy dissipation [Hoshino et al., 2001; Runov et al., 2011b; Angelopoulos et al., 2013]. A number of 2-D reconnection simulations (corresponding to an infinite length x-line) have been carried out to explore the structure of RJFs [Sitnov et al., 2009;Wu and Shay, 2012]. On the other hand, it is unlikely that reconnection in physical systems is 2-D since reconnection very likely onsets in a spatially localized region. Flow bursts and associated RJFs in the magnetotail are localized in the cross-tail (y) direction with DRAKE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3710 Geophysical Research Letters 10.1002/2014GL060249 Figure 1. From the PIC simulation plots of Bz in the x-y plane at the center of the current sheet (z = 0) at (a) t = 0, (b) t = 12Ω−1 ci , and (c) t = 24Ω−1 ci . (d) A similar plot from an MHD simulation with nearly identical initial conditions at the same time as in Figure 1c. characteristic scales of several Earth radii RE [Angelopoulos et al., 1997; Nakamura et al., 2004] and therefore correspond to finite length x-lines. SADs have similarly been interpreted as resulting from reconnection with finite length x-lines [Linton and Longcope, 2006; Cassak et al., 2013]. We show that the structure of the exhaust and its dissipation depends critically on its 3-D structure. Since we are focusing on the structure of the reconnection outflows and the associated RJF and not on the structure of the dissipation region where field lines change topology, we explore the dynamics with the Riemann approach [Lin and Lee, 1995]. Consistent with the observations, we study how the reconnection outflow develops in a 3-D model with a finite x-line by imposing a spatially localized region of reconnected flux Bz on top of a Harris current sheet. A particle-in-cell (PIC) model is used so that the collisionless dissipation of reconnection-driven flows can be studied. The system is initially in pressure balance, but the curvature forces that drive reconnection are not balanced by any other forces and drive the outflow. We explore a system periodic in three directions: with x-z the plane of reconnection and the reconnection outflow along x. Superimposed on a double Harris current layer Bx(z) with a half width of 2.0di (with di the ion inertial length) is a region of uniform magnetic flux Bz(x, y) that is localized with a width of 8.0di in the x-y plane as shown in Figure 1a. There is no ambient guide field. The density in the region of Bz ≠ 0 is equal to the background density n0 of the Harris system. The electron and ion temperatures are adjusted so that the total pressure is balanced with Ti∕Te = 5, which is typical for the magnetosphere. Required currents are carried by both species, in proportionality to their temperature. Unbalanced forces associated with magnetic tension will drive the plasma in the region of Bz ≠ 0 to the left in Figure 1a. The motion of the plasma in the second current sheet is essentially identical but in the opposite direction is and not discussed further. The results of our PIC simulations are presented in normalized units: the magnetic field to the asymptotic value B0 of the Harris reversed field, the density to the value at the center of the current sheet minus n0 = 0.3, velocities to the Alfvén speed cA, lengths to di, times to the inverse ion cyclotron frequencyΩ−1 ci , and temperatures tomic 2 A. The computational domain is 102.4di × 25.6di × 25.6di. Other parameters of the simulations are a mass ratiomi∕me = 25, which is sufficient to separate the dynamics of the two species [Hesse et al., 1999], and speed of light c= 15cA. Shown in Figure 1 is Bz in the center of the current sheet (z= 0) at (a) t= 0, (b) t= 12Ω−1 ci , and (c) t= 24Ω −1 ci . The outflow carries the flux Bz to the left propelled by the unbalanced magnetic curvature forces that drive reconnection. The electron and ion flows in the x-y plane at t= 30Ω−1 ci are shown in Figures 2a–2d. Both species flow to the left in the core of the jet as expected. The strong electron flows at the boundaries of the jet produce a counterclockwise current loop that is the dominant source of the magnetic field Bz shown in Figure 1. A surprise in this data is the strong positive ion flow just below the main flow in a region where Bz ∼ 0, and there is therefore no curvature. The reason for this flow is discussed later. In the core of the flow jet the flux Bz is carried upward in Figure 1, which is in the electron drift direction (Figure 2c), and is compressed at the upper edge. In contrast, the left edge of the jet turns downward, which is in the ion drift direction (Figure 2d). Similar turning in the ion drift direction was seen in 3-D PIC simulations of interchange turbulence in the magnetotail [Pritchett and Coroniti, 2013]. The downward motion of electrons at the front of the jet in Figure 2c, which is opposite to their drift in the initial current layer, is due to an E × B DRAKE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3711 Geophysical Research Letters 10.1002/2014GL060249 Figure 2. As in Figure 1 at t = 30Ω−1 ci plots of (a) vex , (b) vix , (c) vey , (d) viy , (e) Ex , (f ) pixx , (g) Tixx , (h) Te , and (i) the ion heating rate Ji ⋅ E. DRAKE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3712 Geophysical Research Letters 10.1002/2014GL060249 Figure 3. Cuts of the ion density ni (solid), vix (dashed), and Bz (dotted) along x at z = 0 and y = −11.3di at the same time as in Figure 2. drift from an electric field Ex directed to the right (Figure 2e). For ions this drift adds to their ambient downward flow (Figure 2d). The asymmetry of the structure of the jet in the y direction is contrasted with the results of an MHD simulation with nearly identical initial conditions in which the jet forms a symmetrical structure in the x-y plane (Figure 1d). These MHD flows are similar to those from earlier 3-D MHD simulations of plasma interchange-driven flows in the magnetotail [Birn et al., 2004]. The direction and magnitude of the deflections of the front will likely depend on the width of the initial Harris current layer, which controls the magnitude of the initial ion drift speed. A broader initial current layer will lead to deflections in both directions, closer to that seen in the MHD model. Note also that the net displacement along x in the present simulations is far smaller than seen in the satellite data, which is a limitation of the size of the simulation. In Figure 3 are cuts of the ion density (solid), Bz (dotted), and the ion velocity vix (dashed) versus x in the center of the current sheet at t = 24Ω−1 ci . The density drops sharply across the front and into the jet although the density minimum of around 0.7 is well above the initial condition of 0.3. Bz rises sharply across the front and exhibits the distinctive dip and overshoot that are often seen in the observations [Ohtani et al., 2004; Runov et al., 2009]. The overshoot results from local compression at the front, which produces a similar peak in the density. The region of negative Bz ahead of the front can also be seen as the white region in Figure 1c in the interval −35di < x<−25di and −9di > y>−13di. The mechanism for this reversal in Bz appears to be similar to the self-generation of magnetic fields in the Weibel instability and will be discussed more fully in a separate publication. The ion velocity rises gradually ahead of the front as in observations and reaches a plateau around 0.8cA, which is well below that expected based on the upstream Alfvén speed (1.8cA). The velocity vf of the front is around 0.46cA and is calculated by stacking cuts of Bz versus x at several times (Figure 4). The reduced velocity of the front compared with that of the core of the jet results from the buildup of ion pressure ahead of the front shown in Figure 2f. The increase in pressure is largest at the top corner of the front and serves to both slow the jet and deflect it downward. Such pressure enhancements have been documented in satellite measurements [Liu et al., 2013]. The pressure increase is a consequence of the reflection of ions in the current sheet off of the head of the front, which has also been documented in satellite observations [Zhou et al., 2010] and discussed in 2-D reconnection models [Wu and Shay, 2012]. The penetration of high-velocity ions Figure 4. A stack of cuts of Bz along x at z = 0 and y = −11.3di separated by time intervals of 2Ω−1 ci starting from t = 0. The velocity of the front calculated from the peaks of Bz is 0.46cA . in the jet through the front also contributes to the pressure increase. Both classes of particles can be seen to the left of the front in the x − vx phase space in Figure 5a, which is from the center of the current sheet with y=−11.8di and t= 20Ω−1 ci . The cut of Bz in Figure 5b shows the location of the front. As expected, the reflected ions have a velocity close to cA, which is around twice vf . In Figure 2g is the ion temperature Tixx corresponding to the pressure in Figure 2f. The increase in ion temperature associated with the reflected ions is evident. The rate of ion heating Ji ⋅ E is shown in Figure 2i. Ion DRAKE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 3713 Geophysical Research Letters 10.1002/2014GL060249 Figure 5. In (a) the ion phase space vx − x in the center of the current sheet at y = −11.3di and t = 20Ω−1 ci . In (b) a cut of Bz at the same time and location. heating peaks at the front, at the lower boundary of the exhaust and in turbulent fluctuations in a broad region ahead of the front. The source of these fluctuations has not