Plasma Heating and Alfvénic Turbulence Enhancement During Two Steps of Energy Conversion in Magnetic Reconnection Exhaust Region of Solar Wind

We choose a reconnection exhaust region in the solar wind that was encountered by the ACE and the Wind spacecraft on 1997 November 23 (Gosling et al. 2005a; Phan et al. 2009; Pulupa et al. 2014) for a comprehensive study. Figure 1 shows an overview of this event based on the plasma and magnetic field measurements. The magnetic field strength, $| {\boldsymbol{B}}|$, is weakened at the trough in the time profile (Figure 1(a)). The $| {\boldsymbol{B}}|$ trough is bounded by a set of jumps in the vector magnetic field components (Figure 1(b)) and in the proton bulk velocity components (Figure 1(c))—the jumps are marked with two vertical blue dashed lines and a vertical red dashed line on each side. Walén analysis of the negatively and positively correlated $d{\boldsymbol{B}}]$ and $d{\boldsymbol{V}}$ jumps on each side confirms the existence of a pair of RDs (see Figure 2). The slope and correlation coefficient for Walén that test for the preceding RD are calculated to be −0.74 ± 0.02 and 0.95, respectively. The relation between local V_A and V − V_HT of the trailing RD is found to have a slope of +0.76 ± 0.03 and a correlation coefficient of 0.94. Under the global Minimum Variance Analysis (MVA; Sonnerup & Scheible 1998), B_N is quite small, indicating that the RDs propagate upstream of the exhaust region very slowly in the N-direction. In the L and M directions, the magnetic field line kinks of the RDs may move much faster at a substantial fraction of Alfvén speed. This MVA analysis was verified to be insensitive to the choice of the time interval as long as all of the discontinuities were included appropriately in the time interval.

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From the time sequences of proton density (N_P) and temperature (T_P) across the reconnection exhaust (Figures 1(f) and (g)), one may identify four regions (from left to right): there are two distinct regions of dense, cool plasmas separated by a transition (region 1 and region 2), and two distinct sparse, warm plasmas, also separated by a transition (region 3 and region 4). Across the interface between regions 1 and 2, one can see a decrease in $| B|$, an increase in N_P and T_P, as well as an approaching to zero of B_L. This finite-width interface is inferred to be a possible SS according to the MHD Rankine–Hugonoit conservation relation analysis (Koval & Szabo 2008; Wilson et al. 2013). Similarly, the interface between regions 3 and 4 may also be classified as another SS. The upstream and downstream velocities in the shock frames on the two sides of the exhaust are (U_up,region-1 ∼ 31 km s⁻¹, U_{down,region-2} ∼ 21 km s⁻¹) and (U_up,region-4 ∼ 95 km s⁻¹, U_{down,region-3} ∼ 49 km s⁻¹), respectively. The angles between the normal direction and magnetic field direction are (θ_{BN,up,region-1} ∼ 93°, θ_{BN,down,region-2} ∼ 97°) and (θ_{BN,up,region-4} ∼ 45°, θ_{BN,down,region-3} ∼ 41°), respectively. This is only a rough estimate of the shock properties, which may not be highly accurate due to the significant deviation of plasma velocity distribution from local thermodynamic equilibrium, and due to the existence of compound discontinuities that are likely not in a steady state. The small changes of θ_BN between up- and downstreams of the shocks are due to their coexistence with RDs, for which the situation makes them look different from the traditional pristine slow shocks.

Therefore, the pair of back-to-back SSs seems to be concurrent with the pair of back-to-back RDs. The time interval between the RDs is about 10 minutes, which is equivalent to the length of the path across the exhaust region of about 50 Earth radii.

Across the interface between region 2 and region 3 (black vertical dashed line in Figure 1), there is a declining jump in N_P and a rising jump in T_P, maintaining roughly the same thermal pressure on either side. We do not see a dramatic jump in B and V components, although $| {\boldsymbol{B}}|$ changes slightly across the interface. This interface is thus speculated to be a type of "contact interface" that keeps the two distinct materials relatively separate from one another. To see how the particles move and how the electric field self-consistently adapt around the interface, please refer to Section 2.3.

Proton thermal anisotropy, $\left({A}_{\mathrm{th},{\rm{p}}}=\tfrac{{T}_{\perp {\rm{p}}}}{{T}_{\parallel {\rm{p}}}}\right)$, as derived from the Wind/3DP/PESA-low measurements, is found to be smaller than 1 in the exhaust region (Figure 1(h)) where the proton parallel plasma beta (${\beta }_{\parallel ,{\rm{p}}}$) sees a dramatic increase (Figure 1(i)). This indicates a preferential parallel heating of protons in the exhaust region associated with a lesser increment in ${T}_{\perp {\rm{p}}}$. In Figures 1(h) and (i), the proton core and beam populations are treated as a whole when calculating ${A}_{\mathrm{th},{\rm{p}}}$ and ${\beta }_{\parallel ,{\rm{p}}}$.

Pitch-angle distributions of electron differential flux density (e-flux) at two energy channels (47.5 and 228.2 eV) are illustrated in Figures 1(j) and (k). It is found that, in the exhaust region and especially in the downstream of cool and dense plasmas, there is a distinct enhancement of parallel and anti-parallel e-flux at the lower energy channels less than 150 eV. For the higher energies, the electrons are mainly travelling along the magnetic field line. Therefore, it is the lower energy rather than higher-energy electrons that may be trapped and energized by the magnetic field configuration and electric potential distribution within the exhaust region. The direction of the dominant suprathermal electron flux at higher energies indicates that the magnetic reconnection is an interchange reconnection between IMF lines with the same polarity on the Sun, rather than a reconnection between IMF lines of opposite polarities causing disconnection and strahl dropout (Gosling et al. 2005b) or a reconnection between traditional non-kinked open and closed IMF lines (Crooker et al. 2004).

The interchange reconnection between two IMF flux tubes with the same polarity at the solar surface is illustrated conceptually in Figure 3(a). The kinked IMF flux tube, which may be bent by non-uniform flow speeds or formed by an earlier reconnection at a lower altitude or a growing result of kink instability due to strong magnetic twist inside flux ropes (Zaqarashvili et al. 2014), tends to be interchange reconnected with the ambient and relatively straight flux tubes. The reconnection might also be within complex interplanetary coronal mass ejections (ICMEs) with the far-end loosely connected to the Sun due to the existence of asymmetric but still counter-streaming strahl electrons. Figure 3(b) shows how the spacecraft passes through the magnetic reconnection exhaust configuration and what the jet flow velocity vectors look like. The change of state from (large $| {B}_{L}|$, small $| {B}_{M}|$) outside to (small $| {B}_{L}|$, large $| {B}_{M}|$) inside of the exhaust region is also illustrated. Flow velocity vectors, as denoted with yellow arrows, have two main components (V_L and V_M) in the exhaust region. The V_L component is the velocity of the jet flow as accelerated by the slingshot effect of the reconnected magnetic field lines (MFLs). The V_M component is mainly the result of the direction change of plasma momentum in the RD moving frame (one type of De Hoffmann–Teller (HT) frame; De Hoffmann & Teller 1950), in which both the upstream and downstream velocities are field-aligned and of similar magnitude. $| {V}_{M}|$ is approximately equal to V_A, since the RD is propagating mainly in the L-direction at about V_A with respect to the upstream plasma. In the reference frame of the downstream mean flow, V_M changes from one polarity to another polarity in the exhaust region.

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This kind of contact interface is different from the MHD contact discontinuity, since the free penetration of protons across the interface in the collisionless space plasmas is partially held back by a self-consistent electric potential barrier developed around the interface according to kinetic simulation results (see Figure 4).

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To see if the contact interface can be maintained somehow and the protons can be reflected back at the contact interface, a 1D hybrid simulation is conducted to model the time evolution of the contact interface. Note that, in the setup of hybrid simulation, proton kinetics are described with the Vlasov equation and electrons are approximated as a fluid (Ruan et al. 2016). This 1D model provides a rough, but qualitatively useful, approximation to the evolution of spatial distribution of plasma states along the N-direction in the distant exhaust region. Here we neglect the spatial inhomogeneity of magnetized plasmas in the L-dimension, which is assumed to be relatively uniform as compared to the N-dimension in the distant exhaust region far away from the reconnection site. This 1D approximation is inspired by Lin & Lee (1995), who utilized the 1D MHD and hybrid simulations to study the evolution of the reconnection exhaust region by solving the Riemann problem there. Our 1D model differs from the preceding works in introducing counter streams in the opposite directions on either side of the interface to mimic the downstream flows in the HT reference frame, which is moving basically along with the jet flow in the L-direction.

Initially, across the contact interface, there exists a thermal pressure balance between both sides, with a cool and dense plasma and a warm and tenuous plasma on the left and right sides, respectively (see panels (a1), (a2), and (a4) in Figure 4). The plasmas on both sides are flowing in the opposite directions heading toward the contact interface. As the time evolves, a bipolar electric field (see (b5 )in Figure 4) is formed, leading to a positive potential around the contact interface. This positive potential plays a role in reflecting the major part of protons back to their original incident sides, while leaving the other protons penetrating through the interface into the opposite side (see (b1) in Figure 4). By applying the moment analysis to the proton velocity distribution, the density and temperature are found to increase on both sides but still remain as a significant transition (imbalance) across the interface.

The proton heating signature in the exhaust region is illustrated in Figure 5. Eight snapshots of p-VDF are aligned in position to follow the MFL configuration. The p-VDFs at (t1), (t2), (t3, t4) are upstream of the cool and dense plasmas in the transition layer, and in the deep downstream of the cool and dense plasmas, respectively. From the upstream to the downstream, the p-VDF experiences a significant change: development of a beam population parallel to B₀, with the core population heading toward the contact interface. On the other side of the contact interface, the p-VDFs downstream and upstream of the warm and sparse plasmas are displayed in panels (t5)–(t8). The p-VDFs at (t5, t6) have two populations with the main population drifting along the field toward the contact interface and the second population toward the compound structure of RD and SS. The relative drift between the primary and secondary populations at (t5, t6) is larger than that at (t3, t4), causing part of the second population to extend beyond the measured range.

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The core + beam p-VDF in the exhaust region is commonly called a dumbbell distribution if the two components are well detached from and comparable to one another. It is interesting that the p-VDFs show different patterns on both sides of the contact interface. It is expected that the HT (propagating RD) frame is moving mainly along with the jet flow in the L-direction. The upstream plasma in the HT frame moves toward the discontinuity at about V_A, and turns to follow the field line direction in the downstream exhaust region with a slight slow-down in speed due to the higher thermal pressure downstream. Traditionally, in the exhaust region of symmetric reconnection, the major core population may be the plasmas coming from the nearest upstream, while the minor beam population may be from the upstream on the other side. However, in our case with reconnection between asymmetric plasmas, the beam population on one side of the contact interface is distinctly different in the thermal state from the core population on the other side, yet similar to the core population on the same side. Therefore, the beam (second) population might be attributable to reflection at the contact interface by some electric potential barrier yet to be measured and confirmed.

Note that coordinate origin of the proton-VDFs in Figure 5 has been translated to the velocity position with maximum phase space density from the original velocity position of the spacecraft, which can be approximated as static when compared to the supersonic solar wind flow. To illustrate the difference of both bulk velocity and thermal state between the upstream and downstream of the exhaust region, we present the original 3D-VDFs in Figure 6. The VDFs of α particles are also recorded in the figure, showing remarkable expansion of the contour surfaces in the exhaust region, similar to that of protons. The velocity for α particles in the figure is just derived with the proton's mass-to-charge ratio without adopting its real mass-to-charge ratio.

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The electron velocity distribution function (e-VDF) illustrated in Figure 7 also shows a clear signature of the parallel heating of its core component in the exhaust region. As a result of the preferential parallel heating, the pitch-angle distribution of the differential flux density at energies lower than 200 eV is mainly concentrated around 0° and 180° (Figure 1(j)). For the electrons above 200 eV, which do not show a difference in e-VDF between the exhaust and ambient region, they seem not to be affected and trapped by the speculated electric potential. The same dominant direction of the asymmetric, but still counter-stream, strahl electrons above 200 eV (parallel to local B₀) throughout the upstream and downstream regions indicates the nature of the interchange reconnection between two IMF flux tubes (probably affiliated with a complex B-field system involving ICME) with the same (positive) polarity of their near-end footpoints on the Sun. Note that the existence of weak, field-aligned proton heat flux in the upstreams on both sides of the exhaust region, as discerned from the measurements by the 3DP and Solar Wind Experiment (SWE) instruments, also indicates the same polarity of near-end footpoints for these two flux tubes.

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Besides the RDs with steps of correlated/anti-correlated jumps mainly in B_L and V_L components, the fluctuations in other time intervals show a good sense of Alfvénic correlations as well, which are illustrated in Figures 8(a)–(c) showing the cross-correlation spectra of (B_L, V_L), (B_M, V_M), and (B_N, V_N). For example, B_N and V_N are highly anti-correlated on the cool and dense side of the contact interface, while in positive correlation they are on the warm and sparse side. Unlike the single step of jump in B_L and V_L across the RD, the B_N and V_N components oscillate in large amplitude over several cycles near the RD. These features indicate that Alfvén waves, besides the RDs, are propagating in the opposite direction on the either side of the contact interface. There seems to be a wave source near the contact interface, emanating Alfvénic fluctuations outward. The Alfvén waves generated in the exhaust region are stronger in power spectral density (PSD) than those in the ambient undisturbed regions (see Figure 9).

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The free energy to generate these Alfvénic fluctuations may come from the plasma kinetic energy through a certain instability mode, e.g., the magnetic firehose instability (Bale et al. 2009; Maruca et al. 2012; Klein 2017). The magnetic tension can be reduced in the plasma with large ${T}_{\parallel }/{T}_{\perp }$ and/or with relative drift between multi-components/multi-species. As a consequence, the MFL is subject to oscillating deformation and propagating waves. Patchy regions of firehose unstable plasma have been measured in exhausts in the Earth's magnetotail (Hietala et al. 2015). Those studies did not, however, present evidence of excited waves. As illustrated in Figure 5, the p-VDFs with a dumbbell shape may be prone to the firehose instability. Since the 3DP/PESA-low cannot record the full p-VDF at some times, we adopt the parameters of protons and alpha particles derived from the SWE measurements (Kasper et al. 2002; Stevens & Kasper 2007). We calculate ${{\rm{\Lambda }}}_{f}={\sum }_{s}\tfrac{{P}_{\parallel ,s}+{\rho }_{s}\cdot {v}_{d,s}^{2}-{P}_{\perp ,s}}{2\cdot {P}_{B}}$, a parameter that indicates long-wavelength firehose instability when it takes a value greater than 1 (Chen et al. 2016), based on the magnetic pressure, P_B, and the parameter sets (mass density, ${\rho }_{s}$, drift velocity, ${v}_{d,s}$, and parallel and perpendicular thermal pressure, ${P}_{\parallel ,s}$ & ${P}_{\perp ,s}$) of various species denoted as s (proton core, proton beam, and alpha particle). The time sequence of ${{\rm{\Lambda }}}_{f}$ is plotted in Figure 8(f), which shows that ${{\rm{\Lambda }}}_{f}$ is larger than 1 at two moments in time, with the largest one being close to the contact interface. We also scatterplot the ion (protons and α particles) plasma parameters (${\beta }_{\parallel ,{\rm{p}}+\alpha ,\mathrm{eff}}$, $\tfrac{{P}_{\perp ,{\rm{p}}+\alpha ,\mathrm{eff}}}{{P}_{\parallel ,{\rm{p}}+\alpha ,\mathrm{eff}}}$) and compare them with the instability thresholds, finding that the downstream plasma conditions (red solid diamonds and blue solid squares for warm and cool downstreams, respectively) are closer to or even beyond the threshold of firehose instability (Hellinger et al. 2006). The threshold formulas of (${\beta }_{\parallel }$, $\tfrac{{P}_{\perp }}{{P}_{\parallel }}$) for MHD, kinetic parallel, and kinetic oblique firehose instabilities are $A=1-\tfrac{1}{{\beta }_{\parallel }}$, $A=1-\tfrac{0.47}{{({\beta }_{\parallel }-0.59)}^{0.53}}$, and $A=1-\tfrac{1.4}{{({\beta }_{\parallel }+0.11)}^{1.0}}$, respectively (Hellinger et al. 2006). The effective parallel plasma beta, ${\beta }_{\parallel ,{\rm{p}}+\alpha ,\mathrm{eff}}$, is calculated with ${\beta }_{\parallel ,{\rm{p}}+\alpha ,\mathrm{eff}}\,=\tfrac{{P}_{\parallel ,\mathrm{pc}}+{\rho }_{\mathrm{pc}}\cdot {v}_{d,\mathrm{pc}}^{2}}{{P}_{B}}+\tfrac{{P}_{\parallel ,\mathrm{pb}}+{\rho }_{\mathrm{pb}}\cdot {v}_{d,\mathrm{pb}}^{2}}{{P}_{B}}+\tfrac{{P}_{\parallel ,\alpha }+{\rho }_{\alpha }\cdot {v}_{d,\alpha }^{2}}{{P}_{B}}$, where the subscripts "pc," "pb," and "α" represent the proton core, proton beam components, and alpha particles, respectively, and the drift velocities are with respect to the mass center of the proton core, proton beam, and alpha population. The effective pressure anisotropy is determined by $\tfrac{{P}_{\perp ,{\rm{p}}+\alpha ,\mathrm{eff}}}{{P}_{\parallel ,{\rm{p}}+\alpha ,\mathrm{eff}}}\,=\tfrac{{P}_{\perp ,\mathrm{pc}}+{P}_{\perp ,\mathrm{pb}}+{P}_{\perp ,\alpha }}{({P}_{\parallel ,\mathrm{pc}}+{\rho }_{\mathrm{pc}}\cdot {v}_{d,\mathrm{pc}}^{2})+({P}_{\parallel ,\mathrm{pb}}+{\rho }_{\mathrm{pb}}\cdot {v}_{d,\mathrm{pb}}^{2})+({P}_{\parallel ,\alpha }+{\rho }_{\alpha }\cdot {v}_{d,\alpha }^{2})}$.