Observations of Hall Reconnection Physics Far Downstream of the X Line

R. Mistry, J. P. Eastwood, C. C. Haggerty, M. A. Shay, T. D. Phan, H. Hietala, and P. A. Cassak The Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA Space Sciences Laboratory, University of California, Berkeley, California 94720, USA Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, California 90095, USA Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA (Received 27 April 2016; revised manuscript received 10 August 2016; published 28 October 2016)

Magnetic reconnection plays a crucial role in many plasma systems by reconfiguring the magnetic field topology, heating the plasma, and forming jets of fast plasma outflow [1]. Of key importance for collisionless reconnection is the diffusion region, where kinetic effects result in the topological field change. Within this region electrons and ions decouple from the field on different spatial scales, resulting in differential motion between the species and the generation of Hall currents, Hall magnetic fields, and Hall electric fields [2]. Hall magnetic fields in symmetric antiparallel reconnection produce a characteristic quadrupolar Hall field (e.g., Refs. [3,4]), which is often noted as an indicator of proximity to the diffusion region in in situ satellite observations (e.g., Refs. [5][6][7]). In the more general case of guide field reconnection, the Hall field is distorted by Lorentz forces acting on the electron current in the ion diffusion region [8][9][10].
The majority of plasma in the exhaust does not pass through the diffusion region and energy conversions primarily occur across the exhaust boundaries or within the exhaust itself. How this happens is determined by the structure of the exhaust. Understanding the exhaust is therefore important in determining how reconnection affects energy flows in the systems in which it occurs. Reconnection exhausts at large distances from the X line are often described in a magnetohydrodynamics (MHD) framework which does not include kinetic physics (e.g., Refs. [11,12]). Despite this, the kinetic process of ions counterstreaming along magnetic field lines has been observed far downstream in the exhaust region in the solar wind [13]. It is therefore important to understand where non-MHD effects are important in the reconnection process, and whether MHD can sufficiently capture the physics of the exhaust region. In the solar wind, reconnection generally forms quasi-two-dimensional exhausts [14] which are comparable to two-dimensional simulations. Solar wind reconnection occurs with a range of guide field strengths [15] and occurs within a large system (the heliosphere), producing extended exhausts in the outflow direction [16,17]. This makes in situ observations ideal for determining the exhaust structure at much larger distances from the X line than can currently be simulated.
Here we present in situ observations of Hall magnetic fields in solar wind exhausts, revealed by bipolar perturbations to the out-of-plane field. These are compared to an appropriately scaled particle-in-cell (PIC) simulation, showing that the Hall fields are generated by kinetic scale electron flows in the exhaust. These signatures are observed thousands of ion inertial lengths downstream of the X line, indicating that these Hall signatures can persist far downstream and well into regimes typically described with MHD. Figure 1 shows data from the Wind spacecraft [18] on 2002-03-13 (event 1) in a LMN coordinate system determined by hybrid minimum variance analysis of magnetic field data [19]. L is the exhaust outflow direction, M is the out-of-plane direction, and N is the current sheet normal. The rotation in B L at 01∶53∶46-01∶53∶58 UT indicates the passage of a current sheet which is accompanied by an exhaust outflow in the þL direction, [panel (f)]. The outof-plane component of the field (B M ) is 1.3 times the reconnecting field (B L ) in the inflow region. B M is increased within the majority of the exhaust (shown in red). One-dimensional Riemann problems [20,21] and twodimensional hybrid simulations [22] of guide field reconnection show that rotational discontinuities form at the  Figure 2(a) shows the expected Hall field within the ion diffusion region and Wind's trajectory through the reconnection exhaust. The polarity of the observed bipolar perturbation to B M , and that the decrease in B M is smaller in magnitude and duration than the increase, is qualitatively in agreement with previous studies on the distortion of the quadrupole structure in symmetric reconnection [8,10]. Spatial distances in the normal direction corresponding to time intervals (δt) are measured as ðV sw :NÞδt, where V sw is the solar wind velocity. The total exhaust width is measured to be 25d i , where d i is the ion inertial length using the mean ion density in the inflow regions (4.7 cm −3 ).
A quantitative comparison is made between these observations and a fully kinetic 2.5-dimensional PIC simulation using the P3D code [23]. Magnetic field strengths and particle number densities are normalized to their values in the inflow regions, jB 0 j and n 0 , respectively. Lengths are normalized to the ion inertial length d i ¼ c=ω pi0 at n 0 , and velocities to the Alfvén speed c A0 ¼ p ½B 2 0 =ðμ 0 m i n 0 Þ (the speed of light is c=c A0 ¼ 11). Simulations are performed in a periodic domain with a system size of S L × S N ¼ 366.4 d i × 183.2 d i , with 100 particles per grid in the inflow region. The system was initialized with two Harris current sheets superimposed on an ambient population (as detailed in Ref. [24]), with an ion-to-electron mass ratio of 25. The guide field is 1.3 times the reconnecting field, and ion and electron beta are 1.2 and 1.7, respectively, to match observations in the inflow regions. Figure 2(b) shows the simulation out-of-plane magnetic field at a time when reconnection reached a steady state (57 ion cyclotron periods), in the same coordinate system used for observations. The simulation exhaust width at L ¼ 80 d i is comparable to the observed exhaust width. Simulation data from this cut are compared to observed data in Fig. 1 by converting from simulation units to physical units. The shear in V L across the exhaust in the observations is not included in the simulation. Despite this we find excellent agreement between the simulated and observed data, including B M . The width of the exhaust increases with distance from the X line, making it difficult to compare other spatial cuts to the observations. We therefore compare magnetic field hodograms from cuts at 25 ≤ L ≤ 110 d i at 5 d i intervals to the observed data in Fig. 1(i). There is excellent agreement in magnetic structure at all cut locations.
The B M Hall field is associated with a J L Hall current. L components of the current, ion (V iL ) and electron (V eL ) velocities at L ¼ 80 d i are shown in Fig. 2(c). V iL is positive throughout the exhaust. V eL , however, is negative at −11 < N < −9. Further analysis shows that here V eL is largely field aligned, corresponding to electron flow towards the X line. J L is positive, which decreases B M and generates the negative Hall field. Similar electron flows can also be seen closer to the X line in smaller-scale simulations [25].
At −8 < N < 9, the electron velocity is shifted in the -N direction relative to the ion velocity. At −8 < N < −4, V iL < V eL and J L is negative. At 5 < N < 8, V iL > V eL and J L is positive. The Hall magnetic fields are therefore generated by current systems [shown in Fig. 2(a)] associated with an electron flow towards the X line at one separatrix, as well as a relative shift between the ion and electron outflows in the N direction. Note that this shift is qualitatively consistent with the deflection of the in-plane electron current in the ion diffusion region in the presence of a guide field (and is associated with the kinetic Alfvén wave structure of guide field reconnection [26]), and that the negative J L current remains significantly deflected from the midplane far downstream of the X line. Wind ion and electron velocities cannot be resolved at sufficiently high resolution to directly determine J L ; therefore, J L is calculated from Wind magnetic field observations, J L ≈ −dðB M Þ=dN [the contribution from dðB N Þ=dðMÞ is negligible as B N ∼ 0], which shows good agreement with the simulation [ Fig. 1(e)]. The J L current layer between the negative and positive Hall fields is measured to have a full width at half maximum of 1.1 d i and 1.3 d i in the observations and simulations, respectively. The presence of these signatures far downstream of the X line indicates that MHD treatments may be unable to sufficiently describe the exhaust region and its structure.
We identify a total of 8 events (including event 1) which show clear evidence of Hall magnetic fields from a list of 197 solar wind reconnection exhausts observed by Wind by Ref. [15]. An LMN coordinate system was first determined for each event. Identified events were found by a search for clear bipolar perturbations of B M within the exhaust interval. Positive and negative perturbations to B M were not required to be equal in duration or magnitude as this does not occur in general for guide field reconnection, as illustrated by event 1 and the simulation. Events with strong fluctuations in B N or large differences in V L across the current sheet (more than 75% of the exhaust outflow speed) were not considered. No requirement was imposed on the polarity of bipolar B M perturbations. The polarity for all 8 identified events was consistent with that expected for Hall fields; no events were identified with the incorrect polarity. Guide fields for the identified events are between 0.3 and 1.6, whereas the range for all events in the list is 0-10. Figure 3 shows B M for all 8 events as a function of distance through the exhaust in N. At all events the decrease in B M is narrow and confined to the edge of the exhaust. Relative distances from the X line (determined from measurements of the exhaust width and assuming an equal reconnection rate at all events) are shown on the right, indicating that this pattern is observed even at very large distances downstream. From full width at half maximum measurements of J L , the current layers between the negative and positive Hall fields are determined to have widths in the normal direction of 0.8 − 6.0 d i . In addition to these ion-scale structures which are not an MHD phenomenon, the majority of the exhaust shows an increase in B M which is a fluid effect related to the structure of the exhaust boundaries [20][21][22].
In single spacecraft observations the Hall field is observed as a bipolar variation in B M . To identify the full quadrupolar structure both exhausts must be observed (e.g., Ref. [27]). This also allows for a more accurate determination of each spacecraft's distance from the X line [17]. Reference [16] has previously studied event 7 with complimentary measurements from ACE. The two spacecraft were located on opposite sides of the X line, observed oppositely directed jets, and Ref. [16] determined Wind to be ∼9000 d i downstream of the X line. Spacecraft measurements are overlaid in Fig. 4 in the coordinate system defined in the above analysis of Wind data. The passage of a current sheet is detected at Wind (ACE) at 09∶25∶36-09∶28∶47 UT (08∶24∶24-08∶26∶54 UT), and is accompanied by an outflow in the þL (−L) direction.
Having identified bipolar changes in B M in Wind data, we carefully reexamined ACE data. B M is increased within the exhaust of both spacecraft; however, at 09∶25∶ 37.7-09∶28∶41.2 UT and 08∶24∶27.3-08∶24∶33.5UT it is decreased at Wind and ACE, respectively. These decreases correspond to regions near opposing pairs of separatricies [see Fig. 2(a)]. In guide field reconnection the distortion of the Hall field means that the reversal in the bipolar perturbation in B M does not occur at B L ¼ 0 (e.g., Refs. [8,28]), as seen in Fig. 1(i). The value of B L at which this does occur differs at the opposing exhausts. Figure 4 [e.g., Ref. [29]]. Hall signatures were clear in only 8 events (guide field of 0.3-1.6). At larger guide fields the decrease in B M is much weaker [30], making the Hall field more difficult to observe [28]. At smaller guide fields fluctuations in the exhaust can obscure Hall fields (although this is more pronounced at lower beta [31]). Furthermore, plasma asymmetries and flow shear between inflow regions can further obscure the presence of Hall signatures, and it is, therefore, perhaps unsurprising that many events from the survey do not show Hall fields despite having guide fields of 0.3-1.6. A more systematic study is required to identify under exactly which conditions Hall fields are seen.
These observations show that Hall physics can persist thousands of ion inertial lengths downstream of the reconnection X line. Reconnection exhausts can therefore contain localized regions of kinetic dynamics, which may have implications for the interpretation of observational reconnection data and for applications of MHD.