Parker Solar Probe Observations of Magnetic Reconnection Exhausts in Quiescent Plasmas near the Sun

Parker Solar Probe observations are analyzed for the presence of reconnection exhausts across current sheets (CSs) within R < 0.26 au during encounters 4–11. Exhausts are observed with nearly equal probability at all radial distances with a preference for quiescent Tp < 0.80 MK plasmas typical of a slow-wind regime. High Tp > 0.80 MK plasmas of a fast wind characterized by significant transverse fluctuations rarely support exhausts irrespective of the CS width. Exhaust observations demonstrate the presence of local temperature gradients across several CSs with a higher-Tp plasma on locally closed fields and a lower-Tp plasma on locally open field lines for an interchange-type reconnection. A CS geometry analysis directly supports the property that X-lines bisect the magnetic field rotation θ-angle, whether the fields and plasmas are asymmetric or not, to maximize reconnection rates and available magnetic energy. The CS normal width d cs distributions suggest that a multiscale reconnection process through nested layers of bifurcated CSs may be responsible for observed power-law distributions beyond the median d cs ∼ 1000 km with an exponential d cs distribution present for ion kinetic dissipation scales below this median. Magnetic field shear θ-angles are essentially identical at R < 0.26 and 1 au with medians at θ ∼ 55° near the Sun and θ ∼ 65° at 1 au. In contrast, the tangential flow shear distributions are different near and far from the Sun. A bimodal flow shear angle distribution is present near the Sun with strong shear flow magnitudes. This distribution is modified with radial distance toward a relatively flat distribution of weaker flow shear magnitudes.


Introduction
The supersonic solar wind of the inner heliosphere flows away from the Sun's corona at a typical 250-500 km s −1 radial speed in the low-latitude region of the ecliptic plane (Parker 1958;McComas et al. 2008).The fast >500 km s −1 solar wind is associated with open magnetic fields connected to coronal holes (e.g., Phillips et al. 1995;Cranmer 2009;Lionello et al. 2014) and a proton temperature that peaks at Tp ∼ 1.9 MK in fast winds very close to the Sun (Cranmer 2020).Recent numerical studies and remote observations from the Parker Solar Probe (Fox et al. 2016) have proposed that interchange magnetic reconnection (e.g., Fisk et al. 1999;Cranmer & van Ballegooijen 2010) between open coronal fields and adjacent closed-field topologies deep within the corona may be able to explain a plasma acceleration to fast wind speeds (Bale et al. 2023;Drake et al. 2023).Other mechanisms such as turbulent Alfvén wave propagation may also play an important role in addressing the formation of a fast solar wind (e.g., Chandran & Hollweg 2009;van der Holst et al. 2014).The evolution of the variable and slow wind near the ecliptic plane is less certain.However, it is believed to be associated with the dynamics of coronal streamer belts of closed magnetic fields around the Sun (e.g., Borrini et al. 1981;Gosling et al. 1981) and the process of magnetic reconnection near helmet streamers (e.g., Wang et al. 2000;Rappazzo et al. 2012;Pellegrin-Frachon et al. 2023).
Magnetic field reconnection is a universal plasma physics process that results in a change of field topology and plasma mixing across a current sheet (CS) boundary layer.This kineticscale process proceeds by allowing magnetic fields adjacent to a CS to connect within small electron-scale diffusion regions immersed in thin CSs on the order of ∼1-2 ion inertial scale widths (e.g., Birn et al. 2001;Liu et al. 2022).The process results in kinetic-scale dissipation and turbulent plasma heating (e.g., Loureiro & Boldyrev 2017;Mallet et al. 2017;Webster et al. 2018;Dong et al. 2022).However, it has a direct impact also on the large-scale evolution of many plasma systems.The release of magnetic structures off the solar corona, including solar filaments (e.g., Li et al. 2016) and coronal mass ejections (CMEs), is a direct consequence of magnetic reconnection.Understanding where and when the reconnection process occurs near the Sun from in situ observations, and for what general plasma conditions it may be suppressed, is of critical importance to advance the study of solar wind dynamics in a near-Sun regime.
A characteristic signature of magnetic reconnection is the conversion of magnetic energy into plasma thermal and bulk kinetic energy with plasma jetting away from the X-line as two oppositely directed exhausts with speeds limited to the ambient Alfvén speed.The electron-scale dimensions of the reconnecting X-line regions ultimately responsible for these exhausts make it essentially impossible for spacecraft to detect their presence in the solar wind.However, the larger exhausts can extend very far along the CS (e.g., Gosling et al. 2005a;Davis et al. 2006;Phan et al. 2006;Eriksson et al. 2009), which makes them an ideal candidate to conclude whether reconnection occurs within a CS or not as spacecraft traverse these boundary layers in the solar wind.
The solar wind supports reconnection outflows of variable normal widths from direct observations at 1 au (e.g., Gosling et al. 2005a;Phan et al. 2006Phan et al. , 2010;;Enžl et al. 2014;Mistry et al. 2017;Eriksson et al. 2022) and beyond (e.g., Gosling et al. 2006b).Observations of reconnection exhausts sunward of 1 au were first reported by Gosling et al. (2006a) from Helios spacecraft measurements.The two probes of this mission were confined in a highly elliptic orbit with a 0.29 au perihelion near the ecliptic plane.Using the generally accepted signature of an exhaust as an accelerated or decelerated plasma flow confined to a magnetic field reversal region, Gosling et al. identified 28 events from the Helios mission with the most sunward event detected at 0.31 au from the Sun.Fargette et al. (2023) applied an automatic detection algorithm to identify 146 reconnection exhausts across solar wind CSs during a 20.7 day period of Solar Orbiter observations at ∼0.7 au with an average occurrence rate of 7.0 exhausts per day.These events displayed an intriguing clustering tendency, although the exact reason for this remains unclear.Phan et al. (2020) extended the known regime of solar wind reconnection inward with 21 exhaust-associated CSs as measured by the Parker Solar Probe during a 30 day period (October 27 to November 25) of its first 35.7 Rs ∼ 0.17 au perihelion pass in 2018, where 1 Rs = 6.957 × 10 5 km and 1 au = 1.496 × 10 8 km.These CSs, some of which were associated with an interplanetary CME and crossings of the heliospheric CS (HCS ;Smith 2001), lasted between dt cs = 1.6 s and dt cs = 19.2minutes as they propagated past the spacecraft at radial distances of 44.4 Rs to 107.2 Rs or 0.21-0.50au.The width of a CS can be estimated from its dt cs duration and the average of the plasma velocity at the two edges of the CS in the direction normal to the boundary layer (V N0 ) with the normal width obtained from d cs = V N0 * dt cs .The widths reported by Phan et al. (2020) were as narrow as 320 km and as wide as 288 Mm.Intriguingly, this first encounter did not appear to support any reconnection exhausts during a ∼9 day long period centered around the 2018 November 6 perihelion that was dominated by radial Alfvénic jets associated with switchback intervals of the B R component of the magnetic field emanating from an equatorial coronal hole (Bale et al. 2019).
The motivation of this study is to improve our understanding of what plasma conditions allow reconnection to occur near the Sun, to examine whether the Parker Solar Probe sampled a plasma regime typical of this extreme inner edge of the heliosphere during its first close encounter (CE) with the Sun, and to explore whether CSs associated with magnetic reconnection in the very near-Sun regime are different from those recorded at 1 au (Eriksson et al. 2022).The Parker Solar Probe has completed 17 orbits around the Sun to date, since its launch on 2018 August 12, with successively closer perihelion distances of 35.7 Rs (CE 1-3), 27.9 Rs (CE 4-5), 20.4 Rs (CE 6-7), 16.0 Rs (CE 8-9), and 13.3 Rs (CE 10-16).The first of five planned perihelia at 11.4 Rs was recently completed with a 17th encounter on 2023 September 27.This will be followed by at least three planned orbits at 9.9 Rs on 2024 December 24 and 2025 March 22 and June 19.The in situ observations of magnetic fields and plasma parameters recorded near the perihelion of each CE can provide the locations where exhaust-associated CSs occur including the distributions of their orientations, widths, and general plasma conditions.The present study provides results from a survey of exhaust-associated CSs within ∼55 Rs or ∼0.26 au of the Sun for the eight Parker orbits from CE 4 to CE 11 with perihelia that ranged between 27.9 Rs and 13.3 Rs using an automatic running window technique.
The paper is organized as follows.Section 2 presents an overview of the Parker Solar Probe measurements employed in this survey.Section 2.1 describes the methodology of detecting CSs with exhaust candidates and the analyses employed to confirm a candidate time period as a reconnection exhaust.Section 3 presents an introduction to the survey results including a few representative exhaust events in the near-Sun regime of this study.Section 3.1 provides a summary of the 231 exhausts identified across all eight CEs (4-11) with two overview examples for CEs 4 and 10.The complete set of CE figures and tables with detailed information for all 231 events is available via doi:10.5281/zenodo.10257747.The spatial distribution of the events in terms of the radial position of the Parker Solar Probe is also included in Section 3.1.Section 3.2 presents a supporting analysis on determining an optimum coordinate system for a local CS analysis with implications for X-line geometries near the Sun.Section 3.3 presents histograms of several important parameters, including CS orientations, normal widths, magnetic field shear angles, and tangential flow shear across these exhaust-associated CSs.This section also compares a few parameter distributions obtained at the Parker Solar Probe with those recorded by the Wind satellite in the solar wind at 1 au (Eriksson et al. 2022).Section 3.4 provides histograms of the plasma regimes adjacent to the events in terms of magnetic field strength, solar wind speed, and proton temperature and illustrates how these distributions compare with those obtained for the full encounters.Section 4 provides a discussion as to whether and why a particular plasma regime may be more likely to support reconnection across near-Sun CSs.This section also discusses whether, in measurements of the adjacent magnetic field magnitude, reconnection should be considered as allowed or suppressed in the local regime where exhaust-associated CSs were encountered by the Parker Solar Probe.Section 5 provides a conclusion with some implications to further advance the understanding of CS evolution through magnetic reconnection in this extreme near-Sun environment.

Parker Solar Probe: Instrumentation and Measurement Cadences
The Parker Solar Probe (Fox et al. 2016) measurements required for this study are magnetic field observations at "full" cadence (3.3-8.3 ms) from the FIELDS fluxgate magnetometer (MAG; Bale et al. 2016) and Level 3 plasma observations recorded by the ion electrostatic analyzer SPAN-Ion (Kasper et al. 2016;Livi et al. 2022) located on the ram-facing side of the spacecraft.Here, we utilize survey (sf00) cadence ion observations to find exhaust-associated CS candidates and burst (af00) cadence ion observations when available to confirm exhausts across CSs.The magnetic field and ion plasma velocity are measured in the RTN coordinate system with +R (radial) directed from the Sun to the Parker Solar Probe, and +T (transverse) positioned along a direction defined by the cross-product of the Sun's rotation axis with R; R × T = N completes the orthogonal system.Given that the orbit of the Parker Solar Probe is close to the ecliptic plane, +N nearly corresponds to a direction normal to the ecliptic plane.

Methodology to Detect CSs with Reconnection Exhausts
We conduct a survey of Parker Solar Probe CEs 4-11 for CSs with reconnection exhaust signatures using an automatic running window technique in two distinct phases.The first phase identifies unique CSs with candidate exhaust periods across several temporal scales.The second phase adopts an automatic Walen relation (Paschmann et al. 1986) on a list of unique exhaust candidates to verify whether a flow enhancement is consistent with a pair of Alfvén disturbances propagating away from an X-line.The method follows a similar approach to that described and employed for Wind mission data by Eriksson et al. (2022).
The first phase of the Parker survey applies a set of six sliding windows with duration Δt w1 = 20 s, Δt w2 = 60 s, Δt w3 = 120 s, Δt w4 = 240 s, Δt w5 = 600 s, and Δt w6 = 1200 s through magnetic field observations from the MAG instrument and plasma velocity observations recorded in survey mode (sf00) by the SPAN-Ion instrument (Kasper et al. 2016;Livi et al. 2022) within a distance of ∼55 Rs or 0.26 au from the Sun.The survey employs observations at a reduced, timewindow-dependent cadence Δt avg, i = Δt wi /2, where i = [1, 2, K, 6].For example, the shortest-duration Δt w1 = 20 s window applies Δt avg, 1 = 10 s cadence observations of V RTN and B RTN as obtained using a 10 s running average through the original sf00-cadence V RTN and the "full-resolution" B RTN , which results in daily data files of V RTN and B RTN time-stamped to the same center time of each adjacent 10 s time period.The selection of Δt w1 = 20 s as the shortest time window ensures that all eight encounters apply an identical window length through the variable sf00-cadence data with the highest sf00 cadence SPAN-Ion observations ranging from 6.99 s for CEs 4-5 and 3.50 s for CEs 6-8 to 1.75 s for CEs 9-11.The longest-duration Δt w6 = 20 minutes window is chosen to capture the widest known HCS-associated events in the first orbit reported by Phan et al. (2020).It also happens to be the longest-duration running window applied to Wind satellite observations at 1 au by Eriksson et al. (2022).The duration of the intermediate windows is separated pairwise by a factor of 2-3 from the nearest neighbor window duration.
A candidate CS is identified for all periods that satisfy a change |ΔB R | 5 nT or |ΔB T | 5 nT or |ΔB N | 5 nT in a given Δt wi = t 2 − t 1 time period using Δt avg, i = Δt wi /2 cadence data, where ΔB R = B R2 − B R1 is the difference of the time-averaged B R at t 2 (B R2 ) and B R at t 1 (B R1 ).ΔB T and ΔB N are defined in the same way as ΔB R .Each new Δt wi period is advanced in time by Δt avg, i from its preceding time period.The RTN coordinate system of V and B observations is then rotated into a preliminary survey-specific LMN system for each candidate CS period as defined below with ΔB L = B L2 − B L1 .A period is defined as a CS at time t c = t 1 + Δt avg, i in the LMN system for Δt avg, i cadence data if Here, δB L1 is the standard deviation of B L over 5Δt avg, i before t 1 and δB L2 is the standard deviation of B L over 5Δt avg, i after t 2 .
A survey-specific LMN system is defined using a crossproduct normal direction adjacent to the candidate CS from Δt avg, i cadence magnetic fields.Here, B 1 is obtained as the individual, component average over 2Δt avg, i before t 1 and B 2 is obtained as the component average over 2Δt avg, i after t 2 .The out-of-plane direction is defined as M = N × L MVA /|N × L MVA | and L = M × N is the direction of the rotating B L component of the magnetic field and the primary direction of the V L exhaust candidate.Here, L MVA is the direction of the maximum magnetic field variance from t 1 − Δt avg, i to t 2 + Δt avg, i .
We identify a reconnection exhaust candidate across the defined CS if the V L component of the Δt avg, i cadence velocity is a local extremum at time t c of the associated Δt wi window, such that it satisfies either with the additional criteria that δV L1 0.30|ΔV L1 | and δV L2 0.30|ΔV L2 |.Here, δV L1 is the standard deviation of the sf00-cadence V L measurement over Δt avg, i before t 1 and δV L2 is the corresponding standard deviation of V L over Δt avg, i after t 2 .The leading-edge ΔV L1 = V Lex − V L1 and the trailingedge ΔV L2 = V Lex − V L2 employ a smoothed version of the original-cadence V L to first find the local maximum (V Lmax ) and local minimum (V Lmin ) from t 1 to t 2 .Here, Figure 1 illustrates an example time interval of a set of automatically generated output data for an exhaust candidate detected on 2020 September 26 that satisfies the listed criteria.This encounter 6 event is identified at 21.3 Rs for the Δt w = 60 s window as shown between the two solid, black vertical lines at t 1 = 18:51:45 UT and t 2 = 18:52:45 UT with a suggested center time of t c = 18:52:15 UT shown as a solid, red vertical line.The Δt avg = 30 s cadence observations used to detect this candidate event are shown as red solid dots superposed on the full-cadence magnetic field observations and the af00-cadence SPAN-Ion data available at this time.The vector components of B and V are shown in the six lowest panels using the three automatically generated but surveyspecific hybrid-LMN vectors for this event with N = [0.37034,0.10975, 0.92239], L = [0.68552,0.63779, −0.35112], and M = [−0.62683,0.76235, 0.16096].
A radially outward L means that a negative ΔV L < 0 jet candidate with ΔV L1 = −60 km s −1 and ΔV L2 = −22 km s −1 is sunward-directed and consistent with a decrease of the total solar wind speed.This event is also associated with a significant ΔV M > 0 enhancement superposed on a negative V M background flow despite the absence of any large-scale gradients in the B M component of the magnetic field.The measured background flow with an average V L0 = (V L1 + V L2 )/2 or V L0 ∼ 193 km s −1 and V N0 = (V N1 + V N2 )/2 or V N0 ∼ 110 km s −1 adjacent to the event indicates that the Parker Solar Probe traversed the CS in a negative N-direction and in a negative L-direction along this candidate V L jet at a highly oblique ∼60°angle relative to N. The observed rotation from B L > 0 to B L < 0 thus requires a positive J M current density, which means that this current layer could have been supported by the observed ΔV M > 0 protons to carry some J M .
In summary, the initial phase applies time-averaged B L and V L measurements for six different Δt avg, i cadence surveys with no consideration of the full-cadence B L and V L measurements.This means that an exhaust-associated CS can be identified in several windows.A cross-examination of all candidate events results in a total of 5025 unique CSs with a possible exhaust indicated in Δt avg, i cadence V L data for the eight CEs.However, unlike the example event displayed in Figure 1, a significant fraction of these CSs (∼94%) display Alfvénic correlations between B L and V L when examined in the original-cadence measurements of B L (full) and V L (sf00 and af00 cadence) with a total of 306 exhaustassociated CS candidates (∼6%) remaining for further examination across all eight encounters.

Observations
A survey-specific hybrid-LMN coordinate system based on a cross-product normal is not necessarily optimal for a detailed CS analysis, since it relies on Δt avg, i cadence B RTN observations and an actual CS interval is not uniquely determined with the required temporal precision from an automatic time window analysis of B LMN alone.This is illustrated in Figure 1 for a full-cadence B L that can be very asymmetric with one sharp CS edge and one very gradual CS Figure 1.A 6 minute long time interval on 2020 September 26 associated with an example ΔV L exhaust candidate at 18:52:15 UT during CE 6.The top four panels show the proton density (Np), proton temperature (Tp), proton speed (V ), and magnetic field magnitude (B) in full-cadence B and af00-burst-cadence plasma resolution.The bottom six panels show the three components of B and V in a hybrid-LMN system in their optimum cadences for a limited time period centered about the time window shown between the vertical solid lines.
edge.Moreover, although as many as 198 CSs are found entirely within a unique time window, there are 93 CSs with an actual CS start time (t cs1 ) and/or CS stop time (t cs2 ) beyond the time window as determined from a full-cadence magnetic field.
A second exhaust confirmation analysis phase is necessary in which we first obtain two LMN systems from the full-cadence B RTN for each exhaust candidate period.The minimum variance of the magnetic field (MVAB) method (Sonnerup & Cahill 1967) is performed across each CS for two times (t a and t b ) chosen just beyond the CS.This results in N MVA as the minimum-variance direction, M MVA as the direction of intermediate variance, and L MVA as the direction of maximum variance.A local hybrid-LMN system is also obtained at the CS from a cross-product of the magnetic fields Here, Δt = 3 s or Δt = 5 s for shorter-duration CSs, while Δt = 10 s or Δt = 20 s for longer-duration CSs.The angle between the two normal directions, N MVA and N CP , is examined and we rotate N CP by 180°if this angle is larger than 90°with no impact on the hybrid-LMN system, since a CS may be associated with both ±N CP directions.A guide-field direction is obtained as Figure 2 displays a histogram of the angle between the two cross-product N CP normal directions.The survey-specific N CP is essentially generated "blindly" from an automatic analysis of the time-averaged B RTN , since there is no knowledge of a CS location relative to each time window.The manual N CP is obtained using the full-cadence B RTN just beyond the location of a visually confirmed CS.The automatic N CP directions are surprisingly high-quality with a typical 1°.5 offset and a median of only ∼3°between the two N CP vectors.However, there are 50 CSs where this angle is larger than 15°.In 17 cases, the survey-specific N CP normal deviates by as much as 48°(95th percentile); one event even deviates by as much as 89°from a locally obtained N CP .This variability of the automatic N CP naturally follows in the absence of known CS times.
Figure 3 displays one reconnection-associated CS candidate for each of the eight CEs, CEs 4-11, to represent a subset of the many different types of exhausts that the Parker Solar Probe can detect near the Sun.The L RTN = [L R , L T , L N ] vector of the local hybrid-LMN system is shown below each example.The CS start time (t cs1 ) and stop time (t cs2 ) are manually identified from the full-cadence B L component (panel (c)) in the local hybrid-LMN system as the times at the two edges of each candidate V L exhaust (panel (d)) shown as a pair of red vertical lines.The V L component is analyzed using a burst-mode (af00) SPAN-Ion measurement when available, or else from a surveymode (sf00) SPAN-Ion measurement as is typically the case for most of the CE 4 events.The actual CS durations (dt cs = t cs2 − t cs1 ) of the eight exhaust candidates shown here, from the CE 4 event to the CE 11 event, are 7.2, 31.7, 28.8, 21.6, 81.2, 33.6, 7.7, and 63.6 s.
A single V L reconnection exhaust is clearly visible across each B L rotation for most of the CSs.The exception is the CE 9 example on 2021 August 5.This CS displays a multiscale structure with a bifurcated B L rotation of the large-scale CS consisting of two separate steps of the B L rotation at t cs1 and t cs2 (Gosling & Szabo 2008).However, the first edge at t cs1 also displays a B L bifurcation at a smaller scale.In essence, the complete crossing supports two exhaust candidates in opposite directions: a negative jet contained by the first, small-scale bifurcation at t cs1 that is followed by a longer-duration, positive jet until t cs2 .There are 10 such "double" exhaust events included in this survey, which we interpret as the presence of two opposite reconnection exhausts.
The top panels of Figure 3 display the pitch angle distribution (PAD) of the suprathermal electron energy flux at sf0-cadence resolution from the SPAN-E instrument from 0°to 180°.The CS of CE 7 displays a transition between counterstreaming strahl electrons on closed-field lines on one side of the CS and unipolar strahl electrons associated with open-field lines on the other side of the CS.This is an expected transition of the strahl due to interchange reconnection.The CE 6 event is also indicative of an interchange-type reconnection.In this case, however, the counterstreaming energy flux is highly asymmetric with a dominant 180°strahl, which is nearly 10 times as high as the 0°strahl energy flux.The CE 10 event displays a dominant 180°strahl across the CS and while there is no discernible 0°strahl energy flux before the CS, there is a weak 0°strahl after the CS.The longer-duration dt cs > 60 s crossings shown for CE 8 and CE 11 display strahl signatures typically observed near perihelion HCS crossings with the Parker Solar Probe lingering near the HCS on one side of the B L rotation.This is also supported by the "partial" exhaust reentry periods before and after the identified CS of the proposed CE 11 exhaust region.The CE 9 event appears to involve open magnetic fields on both sides of the CS with a unipolar 180°strahl before and after this CS.This may be explained by a B L component mostly aligned with the normal direction of the RTN coordinate system.The CE 4 event is also associated with open magnetic fields on both sides of the CS from the presence of 0°strahl before and after the CS.In this case L CP is mostly directed along R, which means that the CS region is expected to consist either of fields connected to the Sun at both footpoints (Gosling et al. 2006c) or of open fields fully detached from the Sun (Gosling et al. 2005b).However, the 7.2 s duration CS is too narrow for the sf0 cadence of this  SPAN-E measurement to resolve the presence of strahl electrons, which may rather indicate a time aliasing of this single electron measurement at the CS due to the sudden magnetic field rotation.
The proton temperatures (panel (b)) of Figure 3 clearly increase within the CSs for the events during CE 4 and CE 8.However, a local temperature gradient appears to be a more common signature across these example CSs with a relatively higher proton temperature plasma associated with counterstreaming strahl electrons on locally closed field lines, and a lower proton temperature plasma more likely to be associated with unipolar strahl electrons on locally open field lines.This is in contrast to large-scale proton temperature transitions between coronal holes, which are associated with hotter protons on open-field lines, and adjacent closed-field regions of lower proton temperature plasmas (e.g., Kohl et al. 2006;Cranmer 2009).The situation is the opposite for coronal hole electrons, which are cooler than the electrons of neighboring closed-field regions (e.g., Habbal et al. 2011;Boe et al. 2023).
All 306 candidate exhaust periods are analyzed to determine whether the measured V L by the SPAN-Ion instrument satisfies a nearly Alfvénic flow speed across each CS as expected of reconnection outflows.This analysis examines a plasma-densityweighted form of the Walen relation V WL = V L0 ± ΔV AL (Paschmann et al. 1986) across each CS, where is the effective ion plasma mass density due to protons and α-particles.This analysis is typically based on an assumption of 100% protons in the solar wind or N α = 0 and N p = N with N representing the plasma number density or ρ = m p N. However, in this near-Sun regime, we apply a "heavy proton" correction of the form ρ eff = (0.92m p + 0.08m α )N for an assumed constant α-particle contribution consisting of 8% α-particles to the total plasma density and 92% protons or ρ eff = m eff N, where m eff = 0.92m p + 0.08m α with m α = 4m p and m p ∼ 1.67 × 10 −27 kg.This α-particle correction accounts for the presence of helium ions in these same magnetic fields that essentially slows the outflow motion of the magnetic flux from the X-line.The chosen α-particle abundance is higher than the typical 3%-6% α-content during quiet solar conditions to account for occasional solar flare periods when the α-content may increase above 10% (Alterman et al. 2021;Woolley et al. 2021).Subscripts of "0" represent an external (constant) value adjacent to the CS.In performing these Walen tests, we take advantage of the higher af00 cadence data when available for a given exhaust candidate or else use sf00-cadence measurements.
The proton number density (Np) from the ram-facing SPAN-Ion instrument is a partial density moment of the full solar wind proton distribution, and there are times when a fraction of the solar wind proton distribution falls outside the field of view (FOV) of the instrument due to the presence of the heatshield.In order to obtain optimum Walen predictions and verify whether a particular CS is associated with a reconnection exhaust or not, we apply a daily correction to the available SPAN-Ion partial density moment from a comparison with an estimated electron plasma density (Ne) obtained from a quasithermal noise (QTN) measurement (Meyer-Vernet 1979; Kruparova et al. 2023).The daily correction factor f = Ne/Np that we apply here is a median of this density ratio, which is typically calculated for a full 24 hr period.In one exception (2022 March 1), we calculate a median for the first 12 hr period to avoid an extended interval with significantly underestimated partial density on this date.
Table 1 displays the range of daily median ratios for the eight CE periods.In all CEs, the median of the daily Ne/Np ratio is higher on the inbound leg with a trend toward Ne/ Np ∼ 1 at perihelion.The outbound leg typically starts from Ne/Np < 1 at perihelion and gradually increases as Parker moves radially outward.The observed trends likely reflect a heatshield impact on the partial Np density moment.
The Walen predictions V WL = V L0 ± ΔV AL are conducted using 0.25 s interpolated measurements from the full-cadence B L and 0.25 s interpolated measurements from the originalcadence V L and ρ = m eff N.All interpolated quantities use a common 0.25 s cadence time stamp and N = f * Np is the proton density corrected to Ne.The analysis is performed automatically over many time intervals [t cs1 − Δt, t cs2 + Δt] toward the CS, where Δt changes from Δt = 120 s for the first Walen prediction to Δt = 2t s (af00 t s cadence data) or Δt = t s (sf00 t s cadence data) for the final Walen prediction.Each Walen analysis for a given Δt results in two time-series predictions with V WL1 (t) = V L01 ± ΔV AL1 (t) from t cs1 − Δt to t c on the leading side of the CS, and V WL2 (t) = V L02 ± ΔV AL2 (t) on the trailing side of the CS from t c to t cs2 + Δt.The signs of ±ΔV AL1 and ±ΔV AL2 are opposite and are set automatically from the sense of the B L rotation from B L1 to B L2 and the Ldirection of the suggested exhaust.The time t c between the leading and trailing intervals is identified through iteration from t cs1 − Δt to t cs2 + Δt to find the time when V WL1 = V WL2 .The presence of a reconnection exhaust is likely if there is a center time that satisfies t cs1 < t c < t cs2 for a Δt that results in a minimum ΔV L = |V WL − V L |.We typically require a high correlation coefficient R 0 between the complete V WL = V WL1 (t) + V WL2 (t) prediction and the observed V L for this time interval [t cs1 − Δt, t cs2 + Δt] to facilitate the exhaust confirmation.A final exhaust confirmation requires that there is a distinct pair of Alfvén disturbances at the two edges of the exhaust.This decision relies on the presence of two individual linear Pearson correlation coefficients, R 1 between V WL1 (t) and V L for the leading time interval [t cs1 − Δt, t c ] and R 2 between V WL2 (t) and V L for the trailing time interval [t c , t cs2 + Δt], such that their product R 12 = R 1 * R 2 typically satisfies R 12 > 0.60.In a handful of candidate time periods, an additional correction to the daily N = f * Np is required to improve the agreement between a local Ne value and the N adjacent to the CS.The QTN-corrected plasma density often results in a significantly improved exhaust flow prediction.
Figure 4 displays the four exhaust events detected for CEs 4-7 in Figure 3 with the fifth panels presenting the display the PADs for suprathermal electrons at 486 eV, the Tp (MK), the corrected Np (cm −3 ), the B L (nT), the measured V L (km s −1 ) in black and the predicted V L (km s −1 ) in red, the B N (nT) in red and the B M (nT) in black adjusted by their time period average, and the V N (km s −1 ) in red and the V M (km s −1 ) in black with both velocity components adjusted by their respective time period averages.
superposed on the measured V L component in black.The candidate exhausts all satisfy the basic expectation of a reconnection outflow with B L and V L being correlated across one side of the CS, and anticorrelated on the other side of the CS.A green vertical solid line marks the time t c when a transition occurs between leading and trailing Alfvén disturbances.The linear Pearson correlation coefficients for the complete signal (R 0 ) and the combined correlation coefficients (R 12 = R 1 * R 2 ) are marked in the respective plot headers together with the actual CS durations dt cs = t cs2 − t cs1 .The unit vectors of the hybrid-LMN system are shown below each plot for reference.
In three of the four exhausts, there is a clear indication of a ΔV M = V M2 − V M1 flow shear in the M-direction across the CS.There is a weak ΔV M ∼ 8 km s −1 for the CE 4 event on 2020 February 1.However, in addition to the enhanced V M ∼ 60-70 km s −1 flow within the V L ∼ 70 km s −1 exhaust region on 2020 September 26 (CE 6), which may be associated with a current-carrying flow, there is a strong ΔV M ∼ 20 km s −1 shear present across this CS with a similar ΔV M ∼ 20 km s −1 shear for the CE 7 event on 2021 January 20.A corresponding L-direction (ΔV L = V L2 − V L1 ) flow change across the CS is essentially nonexistent for the CE 4 event, and the CE 7 event only indicates a weak ΔV L ∼ 5 km s −1 .In contrast, the CE 6 event supports a strong ΔV L ∼ 40 km s −1 flow shear across the exhaust-associated CS.The CE 5 event on 2020 June 10 displays a similar ΔV L ∼ 30 km s −1 flow shear to that of the CE 6 event, but no ΔV M shear.
Figure 5 displays the same information for the four CE 8-11 candidate events shown in Figure 3.The R 0 correlations are significant between the measured and predicted V L components of the velocity in good agreement with the expected Alfvén speeds of reconnection outflows.The two opposite V L flows of the CE 9 event on 2021 August 5, as mentioned earlier, would require two overlapping Walen predictions.However, it is sufficient for the objective of this study on the nature and characteristics of active CSs near the Sun that one of the flows is consistent with a reconnection exhaust.All three CSs also display a significant 20 < ΔV M < 60 km s −1 flow shear in a co-moving frame of the solar wind.These near-Sun exhaust-associated CSs also occur at the plasma boundary transition between clearly open magnetic fields (unipolar strahl) and a complex region that could be interpreted as a closed-field region with suprathermal electron energy flux present across a wide range of pitch angles.Finally, while three events show a bifurcated B L with a central B L plateau surrounded by two sharper B L rotations at the edges of the CSs, the CE 11 event at 13.4 Rs displays a very sharp B L rotation at the t c center time of the CS.This central CS is embedded within a large-scale and gradual B L rotation.In this sense, it resembles the wide, HCS-like reconnection exhaust with a d cs ∼ 4000 d i normal width that the Wind satellite encountered at 03:14 UT on 2010 August 24 (Eriksson et al. 2022) with a central CS embedded within a gradual B L rotation at 1 au.

Temporal and Spatial Distribution Overview
The automatic Walen analysis of the 306 candidate periods results in a total of 236 CSs with a confirmed reconnection exhaust.In order to estimate the percentage of the proton velocity distribution function within the SPAN-Ion FOV, we fit a Gaussian function to the anode coordinates and sum over all theta angles and energies.We do this for all measurements within a given CS time frame and record how often a measurement occurs for the said exhaust time interval.This investigation shows that a proton distribution is measured within the SPAN-Ion FOV for at least 85% of each CS time interval in a majority of the 236 intervals.In one case, the proton distribution is found in its FOV for 75% of the CS time interval.Five of the 236 events indicate that a full-cadence B L magnetic field does not completely rotate across B L = 0.These five cases are excluded from the distribution analysis.Table 2 summarizes the final list of 231 confirmed exhausts identified over each ∼11 day period centered at the perihelion for CEs 4-11.The listed CE totals of exhausts are comparable with the 21 exhausts detected by the Parker Solar Probe across a 30 day period (October 27-November 25) around the 2018 perihelion of CE 1 (Phan et al. 2020).
In this extended survey for events, CE 5 includes the greatest number of exhausts (49) in 11.5 days with an average of 4.3 events day −1 , while CE 10 includes the lowest number of exhaust encounters (8) over a 10.5 day period or just ∼0.8 events day −1 on average.A major objective is to understand what factors may determine this exhaust occurrence variability in the extreme inner heliosphere from the measurements of B and plasma parameters that Parker encountered adjacent to the exhaust-associated CSs.
Figure 6 provides a histogram of the radial position of the Parker Solar Probe for the center times of the 231 exhaustassociated CSs.The median radial position of the cumulative distribution function (CDF) for a 2.5 Rs bin size is R sc = 37.5 Rs with the bulk of events identified at radial distances beyond ∼25 Rs.The three most sunward exhausts were detected in CE 11 at 13.4 Rs (0.06 au) from the Sun in a 10 minute period between 12:25 UT and 12:35 UT on 2022 February 25.These cases included a 63.6 s duration HCSassociated exhaust at 12:33:45 UT (see Figure 5) and the shortest-duration dt cs = 2.0 s event of the entire survey.This 2.0 s event, which corresponds to a d cs ∼ 205 km normal width exhaust, was encountered at 12:32:08 UT or ∼1.2 minutes before the edge of the HCS-associated exhaust.Figure 6 also compares this radial distribution of exhausts (left) with a histogram of the radial spacecraft locations (middle) for the combined analysis time interval of all eight CEs (4-11).This dwell time distribution uses 1 minute interpolated cadences of the radial positions within 55 Rs.The percentiles of the two CDFs, from the 5th and 25th percentiles to the 50th (median), 75th, and 95th percentiles, are shown in the right plot of Figure 6.The positions of the exhaust distribution clearly reflect an orbital dwell time coverage.This means that exhaustassociated CSs in the 13.4-55 Rs range from the Sun should be expected with equal probability at all radial distances.
Figure 7 displays a select number of parameters for the 11.0 day period of CE 4 (left) and the 10.5 day period of CE 10 (right).The center times of all exhaust-associated CSs (27 exhausts for CE 4 and 8 exhausts for CE 10) during these encounters are shown as vertical dotted lines in red color.There are few events within regions of highly Alfvénic fluctuations  (high ΔB N /B N and ΔV N /V N ) associated with high proton temperature plasmas and enhanced, antisunward V R flow bursts typical of switchback regions and coronal holes.This is particularly the case for CE 10 with no confirmed exhausts during a ∼5 day period on November 16-21 with exceptionally high ΔV N /V N .Otherwise, reconnection events tend to occur in a quiescent and slow solar wind irrespective of scale size for all eight encounters.

Coordinate System Analysis: MVAB and Hybrid-LMN
The following sections present the distributions of various parameters to better understand the occurrences of exhaustassociated CSs near the Sun.However, in order to obtain the distribution of CS orientations and widths along the normal direction to this boundary, it is critical to first verify the optimum three-dimensional geometry for a plasma boundary discontinuity such as a CS.
Historically, one of the most frequently employed coordinate systems involving single-spacecraft measurements has been one obtained from the MVAB.The MVAB system of orthogonal unit vectors is composed of the three eigenvectors L, M, and N with the normal direction (N) to a boundary defined as the direction of the minimum variance of the magnetic field in a time interval across the boundary (Sonnerup & Cahill 1967).The eigenvector direction of the maximum variance of the magnetic field is denoted as L, while the direction of intermediate variance is denoted as M = N × L.An alternative coordinate system may also be obtained using a cross-product normal direction N = B 1 × B 2 /|B 1 × B 2 | to the plane of the boundary from the upstream magnetic fields on the two adjacent sides of the boundary (Knetter et al. 2004).This hybrid-LMN system defines an out-of-plane direction from M = N × L MVA /|N × L MVA | and L = M × N completes an orthogonal set of unit vectors.Here, L MVA is the eigenvector direction of the maximum magnetic field variance across the boundary from the MVAB.The cross-product N-direction, in contrast to a boundary normal obtained from the MVAB, does not consider the presence of magnetic fluctuations and structure within a boundary layer.It is not obvious, however, whether MVAB or hybrid-LMN is the preferred system in general near the Sun, where the L-direction of CSs may be characterized by a preferential radial component of the magnetic field, such as one associated with the HCS.In this scenario, the Parker Solar Probe will traverse a substantial distance along a possibly turbulent reconnection exhaust region (Lapenta et al. 2022) before making a complete crossing of a CS along its normal direction.Highly oblique CS trajectories (V Lcs ?V Ncs ) through exhausts associated with B L ∼ B R could increase the probability of encountering significant variability of the B N component of the magnetic field as opposed to exhaust crossings at right angles (V Lcs = V Ncs ).Early theory (Sonnerup 1974) predicted that the X-line (Mdirection) should bisect the magnetic field rotation θ-angle across a CS for symmetric conditions of magnetic field strength and plasma density.Recent numerical investigations confirm that an X-line bisecting the full rotation angle between the upstream magnetic fields also holds in systems with asymmetric magnetic fields and plasma densities (Swisdak & Drake 2007;Hesse et al. 2013).The reason is that the halfangle direction of the X-line between the upstream magnetic fields maximizes the reconnection rate and the magnetic energy available for reconnection.In an optimum LMN system, the B M /B L ratio will reflect this B M /B L = 1.0/tan(θ/2) expectation, which is shown as a solid, black line in Figure 8.The MVAB-LMN system (Figure 8, left) fails the prediction in a general sense for field shear angles θ < 100°, while the hybrid-LMN system generally follows the prediction.
There are several outliers from the prediction in the hybrid-LMN system for field rotation angles 10°< θ < 90°, where B M1 /B L1 on the low-B L side of the CS and B M2 /B L2 on the high-B L side of the CS are far from the prediction such that |B M2 /B L2 − B M1 /B L1 | > 10.However, the predicted B M /B L ratio remains between the two ratios.It is shown in Figure 9 that the outliers are typically associated with highly asymmetric magnetic field conditions, where B L1 on the low-B L side is significantly lower than B L2 on the high-B L side of the CS.These B L differences bleed into the corresponding B M /B L ratio, such that the two ratios are offset symmetrically relative to the predicted B M /B L for a given field shear angle.
Figure 8 demonstrates that MVAB could not find a correct Mand N-direction for a wide range of field shear angles.The left side of Figure 8   direction" in MVAB is simply closer to the actual M-direction in most of the 231 events.This is supported by the typical agreement of measured and predicted B M /B L ratios in the hybrid-LMN system (Figure 8, right).This result indicates the presence of considerable variation in the actual normal field component (B N ) along the Parker Solar Probe trajectory through an exhaust-associated CS boundary near the Sun that the MVAB method is designed to suppress in obtaining a proposed N-direction.This B N variability may potentially be more prevalent the more oblique a particular CS crossing is with a spacecraft traversing a longer distance in the L-direction of the exhaust as it crosses from one side of the CS to the other.In summary, a hybrid-LMN system is typically more reliable than the MVAB system for a wide range of θ shear angles in finding the L, M, and N orientation of a CS near the Sun.The hybrid-LMN system, therefore, is used throughout this study in obtaining CS widths and orientations in space.

CS Distributions: Parker and Wind
The distributions of the 231 normal directions N RTN = [N R , N T , N N ] of the exhaust-associated CSs on the RTN unit sphere are shown in Figure 10 using a corresponding azimuthal angle f and a polar angle α.The two angles are defined as ) denoting the projection of N RTN onto the RTplane.Here, f = 0°corresponds to The f-angle is only shown in the +T half-sphere (0 < f < π) with all N RTN for N T < 0 transformed from −T into +T using N RTN = −N RTN given that a CS normal is always  associated with a ± direction ambiguity.The polar angle is defined as α = 0°for N RTN = [0, 0, 1] and α = 90°for The histogram of 17 very thin CSs for d cs < 200 km displays a dominant peak at 80°< f < 100°, the origin of which is further discussed in Section 4, and a nearly evenly distributed polar angle range.A population of 26 somewhat wider CSs at 200 < d cs < 500 km shows a similar angular distribution with a wider peak centered at 80°< f < 100°.In contrast, although the 112 thickest CSs with normal widths d cs > 2000 km can be found at all azimuthal angles, there is a preferred peak in the 40°< f < 60°direction.There is also an indication that thick exhaust-associated CSs support two preferred polar angle directions at 40°< α < 60°and 140°< α < 160°.An intermediate population of 76 CSs with normal widths at 500 < d cs < 2000 km displays a broad azimuthal peak with 45 events in the range 40°< f < 100°.This intermediate population also suggests a bimodal-like polar angle distribution with 37 events at 20°< α < 80°and 12 events at 120°< α < 140°.
Figure 11 (top) displays the dt cs distribution of actual CS durations for the 231 CSs in linear (left) and logarithmic (right) formats.The peak is found at dt cs = 10.0 s with a median at dt cs = 15.0 s for a bin size of 5.0 s.The 95th percentile of the CDF is dt cs = 255 s (4.25 minutes).There are 12 events at dt cs > 255 s including the five longest-duration CSs with dt cs = [14.0,14.2, 17.0, 53.0, 151.3] minutes.The two longest-duration events (53.0 minutes and 2.5 hr) were discovered visually during the exhaust confirmation analysis.The survey is able to identify a set of six CSs with actual duration dt cs 5.0 s and 34 CSs in the 5.0 < dt cs 10.0 s range.The six shortest-duration CSs last only dt cs = [2.0, 2.7, 4.5, 4.6, 4.8, 4.9] s.Recall that although the shortest time window of the survey is Δt w = 20 s for the Δt avg = 10 s time-averaged data, a short-duration event may be identified entirely within a 20 s window when employing full-cadence B and burst-mode (af00) cadence SPAN-Ion observations for V to obtain the actual CS durations.
Figure 11 (middle) shows the distribution of the corresponding CS normal widths (d cs = dt cs V N0 ) in Mm with a 500 km bin size.The linear distribution is shown on the left with the corresponding logarithmic distribution shown on the right.The normal width is obtained from the CS duration (dt cs ) and V N0 = (V N1 + V N2 )/2, which is the average of the two adjacent components of V RTN projected onto a locally obtained crossproduct normal N CP to each of the 231 CSs.The peak is contained in the first 0-500 km bin, where the survey uncovers as many as 43 events.Six of these CSs are discovered at ion kinetic scales d cs < 100 km with normal widths d cs = [14, 37, 42, 52, 59, 75] km.
The spectacularly thin d cs = 14 km event was encountered at a center time t c = 22:51:11 UT on 2021 August 10 when Parker was at 21.1 Rs from the Sun during CE 9.The dt cs = 7.9 s  duration of this CS (see psp_ce09_apj_plots_qtn_final.pdf at doi:10.5281/zenodo.10257747)with a low V N0 = −1.8km s −1 is associated with N CP = [0.013023,0.920328, 0.390932] and a positive exhaust with a leading-edge ΔV L1 ∼ 13 km s −1 and a trailing-edge exhaust speed of ΔV L2 ∼ 17 km s −1 directed along L CP = [−0.473504,−0.338674, 0.813077].The CS is asymmetric with a plasma boundary transition from Tp 1 ∼ 0.30 MK and Np 1 ∼ 3371 cm −3 at the leading edge to Tp 2 ∼ 0.23 MK and Np 2 ∼ 2716 cm −3 at the trailing edge.These noncorrected proton densities are somewhat higher than the electron density with a median Ne/Np ∼ 0.78 correction factor likely applicable on this day.The estimated ion inertial lengths are d i1 ∼ 3.9 km and d i2 ∼ 4.4 km for the noncorrected proton densities, and 4.4 and 4.9 km for a corrected Np corr , respectively.These densities, whether corrected to Ne or not, suggest that Parker encountered an exceptionally thin CS with an estimated width of only d cs ∼ 3.4 d i (noncorrected) or d cs ∼ 3.0 d i (corrected).The associated magnetic field shear angle is only θ = 39°across this thin CS.Incredibly, the thin CS is also embedded within a significant ΔV M = 33 km s −1 flow shear that dominates a much weaker ΔV L = 4 km s −1 flow shear in the frame of this CS.
The distribution of CS normal widths associated with reconnection near the Sun is highly weighted toward narrow CSs rather than wide HCS-like events.Figure 11 (middle) shows how the median of the 231 normal widths is d cs ∼ 1000 km near the Sun with the 95th percentile of this width distribution found to be d cs ∼ 18,500 km.In comparison, the distribution of exhaust normal widths from Wind observations at 1 au (Figure 11, bottom) supports a median d cs ∼ 8500 km width and a 95th percentile at d cs ∼ 84,000 km (Eriksson et al. 2022).Exhaustassociated CSs near the Sun are ∼10%-20% the width, in kilometer scales, of those at 1 au.This is mostly due to a higher plasma density at radial distances R < 0.26 au, which results in a shorter ion inertial length.For instance, the average ion inertial length at 1 au is 1 d i = c/ω pi ∼ 100 km, while a near-Sun density of N ∼ 1000 cm −3 corresponds to 1 d i = 7.2 km.In terms of some d i estimates, a median d cs ∼ 1000 km width near the Sun may correspond to roughly d cs < 150 d i for 1 d i = 7.2 km.In comparison, Wind recorded a median d cs ∼ 85 d i normal width distribution (Eriksson et al. 2022).
The CS normal width histogram obtained near the Sun appears to support an exponential distribution f (x) = 40e (− x/2.5) at widths below a median d cs ∼ 1000 km and a power-law distribution the form f (x) = 35x −1.33 for widths above this median as indicated in Figure 11 (middle) by the two curves in blue color (exponential) and red color (power-law).The corresponding normal width distribution of exhaust-associated CSs at 1 au demonstrates that a power law is also present at 1 au and in a very similar form f (x) = 950x −1.33 to that discovered near the Sun.However, the power law at 1 au appears to support a normal width distribution below a median at d cs ∼ 8500 km and down toward a 25th percentile of the CDF at d cs ∼ 3500 km.In contrast, there is less support for an exponential distribution of thin CSs at 1 au.This may be due to the limitations of the 3 s cadence plasma instrumentation on the Wind satellite.The presence of a power-law distribution of exhaust-associated CS widths, whether near or far from the Sun, may indicate a selfsimilar behavior of multiscale magnetic reconnection as discussed, e.g., by Ji et al. (2023).
The 231 events at distances R < 0.26 au, although far fewer than the 3374 events of the Wind study, provide some further striking similarities with those at 1 au, as shown in Figure 12 (left) by a histogram of the magnetic field rotation (shear) angles across these CSs.There is a clear resemblance between the two parameter distributions at R < 0.26 au and 1 au with most events expected at θ ∼ 35°near the Sun and at θ ∼ 45°at 1 au for a 10°bin size of both distributions.The medians are found to be θ ∼ 55°near the Sun and θ ∼ 65°at 1 au.These similarities clearly suggest that the process of magnetic reconnection near the Sun evolves through field rotation angles in a very similar way to that at 1 au.
The reconnection exhaust examples shown in Figures 4 and 5 indicate that a tangential flow shear may typically be present across a near-Sun CS in its co-moving frame of reference.Moreover, this flow shear is often seen along the M-direction associated with the out-of-plane J M current density.A tangential flow shear can be defined in the LM-plane in terms of its magnitude ΔV LM = √(ΔV L 2 + ΔV M 2 ) and direction ψ-angle, where, as before, are the leading-side flow differences relative to the co-moving frame of reference, A definition based on the leading-side V M1 ¢ and V L1 ¢ adjacent to the CS is in fact identical to a definition of the angle using the trailing-edge . This is due to symmetry considerations relative to the co-moving frame of reference V L0 and V M0 , since . The ψangle thus defined covers the range 0°< ψ < 90°with ψ = 0°f or a finite ΔV L flow shear along ±L and ΔV M = 0, and ψ = 90°f or a finite ΔV M flow shear along ±M and ΔV L = 0.
Figure 12 shows the tangential flow shear distributions across all 231 exhaust-associated CSs at R < 0.26 au in terms of the magnitude (middle) and ψ-angle (right).The measured median is ΔV LM = 12.5 km s −1 with a 95th percentile of ΔV LM = 60.0 km s −1 for a bin size of 2.5 km s −1 .Interestingly, the ψ-angle distribution is bimodal with a flow shear that preferentially aligns itself either along L or along M. In other words, there is a local minimum in this 5°bin size distribution at 40°< ψ < 45°.Meanwhile, the tangential flow shear distribution is quite different at 1 au as shown below these Parker results.First, the magnitude is significantly weaker at 1 au with a median ΔV LM = 5.0 km s −1 and a 95th percentile at ΔV LM = 32.5 km s −1 .Second, the ψ-angle distribution is not bimodal at 1 au.It is rather shifted away from M and toward L and ψ < 20°compared to the near-Sun regime.

Plasma Regime Distributions: Local and Encounter-wide
The distribution of reconnection events with respect to distance from the Sun (see Figure 6) indicates that active CSs should be expected with a rather similar probability at all radial distances.However, exhaust-associated CSs clearly display an uneven distribution in time (see Figure 7) with a tendency toward times of relatively lower proton temperatures, which are typically encountered in a quiescent slow wind.
Let us first characterize the CSs in terms of the strength of the magnetic field, the solar wind speed, and the proton temperature measured just upstream of the exhausts and compare these distributions with those present in any given ∼11 day CE for additional clues on the conditions that may result in an uneven temporal distribution of reconnection exhausts near the Sun.The left column of Figure 13 compares the distributions of magnetic field strength (B) at the leading edge of the 231 CSs with those measured during CE 4 (middle) and CE 10 (bottom).The peak and median values are found in the 25 < B < 50 nT bin for both exhausts and plasmas encountered during CE 4, while CE 10 supports a somewhat higher 50 < B < 75 nT range of median field strengths.The 95th percentile of the exhaust CDF is found at 225 < B < 250 nT compared to the lower 100 < B < 125 nT value in CE 4 and the higher 500 < B < 525 nT value in CE 10.
The middle column of Figure 13 demonstrates identical distributions of solar wind speed (V ) at the leading edge of active CSs to those encountered during CE 4 with a median 260 < V < 280 km s −1 and 95% of speeds found below 380 < V < 400 km s −1 .The solar wind during CE 10 generally supports a bimodal distribution with a distinct slow wind maximum at 220 km s −1 and a broader fast wind centered around 500 km s −1 with only 5% of wind speeds measured at V > 600 km s −1 .
The proton temperature distributions tend to reflect the solar wind speed distribution.The median for the exhaust-associated CSs is Tp ∼ 0.20 MK and plasmas measured during CE 4 show a similar median Tp ∼ 0.25 MK.Both distributions support a 95th percentile of the CDF at Tp ∼ 0.70 MK for a bin size of 0.05 MK.In contrast, there are two distinct Tp populations in CE 10: a cooler component peaking at Tp ∼ 0.15 MK and a hotter component with a maximum centered around Tp ∼ 0.80 MK.The CE 10 period measures 95% of protons below Tp = 1.45 MK.This survey of sf00 SPAN-Ion data clearly suggests that a high Tp > 0.80 MK plasma commonly present in a fast wind does not support many exhausts, irrespective of spatial scale size, for the applied window durations of Δt w = 20 s to Δt w = 20 minutes.Figure 14 demonstrates this tendency using the 95th percentiles of the Tp distributions for all eight CEs (4-11) with fewer exhausts expected per day on average for a high-temperature plasma regime near the Sun.

Discussion
The near-Sun survey for CSs associated with reconnection exhausts presented here focuses on a set of six well-separated windows between Δt w = 20 s and Δt w = 20 minutes for sf00cadence SPAN-Ion observations.This approach allows an examination of all CE 4 measurements, for which only a handful of af00-cadence burst observations exist, as well as the capture of wide HCS events.The smallest Δt w = 20 s also allows the capture of a subset of 43 narrow events with normal widths d cs < 500 km as compared with the median 1000 < d cs < 1500 km width for all 231 events.The question is what impacts the chosen time windows may have on the results such as the CS orientations and the associated normal widths.
Let us assume a near-Sun plasma with proton density 100 < Np < 1000 cm −3 and a corresponding range of ion inertial lengths 22.8 > d i > 7.2 km for a common range of plasma velocities 300 < V R < 500 km s −1 .Let us further assume the existence of a thin CS with d cs = 15 d i normal width in this plasma with a normal direction N = [1, 0, 0] along +R, where this study could not identify any thin d cs < 200 km events (see Figure 10).It would only take 0.36 < dt cs < 1.14 s for this 108 < d cs < 342 km wide CS to completely traverse the Parker Solar Probe in a V R = 300 km s −1 slow wind.This interval would further shrink to just 0.22 < dt cs < 0.68 s in a V R = 500 km s −1 fast wind plasma.The best available af00 cadence of the SPAN-Ion data is Δt ∼ 0.44 s in CEs 5-8 and it is as high as Δt ∼ 0.22 s for CEs 9-15.At these optimum cadences, the spacecraft would capture no more than two complete measurements at Δt ∼ 0.44 s or no more than five samples at Δt ∼ 0.22 s in a 300 km s −1 solar wind.In a 500 km s −1 solar wind, this would change to no more than one full sample at Δt ∼ 0.44 s or three complete samples at Δt ∼ 0.22 s.In summary, the Parker mission supports the magnetic fields.In this case the outflow velocity from the reconnection region is c A

= -¢
, where p¢ is the derivative of the total pressure (electron and ion) in the direction normal to the CS for an out-of-plane B z magnetic field.Pressure balance implies p B 8 2 p ¢ = -¢ when the tension from the field line curvature can be neglected.As N, B z , and B all vary across the CS, so does v *x , but less important than its local magnitude is the spatial average across the CS, ) , where L y is the characteristic normal width of the CS.An exact evaluation of this integral requires detailed knowledge about the spatial profiles of the integrands.However, in order to make further progress, we replace N and B z with their averages, 〈N〉 and 〈B z 〉, across the CS.The former has already been implicitly defined from c A 2 Cassak & Shay (2007) from the requirement that reconnecting flux tubes must contain equal magnetic fluxes.In a similar manner we have for the out-of-plane magnetic field 〈B , where it is assumed that the X-line bisects the θ rotation angle.The integral above gives a characteristic diamagnetic velocity, v *x = (c/8πeL y )[〈B z 〉/〈N〉]ln(B 2 /B 1 ) 2 with ln denoting the natural logarithm.Diamagnetic stabilization of reconnection occurs when |v * is the ratio of the total magnetic field strengths of the upstream plasmas with B 2 > B 1 .Here, the definition of the ion inertial length d i incorporates 〈N〉. Figure 15 displays this general stabilization condition for all 231 exhaust-associated CSs near the Sun (left) and the 3374 exhaust-associated CSs at 1 au (right) reported in Eriksson et al. (2022).These results demonstrate how magnetic reconnection is allowed, since f (b) < (L y /d i )tan(θ/2) across all the identified CSs, as we have also confirmed from Walen analyses.
The observations of reconnection exhausts at R < 0.26 au can support a nested layer of two sets of B L bifurcations, with one present across the complete field rotation θ-angle of a large-scale primary CS, and another present across a fraction of the rotation θ-angle at a small-scale secondary CS associated with the boundary of a primary exhaust.This is illustrated across a CS on 2021 August 5 in Figure 3 with each of the two opposite exhausts contained within a bifurcated B L rotation.This multiscale reconnection process is also active at 1 au as demonstrated by Wind satellite observations (Eriksson et al. 2022).
It can be argued that the very similar θ distributions present in the two regimes reflect a combination of turbulent CS formation at small scales and low-shear θ-angles, and a cascade of relatively few large-scale and high-shear CSs into many smallscale and low-shear CSs through reconnection.This multiscale reconnection process through nested layers of bifurcated CSs may indeed be responsible for the observed power-law distributions of CS normal widths with f (x) = A * x −1.33 for A = 35 at R < 0.26 au and A = 950 at 1 au.The indications of an exponential distribution for normal widths below the median d cs < 1000 km at R < 0.26 au likely reflect the presence of ion kinetic dissipation scales.The general absence of an additional exponential distribution of normal widths at 1 au below the 25th percentile of the CDF at d cs ∼ 3500 km is very likely due to the 3 s cadence limitation of plasma instruments in a lower-density plasma regime.

Conclusions
A survey of exhaust-associated CSs at R < 0.26 au from measurements obtained by the Parker Solar Probe during CEs 4-11 shows how reconnection exhausts tend to be observed with equal probability at all radial distances with a preference for quiescent Tp < 0.80 MK plasmas typical of a slow-wind regime.The high Tp > 0.80 MK plasmas of a fast wind characterized by significant transverse ΔV N /V N or ΔV T /V T fluctuations rarely support exhaust-associated CSs irrespective of CS width.
Despite the limitation of this initial study to window durations Δt w > 20 s, there are as many as 43 CSs with exhausts confirmed for normal widths d cs < 500 km and 17 CSs for widths d cs < 200 km.The dominant orientation of such thin CSs at 80°< f < 100°reflects a transverse direction of an N CP normal relative to +R, which this study is able to address.A survey using high-cadence SPAN-Ion observations will likely result in a larger number of active ion kinetic scale CSs at d cs < 100 km widths.However, despite a few reported exhausts in a turbulent and fast wind at 1 au (Gosling 2007), it remains to be seen how common ion kinetic scale events are near the Sun, and whether CSs of a high-temperature and fast wind plasma can support reconnection at R < 0.26 au.The apparent absence of exhausts in high proton temperature plasmas near the Sun for CEs 4-11 is consistent with initial results from the first CE (Phan et al. 2020) with no events present for a ∼9 day period near the perihelion when the Parker Solar Probe mapped to an equatorial coronal hole.It is also consistent with a Ulysses spacecraft survey (Gosling et al. 2006b) that could not confirm any exhaust encounters during a ∼3 yr interval in 1993-1996 when this spacecraft was embedded within a highspeed wind emanating from a polar coronal hole.
This study confirms that in situ signatures of interchange reconnection may be observed at radial distances accessible by the Parker Solar Probe in a slow wind.Several reconnection exhaust examples of this nature demonstrate the presence of a local temperature gradient across the CS with a higher proton temperature plasma on locally closed fields and a lower proton temperature on locally open fields.This is in contrast to largescale plasma transitions between coronal holes, which are associated with higher proton temperature plasmas on openfield lines, and adjacent closed-field regions associated with relatively lower proton temperature plasmas.The individual interchange reconnection events reported here in a slow wind are in general contrast with those proposed to occur deep within the corona, which may involve many instances of interchange reconnection at the scale of supergranulation convection cells.The latter has been proposed as a source of the expanding fast wind and the formation of switchback plasmas within coronal holes (Bale et al. 2023;Drake et al. 2023).
A coordinate system analysis confirms that a hybrid-LMN system based on a cross-product normal provides a highconfidence orientation for all 231 exhaust-associated CSs for all field shear angles θ.In contrast, the MVAB system fails for field shear angles θ < 100°.This conclusion stems from the agreement between the measured B M /B L ratios adjacent to the CSs and the predicted ratio B M /B L = 1/tan(θ/2).Two fundamental lessons can be drawn from this agreement.First, it directly supports the property that X-lines are oriented in such a way that they bisect the magnetic field rotation θ-angle, whether the fields and plasmas are asymmetric or not, to maximize the reconnection rate and the magnetic energy available for reconnection to proceed.Second, it indicates the presence of considerable variation of the normal B N component along the Parker Solar Probe trajectory through an exhaustassociated CS boundary near the Sun.
The normal width distributions appear to support a universal multiscale reconnection process through nested layers of bifurcated CSs that may be responsible for the observed power-law distributions of widths proportional to x −1.33 at R < 0.26 and 1 au.The high-cadence plasma observations near the Sun allow the Parker Solar Probe to sample an ion kinetic dissipation scale.This is likely responsible for the apparent presence of an exponential distribution at scales below the median d cs < 1000 km in addition to the power-law distribution present at relatively larger scales.
The distributions of field shear θ-angles are essentially identical at R < 0.26 au and 1 au with medians at θ ∼ 55°near the Sun and θ ∼ 65°at 1 au, which provides further support for a multiscale reconnection evolution from large shear angles to smaller field shear angles.In contrast, the tangential flow shear distributions are quite different near and far from the Sun.A bimodal flow shear angle distribution is present near the Sun with strong shear flow magnitudes.This flow shear distribution appears to change with radial distance with a weaker tangential flow shear distributed with nearly equal probability along and transverse to the exhaust direction.

Figure 2 .
Figure2.Histogram distribution of the hybrid normal angles as obtained from the automatic survey using time-averaged B RTN and from the manual analysis using full-cadence B RTN for a subset of 291 exhaust-associated CS candidates.

Figure 3 .
Figure 3. Eight candidate exhaust-associated CSs for CE 4-11: (a) pitch angle distribution of the suprathermal electron energy flux at 486 eV (CE 4-9) and 433 eV (CE 10-11), (b) proton temperature (Tp) in megakelvin, (c) B L component of the magnetic field at full-cadence resolution, and (d) V L component of the proton velocity at af00-cadence resolution.Tp observations are shown as both sf00-cadence data (black dots) and af00-cadence data (red curve).
Apart from this multiscale exhaust for a nested set of bifurcated B L fields that Parker detects on open-field lines at R = 46.3Rs from the Sun, the three confirmed exhausts of CE 8 (2021 April 29), CE 10 (2021 November 22), and CE 11 (2022 February 25) are all detected very close to the Sun at radial distances 13.4 Rs < R < 21.7 Rs.

Figure 5 .
Figure 5. Four CSs associated with confirmed reconnection exhausts during CE 8 (top left), CE 9, CE 10, and CE 11 (bottom right).Same format as that of Figure 4.

Figure 6 .
Figure 6.(Left) Histogram of the Parker Solar Probe radial position at the time of all 231 exhaust-associated CSs.(Middle) Histogram of the Parker radial position at 1 minute cadence for the complete duration of all CEs (4-11).(Right) Percentiles of the CDFs of the spacecraft positions when exhausts were detected and all positions for encounters 4-11.

Figure 8
Figure 8 compares the two LMN systems for all 231 exhaust events.Each CS is associated with one magnetic field shear angle (θ) and two B M /B L values, one for each side of the CS.Here, a B M /B L value shown in blue color corresponds to B M1 /B L1 on side 1 of the CS, which is defined as the side with the minimum B L magnitude.A B M /B L value shown in red color corresponds to B M2 /B L2 on side 2 of the CS, which displays the maximum B L magnitude.Early theory(Sonnerup 1974) predicted that the X-line (Mdirection) should bisect the magnetic field rotation θ-angle across a CS for symmetric conditions of magnetic field strength and plasma density.Recent numerical investigations confirm that an X-line bisecting the full rotation angle between the upstream magnetic fields also holds in systems with asymmetric magnetic fields and plasma densities(Swisdak & Drake 2007;Hesse et al. 2013).The reason is that the halfangle direction of the X-line between the upstream magnetic fields maximizes the reconnection rate and the magnetic energy available for reconnection.In an optimum LMN system, the B M /B L ratio will reflect this B M /B L = 1.0/tan(θ/2) expectation, which is shown as a solid, black line in Figure8.The MVAB-LMN system (Figure8, left) fails the prediction in a presents a "B M /B L " ratio with the "Mdirection" being the direction of intermediate B-variance from an MVAB analysis.However, what is shown is closer to an actual B N /B L ratio, which explains the very low values far from the predicted B M /B L = 1.0/tan(θ/2) expectation.The suggested direction of the minimum B-variance as the "N-

Figure 7 .
Figure 7. Two ∼11 day periods are shown for CE 4 (left) and CE 10 (right).The subpanels (top to bottom) display the PADs for suprathermal electrons at 486 eV (CE 4) and 433 eV (CE 10), the Tp (MK), the magnetic field magnitude B (nT), the R-components of B and V, the N-components of B and V, and the Parker Solar Probe radial distance (Rs) from the Sun.The vertical dotted lines in red color mark the center times (t c ) of all reconnection exhausts confirmed by a Walen analysis.

Figure 8 .
Figure 8. Comparing predicted and observed B M /B L ratios with magnetic field shear angle (θ) at the CSs for 231 exhausts using the MVAB (left) and hybrid-LMN (right) coordinate systems.

Figure 10 .
Figure 10.Distribution of CS normal vectors in terms of polar and azimuthal angles.The corresponding histograms apply a 20°bin size from 0°-20°to 160°-180°.Each 20°histogram bar is shown with the first 0°-20°bin located at 0°-10°whereas the second 20°-40°bin is shown for the bar at 10°-30°with all subsequent bars shown at a 10°offset.

Figure 11 .
Figure 11.(Top) Distributions CS durations associated with reconnection exhausts near the Sun.(Middle) Normal width distributions of 231 exhaust-associated CSs at R < 55 Rs from the Sun.(Bottom) Normal width distributions of 3374 exhausts at 1 au (Eriksson et al. 2022).
for the plasma number density (N) and total field strength (B) on the two sides of the CS.Second, we calculate the component of the diamagnetic velocity along the outflow direction,

Figure 15 .
Figure 15.Magnetic field shear angle θ vs. f (b) = [ln(b 2 )√(b)]/(1 + b) at exhaust-associated CSs for R < 0.26 au (left) and R = 1 au (right), where b = B 2 /B 1 is the ratio of the total magnetic field strengths of upstream plasmas with B 2 > B 1 .All cases are found in the f (b) < (L y /d i )tan(θ/2) regime for L y = 2d i , where reconnection is allowed.

Table 1
CE Survey Times (t 1 − t 2 ) and the Associated Minimum, Maximum, and Median Values of the Daily Cadence of the f = Ne/Np Density Ratio Figure 4. Four CSs associated with confirmed reconnection exhausts during CE 4 (top left), CE 5, CE 6, and CE 7 (bottom right).The subpanels (top to bottom)