Characteristics of Multi-scale Current Sheets in the Solar Wind at 1 au Associated with Magnetic Reconnection and the Case for a Heliospheric Current Sheet Avalanche

Wind spacecraft measurements are analyzed to obtain a current sheet (CS) normal width d cs distribution of 3374 confirmed magnetic reconnection exhausts in the ecliptic plane of the solar wind at 1 au. The d cs distribution displays a nearly exponential decay from a peak at d cs = 25 d i to a median at d cs = 85 d i and a 95th percentile at d cs = 905 d i with a maximum exhaust width at d cs = 8077 d i . A magnetic field θ-rotation angle distribution increases linearly from a relatively few high-shear events toward a broad peak at 35° < θ < 65°. The azimuthal ϕ angles of the CS normal directions of 430 thick d cs ≥ 500 d i exhausts are consistent with a dominant Parker-spiral magnetic field and a CS normal along the ortho-Parker direction. The CS normal orientations of 370 kinetic-scale d cs < 25 d i exhausts are isotropic in contrast, and likely associated with Alfvénic solar wind turbulence. We propose that the alignment of exhaust normal directions from narrow d cs ∼ 15–25 d i widths to well beyond d cs ∼ 500 d i with an ortho-Parker azimuthal direction of a large-scale heliospheric current sheet (HCS) is a consequence of CS bifurcation and turbulence within the HCS exhaust that may trigger reconnection of the adjacent pair of bifurcated CSs. The proposed HCS-avalanche scenario suggests that the underlying large-scale parent HCS closer to the Sun evolves with heliocentric distance to fracture into many, more or less aligned, secondary CSs due to reconnection. A few wide exhaust-associated HCS-like CSs could represent a population of HCSs that failed to reconnect as frequently between the Sun and 1 au as other HCSs.


Introduction
The Sun constantly releases a supersonic wind of plasma and magnetic field from the solar corona into the heliosphere (Parker 1958). This inner heliosphere solar wind is commonly observed to move outward at a radial 250-500 km s −1 speed in the ecliptic plane with a fast >600 km s −1 solar wind associated with the open magnetic fields of coronal holes (e.g., Phillips et al. 1995;Cranmer 2009;Lionello et al. 2014). The origin of the slow solar wind is less certain, but it is believed to be associated with coronal streamer belts encircling the Sun (e.g., Borrini et al. 1981;Gosling et al. 1981;Marsch 1999). Parker (1958) first described how the solar magnetic field of the coronal plasma is carried away from the Sun by the solar wind. The solar rotation of the magnetic foot-points of the field and the radial outflow of coronal plasma increasingly bends the solar magnetic field from a dominant radial component close to the Sun into a spiral magnetic field with a dominant azimuthal component far from the Sun. The solar magnetic field at 1 au = 1.496 × 10 8 km heliocentric distance is commonly observed along a 45°Parker-spiral angle off a radial direction from the Sun (e.g., Luhmann et al. 1993;Chang et al. 2019). This Parker-spiral away direction is equivalent to an azimuthal angle f = 135°of the solar magnetic field in a Geocentric Solar Ecliptic (GSE) coordinate system defined as f = arctan(By/ Bx) with f = 0°along +X GSE and f = 90°along +Y GSE , and it follows that a toward Parker-spiral solar magnetic field is equivalent to f = 315°.
The heliospheric current sheet (HCS) defines the boundary between the open coronal magnetic field directed away from one high-latitude polar region, and the open coronal magnetic field directed toward the other polar region (e.g., Schulz 1973;Jokipii & Thomas 1981;Crooker et al. 1993;Winterhalter et al. 1994;Lepping et al. 1996;Banaszkiewicz et al. 1998;Smith 2001). The HCS encircles the Sun as a folded surface near the equatorial plane as a result of solar rotation that Alfvén (1977) referred to as a ballerina skirt. It is often argued that the HCS constitutes the heliospheric extension of a coronal source surface neutral line between the two polarities of the solar magnetic field, which is also known as a coronal streamer belt (e.g., Crooker et al. 1993;Smith 2001), while solar rotation and dipole tilt may contribute to the folds of the HCS (Smith 2001).
Let us define a normal, N GSE = [Nx, Ny, Nz], to this folded HCS surface at 1 au with an azimuthal angle f = arctan(Ny/Nx) in the ecliptic plane and a polar angle θ = arctan(N E /Nz). Here, N E is the magnitude of the projection of N GSE onto the ecliptic plane such that θ = 0°corresponds to a normal along +Z GSE and θ = 90°is an HCS normal contained in the ecliptic plane (Nz = 0). A dominant Parker-spiral solar magnetic field at 1 au along f = 135°therefore corresponds to an HCS normal direction with an azimuthal component aligned with the ortho-Parker direction f = 225°or 45° (Lepping et al. 1996). Winterhalter et al. (1994) analyzed the normal widths for 19 well-isolated HCS crossings at 1 au. They first defined an HCS normal width d cs = Δt cs | N • V sw |, where Δt cs is the duration of a continuous rotation of the maximum variance component of the magnetic field (Sonnerup & Cahill 1967) from one side of the HCS to the other side of the HCS. Importantly, they also applied a normal component of the solar wind velocity (V sw ) by which the HCS moved over the ISEE 3 spacecraft, where N is the direction of minimum variance of the high-cadence (6 Hz) magnetic field. This analysis resulted in a median d cs = 9100 km normal width of the HCS with a range of 3500-12,000 km. The individual HCS normal widths are, perhaps, surprisingly narrow if we consider that the Wind spacecraft obtained a median d i = 97.6 km ion inertial length at 1 au (Klein & Vech 2019). Here, 1 d i = c/ω pi is the ion inertial length, where c is the speed of light and ω pi = √ (N p e 2 /m p ò 0 ) is the proton density (N p ) dependent plasma frequency. Lepping et al. (1996) used Wind spacecraft observations to examine a subset of 212 HCS encounters during an approximate 5 month long interval with the requirement that each HCS had to satisfy a 130°rotation of the azimuthal component of the solar magnetic field. This criterion reflected their assumed definition of an individual HCS crossing as a field transition through about 180°in no more than tens of minutes. They subsequently assumed a 420 km s −1 radial solar wind flow to report an average thickness of 64,000 km. This average HCS width is certainly an overestimate of the actual HCS normal widths of the analyzed events, given the radial flow speed assumption and the histogram distributions of the azimuthal and polar angles of the HCS normal direction also reported by Lepping et al. (1996).
However, it appears that the normal width of the HCS can be expected in a very broad range at 1 au from ∼35-120 d i (Winterhalter et al. 1994) to ∼600-700 d i widths (Lepping et al. 1996) for a statistical median d i ∼ 100 km.
Any given HCS encounter is often associated with many current sheet (CS) crossings occurring over a period that may last up to 1-2 days (e.g., Crooker et al. 1993;Winterhalter et al. 1994;Smith 2001), which is short compared with a 27 day solar rotation period. There is no conclusive interpretation of this swarm of HCS crossings at 1 au on the basis of single spacecraft observations. Early suggestions have included a wave-like signature of the HCS, or multiple helmet streamers associated with multiple parallel CSs, extending out into the heliosphere from the corona (Crooker et al. 1993).
The coherent HCS feature that we ultimately associate with a rotation of an open Parker-spiral solar magnetic field, whether consisting of one or multiple parallel layers of current, is not the only source of CS-associated magnetic field rotations in the 1 au solar wind. At the lower end of a normal width distribution, Vasquez et al. (2007) performed a statistical study of kinetic-scale CSs in 3 Hz cadence magnetic field observations from the ACE spacecraft during a 27 day solar rotation period. This study reported a most probable ∼4 d i normal width for small 3°< θ < 30°magnetic field rotation angles across the CSs, and a most probable ∼8 d i normal width for magnetic field rotation angles θ > 30°. Analyses of 17,043 kinetic-scale CSs with normal widths on the order of 0.1-10 d i by Vasko et al. (2022) resulted in a correlation between this θ-rotation angle and a CS normal width (d cs ) in the solar wind at 1 au such that θ ∼ 19°(d cs /d i ) 0.5 . Vasquez et al. (2007) first associated the source and clustering tendency of kinetic-scale CSs with Alfvénic turbulence in the ecliptic plane of the solar wind. It is well known that the solar wind is in a state of varying degree of turbulence, as reviewed by Bruno & Carbone (2013), from in situ measurements in the ecliptic plane (e.g., Matthaeus & Goldstein 1982) and out of the ecliptic plane (e.g., Chen et al. 2012). Numerical simulations of MHD turbulence further support the formation of coherent structures such as CSs and magnetic islands (e.g., Matthaeus & Lamkin 1986;Servidio et al. 2009Servidio et al. , 2010Zhdankin et al. 2013;Mallet et al. 2016;Dong et al. 2018).
CSs near the ecliptic plane of the solar wind at 1 au, whether associated with a source in solar wind turbulence or with a source in a coronal streamer belt, may disrupt due to a magnetic reconnection tearing instability (e.g., Priest & Forbes 2000) as first reported by Gosling et al. (2005a). Magnetic reconnection is a fundamental plasma physics process that changes the connectivity of magnetic fields within a highly localized region of a CS and allows plasmas to mix across the boundary. Birn et al. (2001) show how a critical CS thickness on the order of 1-2 d i can lead to an explosive type of tearing-mode reconnection (Lakhina & Schindler 1983;Drake et al. 1983).
A major characteristic of reconnection is the conversion of magnetic energy into plasma acceleration from the topological X line in two opposite jets along the CS (e.g., Davis et al. 2006;Eriksson et al. 2009). The maximum jet speed in the CS frame of reference is theoretically limited to the Alfvén speed of the ambient plasma. The jets subsequently expand in a normal direction with downstream distance from the X line into two reconnection exhausts. The opening angle of this normal exhaust expansion is limited to the rate of reconnection at the X line. However, Shepherd et al. (2017) caution that the out-ofplane component of the magnetic field may force the exhaust to remain collimated in a normal direction beyond a critical distance from the X line. An important consequence of this collimation process is that a fraction of solar wind exhausts may not necessarily represent an ever-expanding jet population originating from distant reconnection X lines in very extended and thin, kinetic-scale CSs.
The MMS satellites have encountered many X-line electron diffusion regions in the Earth's magnetosphere (e.g., Burch et al. 2016aBurch et al. , 2016bEriksson et al. 2016;Webster et al. 2018). There are no reports of such fortunate encounters in the vastness of the solar wind. However, there are plenty of Alfvénic reconnection outflows of varying normal widths in the solar wind as recorded by different spacecraft at 1 au (e.g., Gosling et al. 2005a;Phan et al. 2006Phan et al. , 2009Phan et al. , 2010Eriksson et al. 2009Eriksson et al. , 2014Eriksson et al. , 2015Pulupa et al. 2014;Enžl et al. 2014;Mistry et al. 2016Mistry et al. , 2017, Ulysses observations of 91 exhausts beyond 1 au (Gosling et al. 2006a), Helios observations at 0.3-1 au (Gosling et al. 2006b), and Parker Solar Probe observations much closer to the Sun (e.g., Phan et al. 2020Phan et al. , 2021. Osman et al. (2014) employed a method of partial variance increment on 3 s cadence magnetic field measurements to identify 521 CSs deemed to be associated with reconnection exhausts as recorded by the Wind spacecraft to suggest that reconnecting CSs are concentrated in periods of intermittent turbulence in the solar wind. Numerical simulations and in situ observations indeed seem to suggest that turbulence and magnetic reconnection may be two intricately linked processes (Gosling 2007;Retinò et al. 2007;Lapenta 2008;Cho & Lazarian 2009;Servidio et al. 2012;Osman et al. 2014;Loureiro & Boldyrev 2017;Mallet et al. 2017;Dong et al. 2018). Lazarian & Vishniac (1999) proposed that turbulence may enhance the rate of reconnection, and Lazarian et al. (2020) even imply that turbulence may determine the reconnection rate in realistic 3D, large-scale astrophysical systems such as the solar wind.
A major outstanding question, despite all of the reconnection exhaust evidence amassed so far in the ecliptic plane of the solar wind at 1 au, is whether intermittent turbulence of the solar magnetic field drives the process of CS formation and subsequent magnetic reconnection, as first envisioned by Matthaeus & Lamkin (1986) and Osman et al. (2014), and later modeled by Loureiro & Boldyrev (2017) and Mallet et al. (2017), or whether magnetic reconnection X lines and their downstream exhausts lead to the observed intermittent turbulent behavior of solar wind CSs, as implied by Lapenta (2008) and Lapenta & Lazarian (2012). In other words, is it possible that the 1 au solar wind may support two scale-dependent regimes, wherein one scenario dominates the other? Section 2 of this paper describes the sliding window method that we used to identify reconnection exhausts across solar wind CSs in the Wind spacecraft observations, and we provide a few initial examples of exhausts at relatively small scales. Section 3 presents a set of histogram distributions of exhausts at 1 au. In Section 4, we first discuss the nature of exhaust-associated CSs and the orientation of their normal directions in the solar wind.
We also review what is known about reconnection across the HCS, and discuss the large-scale implication of a commonly observed CS bifurcation across reconnection exhaust layers (Gosling & Szabo 2008) for the evolution of the HCS through multi-scale magnetic reconnection. Section 4 provides a summary and conclusions.

CS Identification and Reconnection Exhaust Confirmation
In order to address the fundamental question of the intricate link between turbulence and magnetic reconnection, we opt to exploit the long-term availability of Wind spacecraft measurements (Wilson et al. 2021) from 2004 July 1 to 2014 December 31 in the ecliptic plane of the solar wind to collect a statistically significant sample of reconnection exhausts. We employ magnetic field (B) measurements at 3 s and 92 ms resolution in GSE coordinates from the Wind Magnetic Field Investigation instrument (Lepping et al. 1995) and 3 s cadence plasma measurements of density N p , proton temperature T p , and velocity V in GSE coordinates from the Three-Dimensional Plasma (3DP) instrument (Lin et al. 1995).
Individual periods of 3 s cadence B, N p , and V measurements are obtained from the NASA CDAWeb with the plasma observations first interpolated to the same time as B. The B measurements are then surveyed for changes in any of the three GSE components (Bx, By, Bz) individually within each time period of a sliding window of constant duration that we advance forward in time by the length of the window. In these Wind data, we required |ΔBx| 1 nT or |ΔBy| 1 nT or |ΔBz| 1 nT in a given time window to be classified as a potential CS. The three components of the average magnetic field B 1 and B 2 adjacent to each time window containing this change in B are obtained as individual three data-point averages. The magnetic field centered at time periods of potential CSs and the corresponding interpolated V are then rotated from GSE to a boundary-normal coordinate system that we define using a cross-product normal N = B 1 × B 2 /| B 1 × B 2 |. The routine finds a maximum variance L m direction from a minimum variance analysis of B (Sonnerup & Scheible 1998) across the field gradient. Finally, the two orthogonal unit vectors to N are defined as M = N × L m /| N × L m |, which is also referred to as the out-of-plane or guide-magnetic field direction, and L = M × N, which is close to the direction of maximum variance. In the presence of magnetic reconnection across a CS, this L direction corresponds to the component of the magnetic field that reconnects across the CS and the direction of the reconnection exhaust. This boundary-normal LMN system is more robust than using the three eigenvectors of the minimum variance analysis of B (Knetter et al. 2004;Vasquez et al. 2007). A cross-product normal is also preferred when examining a CS for the presence of a reconnection exhaust for two other reasons. First, particle-in-cell (PIC) simulations of magnetic reconnection show that a CS normal component of B can experience relatively large fluctuations across a CS in the presence of exhaust structure, e.g., magnetic islands (Eriksson et al. 2014(Eriksson et al. , 2015. This variability is suppressed by default along a minimum variance normal direction. Second, PIC simulations typically show a very small magnitude B N component away from the reconnecting CS layer, which is not always the case when using a minimum variance N direction in the solar wind. Finally, we define a CS from the requirements that the gradient of the B L component of the surveyed lower-cadence magnetic field across an identified time window be monotonic with |ΔB L | 1 nT and that B L changes sign. Each CS is subsequently examined for the presence of a reconnection exhaust following the observation signatures first reported by Gosling et al. (2005a) that B L and V L need to be correlated on one side, and anticorrelated on the other side of the CS. In other words, we require that the V L component of the 3 s (interpolated) V peaks, with |V Lpeak | as the local maximum or local minimum, during the B L rotation. The jet candidate is obtained as ΔV L1 = |V Lpeak -V L1 | on the leading edge of the window, and ΔV L2 = |V Lpeak -V L2 | on the trailing edge of the window. Here, V L1 and V L2 are the two values adjacent to the sliding window. Each exhaust candidate is stored separately for each of the chosen time windows for later consideration of whether it may also satisfy the Walén relation V WL = V L0 ± ΔV AL as expected for a magnetic reconnection exhaust (Paschmann et al. 1986), where ΔV AL is given as Here, μ 0 = 4π × 10 −7 Vs/Am is the permeability of free space and the other parameters indicated with a subscript "0" (V L0 , B L0 , ρ 0 ) correspond to the given external parameter at the start time of the Walén prediction, whether that is before the CS (leading side) or after the CS (trailing side). The positive and negative signs of ΔV AL are chosen automatically according to the direction of the potential jet (ΔV L > 0 or ΔV L < 0). The reconnection exhaust confirmation is conducted semimanually for each unique jet candidate as follows. We first obtain the original Wind B and V data in a GSE coordinate system, rotate the 3 s cadence V and the high-cadence 92 ms B from GSE to the preliminary LMN system as previously stored from the initial CS survey, and manually select new times adjacent to the highly resolved CS using software publicly available from the SPEDAS libraries (Angelopoulos et al. 2019). This allows us to obtain a revised determination of the cross-product normal N vector and to update the pseudomaximum variance L vector and the M vector accordingly for an optimized LMN system. This optimization step is taken, since the times of the automated sliding window procedure that applies a lower-cadence B may have clipped a local CS when viewed in a higher 92 ms cadence B. We subsequently rotate the 3 s V and the 92 ms B from GSE to the revised LMN system and determine the actual CS duration by selecting a start time and a stop time of the B L rotation period of the CS on the basis of the high-cadence B L . Finally, we examine whether the suggested enhancement of the plasma flow across the CS is consistent with a magnetic reconnection exhaust by performing the Walén test V WL = V L0 ± ΔV AL on the L component of the proton velocity (V L ) based on a tangential momentum balance (e.g., Sonnerup et al. 1981;Paschmann et al. 1986;Eriksson et al. 2009Eriksson et al. , 2014. This test is performed from each side of all CSs separately, since V L and B L need to be in phase across one exhaust boundary and they need to be out of phase across the other exhaust boundary. The Walén test applies the highcadence B L magnetic field at 92 ms and a mass density ρ = N p m p interpolated to this B L . We applied the sliding window on Wind spacecraft measurements using different time-averaged Δt avg cadence data for a total of six sliding window durations: Δt = 12 s, 18 s, 2 minutes, 4 minutes, 10 minutes, and 20 minutes from 2004 July 1 to 2014 December 31. Here, Δt avg = 3 s cadence data are used for the small windows, Δt = 12 and 18 s, time-averaged Δt avg = 1 minute data are used for the intermediate duration windows Δt = 2 and 4 minutes, and time-averaged Δt avg = 5 minute data are used for the long-duration windows Δt = 10 and 20 minutes. The six sliding window surveys resulted in a total of 3374 confirmed reconnection exhausts following the Walén analysis from an initial pool of 4945 candidate exhaust events. The discarded events were associated with data gaps, data spikes, underresolved CSs in plasma data, or displaying an Alfvénic perturbation of only one sense (correlated or anticorrelated B L and V L ) across the entire CS. The set of 3374 exhaust-associated CSs that the Wind spacecraft encountered should be considered as the tip of the proverbial iceberg, if we consider that many other discrete time duration windows can be applied to Wind spacecraft measurements for this 10 yr interval. However, the confirmed exhaust-associated CSs represent a statistically significant data set as compared with the 188 exhausts reported by Mistry et al. (2017), 197 exhausts by Phan et al. (2010), 418 exhausts by Enžl et al. (2014), or 521 exhausts reported by Osman et al. (2014), all of which also relied on Wind spacecraft observations due to its long-term presence collecting 3 s cadence plasma observations in the solar wind. Figure 1 illustrates the measurements of magnetic field (panels (a)-(c)), proton velocity (panels (d)-(f)), plasma number density (g), proton and electron temperatures (h), pressures (i), and plasma β (j) for three examples of confirmed reconnection exhausts in their individual LMN coordinate systems. The electron temperature (T e ) and electron plasma pressure (P e ) are measured by the Solar Wind Experiment (SWE) instrument (Ogilvie et al. 1995;Wilson et al. 2018) at 9 s cadence or longer. The total pressure P tot = P B + P p + P e , as displayed in Figure 1(i), is shown at the 3 s cadence of the proton plasma pressure (P p ) with the 92 ms magnetic field pressure (P B ) and the variable cadences of P e interpolated to the fixed 3 s cadence of P p to indicate whether a given exhaust-associated CS is in overall pressure balance. The total plasma β = (P e + P p )/P B is analyzed at the SWE instrument cadence.
The three examples of exhaust shown in Figure 1 were identified using three different durations of a sliding window with Δt = 12 s (left), Δt = 18 s (middle), and Δt = 2 minutes (right). The actual durations of these CSs, which are indicated between the two vertical dashed lines, are Δt cs = 10.9 s, Δt cs = 13.3 s, and Δt cs = 58.0 s with normal widths d cs = 14.5 d i , d cs = 34.5 d i , and d cs = 149.6 d i . The normal widths were obtained as d cs = Δt cs |N • V sw | or d cs = Δt cs V Navg , where V Navg = (V N1 +V N2 )/2 with V N1 and V N2 being the average normal component of the solar wind velocity before and after the CSs. In the three cases shown in Figure 1, V Navg ∼ 89 km s −1 , V Navg ∼ 232 km s −1 , and V Navg ∼ 384 km s −1 , respectively (see Figure 1(f)), while the average ion inertial lengths are d i = 67 km, d i = 89 km, and d i = 149 km. The CS start and stop times are listed in Table 1 for the three exhausts as well as the CS normal speeds, normal widths, and the magnetic field rotation angle θ = acos(B 1 • B 2 ) across each CS, where B 1 and B 2 are the time-averaged magnetic fields at the leading and trailing edges of the CSs. Table 1 also includes the N GSE and L GSE unit vectors of the CSs in GSE coordinates. The third M GSE unit vector is obtained as The jet speeds measured from the two sides of the external V L flows (see Figure 1(d)) into the exhaust are as low as [ΔV L1 , ΔV L2 ] = [9.6, 13.1] km s −1 for the first event (Figure 1, left) and only [ΔV L1 , ΔV L2 ] = [9.1, 6.6] km s −1 for the second event ( Figure 1, middle). The low jet speeds are due to low magnetic field rotation angles of just θ = 34°across the first CS and θ = 21°a t the edges of the second CS with an associated smaller reconnecting B L component of B, and the relatively high solar wind Alfvén Mach numbers of M A ∼ 7.2 adjacent the first CS and 7.9 < M A < 8.1 adjacent the second CS. These M A values were obtained from the total magnitude of B (see Figure 1(a)). In contrast, the 58 s duration event (Figure 1, right) supported an unusually fast jet at [ΔV L1 , ΔV L2 ] = [107.5, 116.5] km s −1 , which is due to the amount of available ΔV AL on the two sides of the CS as a result of a higher θ = 75°and an unusually low Alfvén Mach number 2.7 < M A < 2.9 in the two regions adjacent this exhaust. The predicted outflow velocities, based on the highcadence B L of Figure 1(b) and the interpolated plasma density N p of Figure 1(g), agree with the observed outflows, as demonstrated from the two V WL = V L0 ± ΔV AL predictions from the two sides of each CS and shown in Figure 1(d) as the red and blue colored traces, respectively. Figure 2(a) shows the distribution of actual CS durations with a peak at Δt cs = 10 s, a median at Δt cs = 40 s, and a 95th percentile at Δt cs = 340 s for a 5 s bin size. Figure 2(b) shows the d cs distribution of CS normal widths associated with reconnection exhausts in the ecliptic plane at 1 au with a peak at d cs = 25 d i and a median at d cs = 85 d i . The d cs distribution supports an extended tail with the 95th percentile of the cumulative normal width distribution at d cs = 905 d i for a bin size of 5.0 d i . There are 144 exhausts beyond the displayed 1000 d i maximum of this d cs distribution with the widest exhaust of the study discovered at d cs = 8077 d i . The 144 exhausts are distributed as shown in Table 2. It would seem that CSs in a range d cs > 9000 d i are not very likely to be associated with a reconnection exhaust observation at 1 au from this distribution of exhaust-associated CS normal widths. This result could potentially also reflect a general absence of CSs associated with normal widths >9000 d i in this sliding window survey for a maximum Δt = 20 minute window.

Statistical Exhaust Histogram Distributions at 1 au
The 5th percentile of the d cs distribution at d cs = 10 d i and the apparent drop-off from a peak at d cs = 25 d i inevitably reflects the limitation of the 3 s cadence of the Wind 3DP plasma instrument to resolve more reconnection exhausts in this kinetic-scale regime of CSs in the solar wind (e.g., Vasquez et al. 2007;Vasko et al. 2022). The fact that Wind could even resolve any exhaust in this kinetic regime is due to fortunate CS orientations relative to the solar wind velocity and a variable plasma-density dependent d i parameter. Figure 2(c) displays the distribution of solar wind speeds (V sw ) at the leading edge of the events. It shows a broad distribution with 90% of all cases occurring at speeds in the 290-560 km s −1 range for a V sw = 370 km s −1 median, and with the upper 5% of the exhaust distribution occurring at speeds V sw > 560 km s −1 that we typically associate with ICMEs and fast solar wind streams originating from coronal holes. Figure 2(f) displays the V sw distribution of the 1 hr cadence solar wind speed measurements from the ACE spacecraft for the same overlapping 10 yr interval at a similar upstream L1 location as the Wind measurements of this study of exhausts. This comparative ACE distribution contains 90% of solar wind speeds at 280-610 km s −1 with the upper 5th percentile of the CDF found at similarly fast V sw > 610 km s −1 solar wind speeds. The exhaust-associated V sw distribution at the Wind spacecraft is not that different from this background V sw distribution at ACE for the same time period and a similar L1 location. Both V sw distributions, e.g., display a shoulder near V sw ∼ 600 km s −1 , which is likely due to a population of highspeed streams. In other words, reconnection exhausts should be expected across CSs of any solar wind speed regime. Figure 2 also displays the distribution of the leading-edge exhaust flows (ΔV L1 ) in two different ways. First in units of average temperatures for protons (T p in black) and electrons (T e in green), (i) pressures (proton plasma pressure P p ; electron plasma pressure P e ; magnetic field pressure P B ; total pressure P tot = P p +P e +P B ), and (j) proton β p = P p /P B (blue), electron β e = P e /P B (green) and total β tot = β p +β e (black). The plasma measurements are shown at 3 s resolution (3DP proton data), typically ∼ 9 s resolution (SWE electron data), and magnetic field data are shown at 92 ms cadence. A pair of vertical dashed lines mark the start and stop times of the CS and the associated exhaust for each event.
kilometers per second with a modest median of ΔV L1 = 15 km s −1 and a 95th percentile at ΔV L1 = 50 km s −1 as shown in Figure 2(d), and also as a normalized ratio |ΔV L1 |/|ΔV WL1 | as shown in Figure 2(e). Here, |ΔV WL1 | = |V WL -V L1 | and V WL is the predicted maximum value of the speed of the exhaust from the Walén relation. Most cases display |ΔV L1 |/|ΔV WL1 | < 1, which is consistent with previous findings (e.g., Phan et al. 2020), although not yet fully understood. That is, measured exhaust speeds are often somewhat slower than predicted by the Walén relation in the solar wind. Figure 2(g) displays the distribution of the proton plasma β p1 at the leading edge of the exhaust-associated CSs with 90% of the 3374 events found at 0.05 < β p1 < 2.15 and a median β p1 = 0.55 for a 0.05 bin size value, in agreement with earlier reports (e.g., Gosling et al. 2007b;Phan et al. 2009). This typically low-β p regime essentially reflects a background proton β p distribution of the solar wind in this same 10 yr period as measured by the ACE spacecraft (not shown) with a most probable (peak) value at β p = 0.35, a median β p = 0.40, and a 95th percentile of the CDF at β p = 1.25 for a 0.05 bin size of the 1 hr cadence ACE observations. Figure 2(h) shows θ, the magnetic field rotation angle (a.k.a. the magnetic field shear angle), across these exhaust-associated CSs. The θ distribution is broad with a median at θ = 67.5°, and it appears that the number of events increases linearly from only a few cases near 170°< θ < 180°toward a broad peak at 35°< θ < 65°with an apparent drop-off at low-shear angles with a 5th percentile at 20.0°. Figure 2(i) displays the magnitude of the L component of the ion velocity difference across the CS, ΔV LS = |V L2 -V L1 |, which is normalized to the difference in the L component of the external Alfvén velocity, ΔV ALext = |V AL2 -V AL1 | across the CS. The 95th percentile of this flowshear distribution at 0.36 suggests that a critical flow shear ΔV LS /ΔV ALext > 0.5 along a reconnection jet flow direction may inhibit an onset of magnetic reconnection across a CS as predicted by Cassak & Otto (2011). The 0.10 median of this flow-shear distribution is very similar to the 0.12 median reported by Phan et al. (2020) on the basis of 196 Wind exhausts at 1 au. Swisdak et al. (2003Swisdak et al. ( , 2010) employed a numerical simulation to predict that reconnection should be suppressed if the drift speed of the X line along the CS, due to a plasma pressure gradient across the CS, is faster than the exhaust outflow speed. This suppression prediction may be expressed as Δβ > 2(L/d i )tan(θ/2), where Δβ = |β 2 -β 1 | is the change in total plasma β = (P p +P e )/P B and θ is the magnetic field rotation angle across the CS. L is a normal width of the CS near the X line in terms of the ion inertial length. Figure 3(a) displays the distribution of the total β 1 at the leading edge of a subset of 3011 exhaust-associated CSs for which an electron plasma observation is available from the SWE instrument within 35 s of each of the two CS edges. The median time separation is only 7 s between the SWE measurements and the CSs, while the median of the CDF of the relative total pressure differences across the 3011 CSs is only |P tot2 -P tot1 |/P tot1 = 2%. The exhaust-associated CSs are in pressure balance. The total β 1 distribution shown in Figure 3(a) peaks at β 1 = 1.3 with a median β 1 = 1.7 value for a 0.1 bin size with 90% of all cases occurring at 0.4 < β 1 < 6.8. Figure 3(b) displays the Δβ = |β 2 -β 1 | distribution with a median of the CDF at Δβ = 0.35, a 95th percentile at Δβ = 3.90, and a maximum Δβ = 67.7 value. Figure 3(c) shows the corresponding Wind observations of the field rotation angle θ and the change of this total Δβ across the 3011 exhaust-associated CSs. There are 2600 events in the regime to the left of a thick, solid line for L 1 d i and Δβ < 2(L/d i )tan(θ/2) where reconnection should be allowed as also confirmed from the Walén prediction analyses. In using the observed Δβ and θ shear angle of the 2600 exhausts, we find that most of the reconnection exhausts satisfy the Δβ < 2(L/d i )tan(θ/2) condition even with L ∼ 0.22 d i as the median of the CS thickness near the X line. This result is in general agreement with earlier reports (Phan et al. 2010;Gosling & Phan 2013). However, there is a noticeable spread in the distribution with 342 events present for 1 < L 3 d i between the thick, solid line and a middle, thin solid line at L = 3 d i . An additional 41 events are present at 3 < L 6 d i between the pair of thin lines and there are 28 confirmed exhausts to the right of the thin, solid line for L > 6 d i . The 28 exhausts of this unusual L > 6 d i regime were associated with 8.8 < Δβ < 67.7 and field shear angles in a range 26°< θ < 138°. The large Δβ values correspond to a highly asymmetric total plasma β with an exceptionally high 10.3 < β < 79.1 on the high-β side of the exhaust as compared with the entire β 1 distribution shown in Figure 3(a).
Three reconnection exhausts discovered in this exceptional Δβ regime are displayed in Figure 4 (see Table 1 Table 1 Start (t 1 ) and Stop (t 2 ) Date/Times in the Format yyyymmdd/hh:mm:ss.s of Several Exhaust-associated CSs Including the CS Normal Speed, Width (d cs ), Magnetic Field Rotation Angle, and the CS Unit Vectors N GSE and L GSE for Each Event exhaust was observed in a presence of β 1 = 1.9 and β 2 = 17.2 at the edges of the CS. However, whereas all magnetic field components are highly structured across the d cs = 28.8 d i exhaust on 2007 September 30 (Figure 4, middle), there is a clear presence of a measured V L reconnection exhaust despite a large β 1 = 24.2 and β 2 = 1.5. The total β asymmetries of the three exhausts are primarily reflected as gradients in the proton plasma pressure and the magnetic field pressure. The electron pressure is less variable as a result of a relatively stable electron temperature across the three CSs as compared with the proton temperature. The three exhausts shown in Figure 4 were also associated with a highly asymmetric B L rotation with the high β side displaying a weak B L value and the low β side displaying a significantly stronger B L component. This was typical of the reconnecting component of the magnetic field in all 28 cases of an exceptionally large Δβ as may be expected from a total pressure balance (e.g., Vasko et al. 2021). Two of the events displayed in Figure 4 were associated with a high V > 600 km s −1 solar wind speed. However, there are only four cases of this high Δβ regime in a high-speed solar wind V 575 km s −1 , while the median of the other 24 cases displayed a more typical V 1 = 344.5 km s −1 solar wind speed at the leading edge of the CSs. The high Δβ cases were associated with a wide range of CS normal widths, 19 < d cs < 836 d i , with a median value of d cs ∼ 126 d i . In knowing that reconnection was not suppressed across the 28 CSs from the local Wind exhaust observations, we may use the observed values of Δβ = |β 2 -β 1 | and field rotation angle θ of Figure 3(c) for L > 6 d i to estimate the presumed CS normal widths near the X lines. The Wind observations suggest that the X line regions may have been associated with a CS thickness on the order 6.1 < L < 27.2 d i with a median L = 8.8 d i normal width for the 28 exhausts that displayed a high β asymmetry.

Discussion
A primary motivation of this work is to better understand the intricate relationship between magnetic reconnection and turbulence in the solar wind. The first result that we need to address is the possible origin of the rapidly decaying d cs distribution of exhaust-associated CS normal widths at 1 au (see Figure 2(b)), and by extension the nature of the CSs that support this reconnection activity in the solar wind. It is most definitely true that Wind spacecraft observations contain many more reconnection exhausts that could be identified using several other discrete time window durations than the set of six separate windows applied in this study. However, Figure 2(b) does not indicate any significant breaks of a mostly continuous CS normal width distribution of 3374 exhaust-associated CSs, suggesting that additional exhausts will further build upon the obtained distributions and corroborate that the equatorial plane of the solar wind contains a rapidly decaying distribution of exhaust-associated CS normal widths at 1 au. The prevalence of kinetic-scale CSs in the solar wind for normal widths below the d cs = 25 d i peak of the present Wind exhaust width distribution (Vasquez et al. 2007;Osman et al. 2014;Vasko et al. 2022) certainly means that a true exhaust width distribution, which is only accessible to still higher plasma cadence measurements, will likely peak at a higher number of events and well below d cs = 25 d i .

Exhaust-associated CS Normal Orientations
Let us first examine the orientation of the CS normal directions N GSE = [Nx, Ny, Nz] on the unit sphere for all the 3374 reconnection exhausts. In other words, let us find the two angles θ and f in a spherical coordinate system for each N GSE unit vector, where θ = arctan(N E /Nz) is the polar angle, f = arctan(Ny/Nx) is the azimuthal angle, and N E is the magnitude of the projection of N GSE onto the ecliptic plane as we also introduced in Section 1. We recall here that the current density vector itself is directed primarily along M GSE and that the reconnecting component of the magnetic field is aligned with L GSE such that N GSE × L GSE = M GSE . Figure 5 displays the resulting distribution of spherical angles θ and f for all 3374 CSs associated with a confirmed reconnection exhaust, where we have color-coded a total of five subsets of the full d cs distribution. There are 370 exhausts in a proton kinetic range d cs < 25 d i (blue), 710 exhausts in a super-kinetic range 25 d cs < 50 d i (light blue), 666 exhausts populated a sub-HCS scale range 50 d cs < 100 d i (green) with as many as 1198 exhausts in an HCS-like range 100 d cs < 500 d i (yellow). Finally, there are 430 exhausts that we opt to define as a super-HCS range with normal widths d cs 500 d i (red). It appears that these very wide events are particularly concentrated in f space toward f ∼ 30°and f ∼ 210°as compared with narrower events. There is also a noticeable absence of cases near f = 90°and f = 270°as well as θ = 0°and θ = 180°. Normal directions associated with these spherical angles correspond to orientations of any CS, whereby a spacecraft in the solar wind would spend a significant time traveling along the plane of the CS before making the transition across the CS. That is, the solar wind velocity would in general be nearly aligned with either M GSE or L GSE with a very small normal V N component of the solar wind velocity adjacent to any such CS. The absence of events near these angles are, at least partially, explained then by a maximum 20 minute window duration in the present survey. The longest exhaust-associated CS duration of this survey is  Figure 6 displays the actual histograms of the azimuthal f angle (panel (a)) and the polar θ angle (panel (b)) of the exhaust-associated CSs shown in Figure 5, using the same color-coded subsets of the CS normal widths as shown in Figure 5. The 430 cases of super-HCS exhausts at d cs 500 d i (red) clearly display a preference for a range of azimuthal angles centered about 5°< f < 35°and 185°< f < 215°, and with a broad range of polar angles centered near 60°< θ < 120°. The azimuthal f angles of the very thick CSs are in general agreement with the typical Parker-spiral magnetic field direction at 1 au and a CS normal along the ortho-Parker direction at f ∼ 225°or f ∼ 45°(e.g., Lepping et al. 1996). The broad range of polar θ angles centered about 90°(Nz ∼ 0) is consistent with a highly folded or wavy HCS at 1 au (Smith 2001). We interpret these wide CSs as members of the HCS population at 1 au. A pitch-angle distribution of suprathermal strahl electrons as measured by Wind at, e.g., 270 eV (Gosling et al. 2007a) would need to be analyzed to corroborate how close the very thick, exhaust-associated CSs are to a true sector boundary, where strahl electrons change between a parallel and antiparallel direction, which is beyond the scope of the present study.
The angular distributions for normal widths in the HCS-like range at 100 d cs < 500 d i (yellow) are centered about a very However, the f distribution and the θ distribution of the 370 CS exhaust events in a proton kinetic range (d cs < 25 d i ) are essentially isotropic in comparison with the organized CS normal directions for normal widths d cs 50 d i . There is nearly no preference for any particular CS normal direction in either azimuthal angles or polar angles with only a few exceptional events at 40°< f < 50°and 220°< f < 230°. This proton kinetic-range population also tends to be overrepresented in the aforementioned void regions near f = 90°and f = 270°, and they tend to be underrepresented around θ ∼ 90°as compared with the wider d cs 50 d i events. We interpret these typically isotropic CS normal directions of thin CSs below 25 d i as reconnection exhausts associated with true solar wind turbulence in the ecliptic plane at 1 au without a preferred CS normal direction.
Finally, we find that the 710 CS events in a super-kinetic range 25 d cs < 50 d i (light blue) align their N GSE normal directions near 10°< f < 40°and 180°< f < 230°in the ecliptic plane, while showing a broad polar angle range 55°< θ < 140°centered about θ ∼ 90°. That is, it appears that these 25-50 d i wide CSs are associated more with reconnection of the HCS-aligned populations for d cs 50 d i than they are with an isotropic, turbulent CS population for d cs < 25 d i . This result is consistent with the narrow ∼35-120 d i normal width dimensions of the 19 HCS events reported by Winterhalter et al. (1994).
It may be argued that the exceptional events of the kinetic-scale d cs < 25 d i CSs near f ∼ 45°and f ∼ 225°could potentially be members of the same HCS-aligned group of CSs rather than a purely turbulent CS population, although the normal dimension of these exhaust-associated CSs is so narrow compared with the typical expectation of a high-shear and very wide HCS (Lepping et al. 1996). Figure 7 appears to support this suggestion, where a subset of 1746 CSs with normal widths d cs < 100 d i is examined in five groups of nearly equal number of exhausts. Despite a relatively small number of 109 exhausts in the kinetic range d cs < 15 d i (blue) and 261 exhausts in a somewhat wider group at 15 d cs < 25 d i (light blue), it seems that the exceptional events in the ortho-Parker direction at f ∼ 45°and f ∼ 225°of kineticscale CSs at d cs < 25 d i (see, e.g., Figure 6(a)) are potential HCS-like members of an exceptionally narrow 15 d cs < 25 d i population.

Comparing Reconnection Exhausts across Very Wide CSs at 1 au and Near the Sun
Before we go on to address a potential interpretation of the very smallest spatial scales of the d cs distribution that the Wind spacecraft can resolve at 1 au, we will first review what is known about reconnection across the very wide end of the CS distribution in the solar wind. Understanding these very large-scale CSs is going to be key in also understanding and appreciating the very small-scale end of the d cs distribution. Gosling et al. (2005bGosling et al. ( , 2006c reported the very first observations of reconnection exhausts across two confirmed HCS layers at 1 au by the ACE spacecraft. One exhaust was encountered anti-sunward of an X line on 1998 September 17. Gosling et al. (2005b) suggested that the θ ∼ 141°magnetic field rotation of this HCS crossing occurred between ∼03:17:33 and ∼03:20:29 UT from 16 s cadence ACE magnetic field data (Smith et al. 1998) and they proposed a roughly ∼ 53,000 km thick HCS exhaust. The other HCS-associated exhaust was encountered by ACE on the sunward side of an X line on 1998 December 25 . However, since Gosling et al. (2006c) neither stated the exact time interval of this θ ∼ 127°fi eld rotation, nor the estimated normal width of this HCS exhaust, we first revisit the 1 s cadence ACE magnetic field observations in GSE coordinates to obtain the orientation of the two HCSs on the basis of the same hybrid-LMN system that we employed in this  Table 3 shows the slightly revised HCS times from a rotation of the 1 s cadence B L component of the magnetic field as well as the N GSE and L GSE directions of the two exhaust-associated HCS events. A somewhat lower 41,204 km or 519 d i normal width is suggested for the HCS on 1998 September 17, while we obtain a 60,644 km or 1046 d i normal width for the HCS on 1998 December 25. The N GSE orientations of the two HCS confirmed exhausts correspond to azimuthal angles f ∼ 10°a nd f ∼ 38°with polar angles θ ∼ 92°and θ ∼ 106°. That is, the two reported ACE events at 1 au are rather typical cases of the exhaust normal width category of 430 events in the present Wind data survey that we have referred to as super-HCS exhausts with normal widths 500 d i d cs 8077 d i (see, e.g., Figure 2(b) and Table 2) and a preferred range of azimuthal angles near 5°< f < 35°and a broad range of polar angles near 60°< θ < 120°(see Figures 5 and 6).  Table 1 including the CS start and stop times, normal speeds, d cs widths, and θ angles. Figure 8 (right) illustrates a third super-HCS example on 2008 July 12 that we discovered immediately adjacent to a relatively low-shear (θ = 67°) and short-duration (Δt cs = 44 s) exhaust-associated CS of the main survey. That short-duration, d cs = 210 d i wide CS, which is also listed in Table 1, is marked in Figure 8 Figure 8(d) illustrating this CS shows a negative ΔV L ∼ −60 km s −1 change in the proton velocity as B L rotates from ∼14 to ∼5 nT across the first edge. The proton flow remains at a significant V L ∼ −50 km s −1 speed across most of the CS until the initial green solid line at 01:00:00 UT, when it displays a positive ΔV L ∼ 85 km s −1 change in time, coincident with a B L rotation of this thick CS from ∼ 3 to −4 nT. The negative ΔV L ∼ −50 km s −1 flow deflection is typically consistent with a reconnection exhaust across a major section of the complete CS as suggested by a long-duration Walén prediction (see, e.g., first V WL1 in red and V WL2 in green in panel (d)). The primary exceptions to this overall agreement are two regions of elevated plasma density at ∼00:40:00 and ∼00:55:00 UT deep within the super-HCS when Wind also recorded sizeable B L fluctuations indicative of internal exhaust structure.
The first d cs = 784 d i wide super-HCS exhaust on 2004 October 8 displays a spectacular CS bifurcation, which is commonly observed (Gosling & Szabo 2008) across many exhaust-associated CSs in the solar wind, with two very sharp (narrow) CSs across each edge of the main exhaust region. A close examination of the B L component (Figure 8(b), left) appears to show another smaller-scale bifurcation of the first CS. This is highlighted between a pair of solid green vertical  Table 1 for N GSE and L GSE of the primary CS). The local M GSE = [0.08662, 0.85218, −0.51604] vector is 24.0°off the M GSE direction of the primary CS. Figure 9 (left) shows a 22 s interval from 07:05:37-07:05:59 UT on 2004 October 8 around this first CS with the components of B GSE and V GSE displayed in the primary LMN coordinate system for sake of clarity. The B L rotation is clearly bifurcated across this narrow CS with two, discrete steps of B L . Figure 9(d) (left) compares the Walén prediction of the large-scale V L exhaust, shown here as the red and blue colored curves as in Figure 8(d) (left), with a localized Walén prediction of the measured V L component of the solar wind velocity. The local V L prediction is shown as a slightly thinner green curve. The green Walén prediction follows the red Walén prediction perfectly across a first B L step, until the second B L step of this small-scale CS bifurcation that turns the prediction back toward the actual V L measurement within the main exhaust region. Two very important results may be concluded from this local analysis. First, in this particular case, it would seem that an ∼10 km s −1 offset of the large-scale V L prediction can be traced to the presence of a second, very narrow CS bifurcation at the edge of the main exhaust. Second, despite the availability of only one complete 3DP plasma measurement within this narrow CS, there is a strong indication of a small-scale reconnection exhaust present across this first CS, which is further supported by a bipolar B M variation as shown in Figure 9(c) (left) with the expected sense of a Hall magnetic field. That is, the large-scale CS of 2004 October 8 supported a layered set of several bifurcated CSs, which is present at vastly different spatial scales.
The much wider d cs ∼ 12,233 d i exhaust on 2008 July 12 (Figure 8, right) displays a similarly bifurcated super-HCS as the 2004 October 8 event, and it is clearly associated with a secondary bifurcation of the final B L rotation as indicated between the pair of solid green vertical lines at 01:00:00 and 01:07:50 UT as Wind exited the large-scale exhaust boundary. A local V Navg ∼ 417 km s −1 (see Figure 8(f), right) across this second Δt cs = 470 s or 7.8 minute duration, two-step B L rotation with a θ ∼ 76°magnetic field shear angle corresponds to a d cs = 2403 d i CS for an average d i ∼ 82 km. This two-step CS supports a positive reconnection exhaust (see, e.g., the second V WL1 Walén prediction in red and V WL2 in blue in Figure 8(d) (right) immediately adjacent to the much largerscale and negative exhaust. The final, two-step CS is associated with a local L GSE = [−0.19957, −0.17395, 0.96432], which is deflected by ∼31°from the primary exhaust L GSE direction, and a local N GSE = [−0.85454, −0.45068, −0.25815] normal vector, which is only 2.4°off the main super-HCS normal direction. Figure 9 (right) displays a detailed view of the initial exhaust-associated CS in its local LMN system (see Table 1)  of this initial, short-duration CS is, again, deflected by a small 3.2°r otation relative to the N GSE of the main super-HCS. However, the local L GSE direction of this exhaust is deflected by as much as 54°from the L GSE of the primary super-HCS. The rather significant L GSE direction offsets of the two edge-associated exhausts explain the apparent V M components of the two jets (see Figure 8(e), right) when displayed in a non-local LMN system of the super-HCS. Phan et al. (2021) discuss how reconnection exhausts appear to be common across the near-Sun HCS from Parker Solar Probe (PSP) spacecraft observations at heliocentric distances of 29.5-107 R ☉ . They reported normal widths for five welldefined and complete exhaust-associated HCSs near the Sun in a range d cs = [240, 890, 1320, 4820, 8220] d i . Despite this HCS location very close to the Sun, we find that four of the five PSP events fall into the same super-HCS category of 430 Wind events at 1 au (see Figure 8) as the two ACE events summarized in Table 3. The d cs = 8220 d i PSP event is only 143 d i wider than the widest 8077 d i event of this Wind survey at 1 au, and it is ∼4000 d i off from the super-HCS exhaust on 2008 July 12. The relatively narrow d cs = 240 d i exhaustrelated HCS near the Sun is comparable in size with the d cs = 210 d i exhaust shown in Figure 9 (right), and both events are examples of a population of 1198 exhausts in a category that we refer to as the HCS-like range (100 d cs < 500 d i ) at 1 au on the basis of a few early HCS studies (Winterhalter et al. 1994;Lepping et al. 1996). It is clear from our extensive survey of 3374 exhausts of many different normal widths (see Figure 6) that reconnection exhausts are not as rare across wide, HCS-like CSs as initially reported at 1 au (e.g.,  The normal widths of all these HCS-like reconnection exhausts, whether associated with the HCS on the basis of a typical ortho-Parker direction at 1 au (see Figure 6) or confirmed as such from pitch-angle observations of suprathermal strahl electrons at 1 au and near the Sun, are considerably wider than the kinetic scales that we assume to be required for a spontaneous, tearing-unstable, and explosive onset of magnetic reconnection (e.g., Birn et al. 2001). The proposed prevalence of reconnection exhausts across a near-Sun HCS , and potentially across wide CSs associated with an ortho-Parker direction in the solar wind at 1 au, imply that magnetic reconnection may be triggered by external disturbances near the HCS to support reconnection onset. The presumed turbulent regime adjacent to near-Sun HCSs may be one such trigger mechanism that could potentially allow for a faster rate of reconnection R > 0.1 (Lazarian & Vishniac 1999;Lazarian et al. 2020).

Large-scale Implications of a Two-step Bifurcation of Exhaust-associated CSs
The observation of reconnection exhausts across several wide near-Sun HCS has an important consequence for the observed d cs distribution of reconnection exhausts at 1 au and the realization that CSs with a wide range of normal widths from 15-25 d i to well beyond 500 d i are organized by a Parker-spiral magnetic field direction. The implication of reconnection across the near-Sun HCS centers on a common, although not universal, bifurcation of the B L profile across a CS in this Wind spacecraft distribution of exhausts at 1 au. That is, there are two mostly parallel CSs directed along the M GSE direction at the edges of many reconnection exhausts, rather than one continuous B L rotation of a broad Harris-type J M current layer across the entire exhaust. The two CSs are reflected as the two separate and step-like rotations of the B L component. The two parallel J M layers are often separated by a more gradual B L rotation that often appears as a plateau as, e.g., nicely illustrated by La Belle-Hamer et al. (1995). This bifurcation is clearly present for two kinetic-scale exhausts with normal widths d cs = 14.5 d i on 2004 July 9 (Figure 1

On the Large-scale Evolution of the HCS
We propose that the surprising alignment of narrow exhaustassociated CSs at 1 au with the ortho-Parker azimuthal direction of the large-scale HCS in the ecliptic plane is a consequence of reconnection-mediated CS bifurcation and turbulence within the HCS exhaust. That is, the turbulent fields of the exhaust region may trigger an onset of reconnection (Lazarian & Vishniac 1999) of the two adjacent bifurcated CSs. The proposed HCS-avalanche scenario suggests that the underlying large-scale parent HCS closer to the Sun evolves with heliocentric distance to fracture into many, more or less aligned, secondary CSs due to reconnection.  Table 3 Start (t 1 ) and Stop (t 2 ) Date/Times of Two Reconnection Exhausts Associated with the HCS at 1 au as Encountered by the ACE Spacecraft Note. The HCS durations Δt cs are listed including N GSE and L GSE and the average normal speed of each HCS to obtain a normal width d cs . The f and θ spherical angles corresponding to N GSE are also listed.
The general CS alignment is further supported by the small <10°d eflection between the local N GSE normals of the bifurcated CSs relative to the large-scale parent CS. Each new set of two bifurcated CSs that typically display a lower magnetic field shear angle will have some probability to reconnect driven by the turbulent fields of the adjacent exhaust. This cascade process results in two still smaller-scale exhausts and a set of four CSs, and so on, to explain the HCS alignment of the azimuthal angle distributions down to 15 d cs < 25 d i that we find in a Wind survey of 3374 reconnection exhausts. Figure 10 summarizes the proposed cascade in a simplified schematic, whereby one HCS reconnects at time t 1 to form two bifurcated CSs adjacent to one wide and primary exhaust at time t 2 , with each of the two CSs (J M1 and J M2 ) able to support a bifurcation through secondary magnetic reconnection toward both smaller spatial scales and lower magnetic field shear angles of four exhaust-associated CSs J 1 -J 4 at a later time t 4 .
The proposed cascade evolution from large to small scales also seems to address the linear increase of the number of exhaust-associated CSs at 1 au from a few high-shear cases at θ > 147.5°toward a peak at θ = 62.5°(see Figure 2(h)). Indeed, the apparent drop-off of events for shear angles below θ < 40°shown in Figure 2(h) could very well originate from an inability to resolve exhausts across kinetic-scale CSs that typically support a very low-shear magnetic field rotation angle (Vasquez et al. 2007;Vasko et al. 2022). The proposed insideout evolution scenario from a set of relatively fewer, but wide exhaust-associated HCSs close to the Sun to a set of many relatively narrow HCS-aligned exhausts at 1 au represents a different interpretation of the exhaust d cs distribution at 1 au as compared with a notion of ever-expanding jets originating from many kinetic-scale turbulent CSs into a super-HCS d cs 500 d i exhaust population in the 1 au solar wind. Shepherd et al. (2017) also caution against an ever-expanding jet evolution, since an out-of-plane guide field component of the magnetic field, which does not participate in the merging process, will force the exhaust to remain collimated in a normal direction beyond a critical distance from the X line. The proposed conceptual framework suggests that the set of much fewer and wider exhaust-associated HCS-like CSs at 1 au could rather represent a population of a few HCSs that failed to reconnect as frequently between the Sun and 1 au as some other HCSs.    Table 1). Same panel information as on the left with a local Walén prediction shown in red (V WL1 leading edge) and in blue (V WL2 trailing edge). that support a separate and wide d cs ∼ 337 d i reconnection exhaust in overall agreement with a Walén prediction for a local V Navg ∼ 281 km s −1 and d i ∼ 86 km. The θ ∼ 83°and d cs ∼ 1108 d i wide primary CS on 2012 September 24 is bifurcated, and each of the two lower-shear CSs were in turn bifurcated to support four CSs in total and what appears as two separate reconnection exhausts. In this case, the two jets were directed in opposite directions relative to the primary L GSE direction.
What makes this 2012 September 24 event exceptionally intriguing, however, is that each of the two initial CSs appear to support a set of two kinetic-scale reconnection exhausts as shown in Figure 11 (right) for the time period 13:05:10-13:07:50 UT. This is especially clear for the Δt cs = 7.3 s duration CS between 13:07:13.6 and 13:07:20.9 UT that we associate with a local θ ∼ 29°shear angle and a d cs = 26.7 d i normal width in the local LMN system stated above for V Navg ∼ 302 km s −1 and d i = 82.5 km. A local Walén prediction, which is shown here as a red and green curve in Figure 11(d) (right), follows the measured negative V L jet nearly perfectly as compared with the overall Walén prediction, which is shown as a blue curve. The blue curve clearly overpredicts the measured V L jet across the complete B L rotation by about 5-10 km s −1 depending on the specific location within this exhaust region. The Δt cs = 3.9 s duration of the first CS between 13:05:36.4 and 13:05:40.3 UT, with a local θ ∼ 13°s hear angle, translates to a kinetic-scale d cs = 13.2 d i normal width for V Navg ∼ 301 km s −1 and d i = 89.1 km. This thin CS, despite being associated with only one complete measurement of the 3DP instrument, does indicate the presence of a positive V L exhaust from a local Walén prediction (red and green curves). Rather than supporting two exhausts across the full CS, it appears that the initial overpredicted exhaust supports two additional kinetic-scale exhausts with a grand total of four exhausts.

Potential Consequences of a Cascading HCS through Multiscale Reconnection
The rather common observation that measured exhaust speeds are lower than the predicted exhaust speed in the solar wind (see Figure 2(e)) may potentially be associated with exhaust structure, e.g., magnetic islands that act as an obstacle to the magnetic field and plasma of the L-directed exhaust outflow to force a flow diversion and exhaust deceleration away from the L direction. However, the two large-scale exhaust events of 2004 October 8 (see Figures 8 and 9) and 2012 September 24 (see Figure 11) clearly suggest another plausible explanation in terms of additional small-scale reconnection jets, some of which may not even be resolved by a 3 s cadence plasma measurement. When such small-scale jets are present at the edges of bifurcated and large-scale CSs, they will lead to an overprediction of the large-scale V L exhaust speed.
The swarm of multiple HCS-like crossings, which are commonly observed at 1 au over a period of 1-2 days around sector boundary encounters (e.g., Crooker et al. 1993Crooker et al. , 1996Winterhalter et al. 1994;Smith 2001), has been explained as a possible extension of multiple parallel CSs from the corona into the heliosphere and associated with multiple helmet streamers (Crooker et al. 1993). The proposed HCS avalanche through turbulence-driven reconnection from within the HCS layer offers an alternative mechanism to explain a swarm of HCS-like crossings around sector boundaries, whereby one HCS is fractured by reconnection into many HCS-like and mostly parallel CSs, with each smaller-scale CS typically associated with a smaller magnetic field shear angle. A major difference between the two mechanisms is that multiple helmet streamers appear to result in a series of parallel CSs of alternating CS direction (Crooker et al. 1993), while an HCS cascade through reconnection is expected to result in a series of parallel CSs in the same general direction. Figure 10. A schematic interpretation of a proposed time evolution (t 1 < t 2 < t 3 < t 4 ) of a cascade process from one large-scale CS to many, typically parallel and small-scale CSs in the solar wind through sequential CS bifurcation associated with magnetic reconnection. It is assumed that all CSs J M0 , J M1 , J M2 , and J 1 -J 4 in the regions of dark blue are directed along the out-of-plane M direction for the indicated in-plane directions of the magnetic field (B, black arrows). Appearances of reconnection X lines are indicated at times t 1 and t 3 in separate CSs. Two opposite reconnection exhausts are displayed in a spatial region at time t 2 , which is bounded by two CSs (J M1 and J M2 ) as a result of a reconnection-mediated CS bifurcation of one original J M0 . Subsequent X lines within J M1 and J M2 at t 3 bifurcates J M1 into J 1 and J 2 , and J M2 bifurcates into J 3 and J 4 . Opposite exhausts (yellow) from the subsequent X lines form between the new pair of CSs. All exhaust regions (lighter shades of blue) are assumed to be associated with a plateau of the B L component of the rotating B. A locally more intense CS is expected at the interface of oppositely directed and adjacent exhausts.
The observed distributions of CS normal orientations (see Figures 5-7) of different CS normal widths suggest that there is a transition region of exhaust-associated CS widths in an approximate range from ∼15 to ∼25 d i where two populations of CSs coexist in the 1 au solar wind. This range of normal widths appears to represent an upper limit of exhausts associated with a truly turbulent solar wind of isotropic angle distributions of a CS normal direction that likely occurs in between sector boundary traversals. The same transition region also appears to represent a lower limit of the turbulent cascade of the HCS-aligned exhausts at 1 au.
The isotropic distribution of CS exhaust events in the proton kinetic range (d cs < 25 d i ) corresponds to a physical scale size of about <2500 km. This value lies within a range of previously published Taylor-scale estimates from two-point turbulent magnetic field measurements, which is about 1400 km (Weygand et al. 2011). The Taylor scale is important here, as it is also the scale at which the damping of turbulent eddies within a turbulent cascade begins to become a dominant force. A tantalizing question, beyond the scope of the present work, is whether the isotropic angular distribution of the CS exhaust normal directions of a proton kinetic range (d cs < 25 d i ) is potentially related to the isotropic distribution of the Taylor scale with respect to the mean magnetic field direction.
In order to further characterize the two exhaust populations of the equatorial plane solar wind CSs at 1 au, we explored the possible impact of magnetic rotation angle θ across the CSs on the distribution of normal widths. Figure 12 displays four nearly equal subsets of the full distribution. The figure only shows histograms below a truncated 250 d i value due to the extended tails. There were 666 exhausts with a large shear angle θ > 115°(blue), 928 exhausts with a moderate shear angle 75°< θ 115°(light blue), 974 exhausts in a low-shear regime 45°< θ 75°(yellow), and 806 exhausts coincided with a very low-shear angle in the range θ 45°(red). The median is d cs = 45 d i for CSs of the very lowest shear angle range. The medians then doubled, first from d cs = 60 d i for low-shear angles (45°< θ 75°) to d cs = 120 d i for CSs with moderate shear angles (75°< θ 115°), and then nearly doubled again to a median d cs = 205 d i width for CSs of the highest shear (θ > 115°). This trend toward wide and highshear CSs is in general agreement with the expectation of most of the largest scale HCSs (Lepping et al. 1996). However, it is also clear from Figures 2(h) and 12 that a solar magnetic field may rotate by a relatively smaller angle across HCS-aligned exhaustassociated CSs at 1 au. The smaller field rotation angles θ < 180°c orrespond to finite guide-magnetic fields, such that the HCS-like exhausts do not require the solar magnetic field to be oppositely directed on either side of the CS to reconnect. It is very likely that the proposed HCS-avalanche process through reconnection naturally results in this trend toward successively thinner CSs with smaller shear angles. It is also known that narrow, kinetic-scale CSs more typically correspond to very low-shear CSs (Vasquez et al. 2007;Vasko et al. 2022). That is, pure solar wind turbulence likely supports many of the observed very thin exhaust-associated CSs, while the fracturing of HCS-aligned CSs into many different widths as indicated in Figures 6-12 is consistent with turbulence inside the exhausts of active HCSs.
It is not exactly clear why the solar wind would support a transition region of a critical CS dimension at 1 au between the two CS populations, or rather why there is no HCS alignment of CSs below a critical CS width. However, it appears from a Taylor-scale argument that exhausts much wider than d cs ∼ 25 d i may be unlikely to evolve from a truly turbulent CS population due to a damping force of turbulent eddies within a turbulent cascade that may start to become important at a Taylor scale of d cs ∼ 14 d i or so.
In extending the proposed HCS-avalanche cascade evolution radially outward into the heliosphere, one could expect a fracturing of the HCS to continue with heliocentric distance, perhaps leading to more parallel HCS-like sheets of current that could further bring the critical width of a transition region lower than 25 d i . That is, the number of HCS-aligned CSs associated with reconnection exhausts could potentially increase from the Sun with an increased number of the very narrow CSs. The expansion of the solar wind volume itself may eventually impact the efficiency of exhaust turbulence to drive magnetic reconnection of bifurcated CSs, while the linearly increasing d i -scale with heliocentric distance due to the radial profile of the plasma density may impact the transition region in terms of the d i -scale.

Summary and Conclusions
We conclude from the Wind spacecraft observations of 3374 exhausts at the L1 point that the solar wind of the ecliptic plane supports two scale-dependent regimes of reconnection-associated CSs at 1 au. One small-scale CS population exists with normal widths d cs < 25 d i that display an isotropic distribution of CS normal directions in agreement with a source in Alfvénic solar wind turbulence. A second and significantly larger distribution of normal widths 25 < d cs < 8077 d i displays a distribution of CS normal directions organized by an ortho-Parker direction in general agreement with a source in a largescale HCS. It is possible that a turbulent source of exhausts may not support CS widths much larger than d cs ∼ 25 d i from a consideration of a Taylor-scale limitation. However, it is unclear why there are so few HCS-aligned exhausts below d cs ∼ 25 d i at 1 au. In summary, it appears that there is a transition region around 15 < d cs < 25 d i in the 1 au solar wind, where the two CS populations of different source regions may coexist.
We propose that a commonly observed process of CS bifurcation across reconnection exhausts can support a cascade of the HCS from potentially fewer and wider HCSs near the Sun to many often narrower HCS-aligned CSs at 1 au. This is in general agreement with the obtained field shear angle distribution. Several Wind spacecraft examples were presented in support of the proposed HCS-avalanche process, which is summarized in a Figure 10 schematic, whereby one HCS reconnects to form two bifurcated CSs adjacent to one wide and primary exhaust, with each of the two CSs supporting a cascading bifurcation process through secondary magnetic reconnection toward smaller scales and lower magnetic field shear angles of exhaust-associated CSs. Some events of this cascading nature apparently support jets in both L directions immediately adjacent to a large-scale exhaust. Other events simply display an absence of a large-scale exhaust, for unknown reasons, and rather support two spatially removed exhausts toward the edges of the large-scale CS.
Examples of a localized Walén prediction of the measured V L component of the solar wind velocity strongly suggest that some cases of overpredicted reconnection exhausts are associated with a presence of bifurcated CSs and localized jets at the exhaust edges. Very small-scale exhaust-associated CS bifurcations can thus impact the predicted V L flows at much larger scales.
It is possible that turbulence within the HCS exhaust region may be driving this secondary reconnection of the two bifurcated, and nearly parallel CSs, at the exhaust boundary to explain a general alignment of the normal of exhaust-associated CSs with the ortho-Parker spiral direction. The presence of fewer, but wider, exhaust-associated CSs at 1 au may simply reflect a population of HCSs that failed to reconnect as frequently between the Sun and 1 au as some other HCSs. In the sense of a reconnection-driven HCS avalanche, it may be concluded that magnetic reconnection and the downstream exhausts may lead to an intermittent turbulent behavior of the solar wind for spatial scales larger than d cs ∼ 25 d i .
The commonly reported swarm of HCS crossings over several days surrounding sector boundaries at 1 au may in certain cases be linked to the proposed reconnection-driven HCS-avalanche process as an alternative to multiple parallel CSs of alternating current direction, which has been proposed to extend out to 1 au from multiple helmet streamers of the solar corona.