Introduction

Magnetic reconnection is the process in which magnetic field lines break and reconnect, converting magnetic energy into motional energy of charged particles in various natural and controlled environments, including terrestrial and planetary magnetospheres, solar and stellar flares, and fusion devices (D. I. Pontin & E. R. Priest 2001; J. F. Drake et al. 2006; T. D. Phan et al. 2018;G. D. Fleishman et al. 2022). In the heliospheric current sheet (HCS) where the interplanetary magnetic field (IMF) reverses its polarity, past spacecraft observations have shown that magnetic reconnection dissipates the Parker spiral magnetic field, generating high-speed flows and energizing particles (J. T. Gosling et al. 2005bGosling et al. , 2006;;B. Lavraud et al. 2020; T. D. Phan et al. 2021;A. Szabo et al. 2020;S. Eriksson et al. 2022). However, there is vigorous debate about the extent of reconnection-associated particle energization in the HCS (J. T. Gosling et al. 2005a; O. Khabarova et al. 2020).

A key parameter that controls the heating and energization of electrons and ions during reconnection is the magnetic energy released per particle m i C A 2 , where C A is the Alfvén velocity associated with the plasma parameters upstream of the reconnecting current layer (T. D. Phan et al. 2013Phan et al. , 2014;;M. A. Shay et al. 2014;M. Øieroset et al. 2023). In reconnection events with direct evidence of strong particle energization, such as Earth's low-density magnetotail and solar flares, m i C A 2 is typically above 10 keV (H. Arnold et al. 2021; M. Øieroset et al. 2023). Conversely, the origin of the ∼MeV energetic ions observed near HCS crossings around and beyond Earth's orbit (G. P. Zank et al. 2014; O. Khabarova et al. 2015; V. Zharkova & O. Khabarova 2015) remains under debate since, at these distances, the corresponding m i C A 2 values are lower than 100 eV (J. T. Gosling et al. 2005a;J. F. Drake et al. 2009;G. Murtas et al. 2024). Recent observations from NASA's Parker Solar Probe (PSP) have revealed unexpected ∼20-100 keV suprathermal (ST) proton intensity enhancements during several near-Sun HCS crossings, despite having m i C A 2 values around 0.2 keV (M. I. Desai et al. 2022; T. D. Phan et al. 2022). However, since these energetic protons were found to propagate away from the Sun, it was unclear whether they originated from the Sun or from the HCS reconnection sites located sunward of PSP (M. I. Desai et al. 2022), thus leaving the possibility of strong particle energization during reconnection at the HCS as an open question.

Here we report direct evidence of reconnection at the near-Sun HCS accelerating protons up to ∼400 keV. Since m i C A 2 for this event was only ∼0.5 keV, surprisingly, the most energetic protons had energies nearly 3 orders of magnitude greater than the available magnetic energy per particle. A key component of these PSP data is the observation of a sunward-directed reconnection exhaust (T. Phan et al. 2024) and the concurrent detection of sunward-streaming energetic protons within the exhaust. Therefore, this event clearly demonstrates that energetic protons up to ∼400 keV are accelerated at the HCS reconnection sites located antisunward of PSP and not by unrelated processes at the Sun.

PSP Observations

We use solar wind ion and electron data from SWEAP/SPAN (J. C. Kasper et al. 2016;P. L. Whittlesey et al. 2020;R. Livi et al. 2022), magnetic field data from FIELDS (S. D. Bale et al. 2016), and energetic proton measurements from ISIS (D. J. McComas et al. 2016;M. E. Hill et al. 2017). Figure 1 shows that the HCS crossing studied here occurred over a long duration (∼3.7 hr) on December 12 from ∼06:20 to ∼10:00 UT during PSP solar encounter 14 (E14) at a distance of ∼16.25 solar radii (R s ) from the Sun. The HCS crossing is recognized by the rotation of the radial component B R of the IMF from -650 to +470 nT (Figure 1(h)), the flipping of solar-origin strahl electron pitch-angle (PA) fluxes from 180°to 0°(Figure 1(e)), and the factor of ∼10 density enhancement (Figure 1(f)) relative to the solar wind across the current sheet. Figure 1(g) shows that relative to the solar wind speeds outside the HCS, the plasma speed inside the HCS was smaller due to the persistent presence of a sunward-directed plasma jet emanating from a dominant reconnection site located antisunward of the spacecraft (T. Phan et al. 2024). The magnetic shear across the HCS was ∼162°. Note that across the core of the exhaust B R < 0. This is a consequence of the differing Alfvén speeds on the two sides of the HCS. The magnetic field within a reconnection exhaust is tilted when the upstream Alfvén speeds differ (Y. Lin & L. C. Lee 1993). The sketch in Figure 1(i) illustrates the approximate trajectory of the spacecraft through the HCS based on the variations of B R . Since the outflow was continuously observed for 3.7 hr and the reconnection X-line driving this outflow was convecting outward with the ambient solar wind above 200 km s -1 , the inferred radial scale length of the exhaust as sampled by PSP was at least ∼5 R s .

The proton intensities between ∼67 and 536 keV (Figure 1(a)) start increasing just before PSP enters the HCS at ∼06:20 UT; those measured in the lowest energy range increase by nearly 4 orders of magnitude, while those measured at higher energies show clear but somewhat smaller (between ∼1 and 2 orders of magnitude) enhancements within the HCS. During the onset of the proton intensities (06:20-06:25 UT; Period 1 in Figure 1(a)), PSP traverses open field regions, as evidenced from the antisunward strahl electrons seen near PAs of 180°in Figure 1(e). Here, the energetic proton population flowing back toward the Sun shown in Figure 1(b) is not only more intense but also extends to higher energies up to ∼400 keV when compared with that flowing away from the Sun shown in Figure 1(c). The pitch-angle distributions (PADs; Figure 1(d)) during the initial portion of the flat-top intensity enhancement show sunward-propagating energetic protons transitioning into near-isotropy, followed by a peak near ∼90°toward the end of Period 2. Just before the polarity reverses. i.e., throughout Period 3, PSP traverses a region where the PADs peak at 90°, indicating a trapped population of energetic protons where the nearly field-aligned and anti-fieldaligned particles have escaped into the solar wind (see Figure 2 for details).

After the magnetic field reverses polarity at ∼06:47 UT and until PSP exits the HCS at ∼10:00 UT, the ∼67-134 keV proton intensities decrease by approximately 2 orders of magnitude but are still ∼100 times greater than those measured outside the HCS. The proton intensities exhibit at least two separate increases from ∼07:17-08:05 UT and ∼08:06-08:45 UT, labeled A and B in Figure 1 Here, since B R points away from the Sun (Figure 1(h), B R > 0), most of these energetic protons originate from sources located antisunward of PSP and not the Sun. The intermittent presence of counterstreaming strahl electrons (Figure 1(e)) throughout the HCS encounter is another strong indicator that PSP is located sunward of the reconnection X-line and traversing reconnectiongenerated closed-field lines with both footpoints anchored at the Sun (J. T. Gosling et al. 2006). This is in contrast to the strahl dropouts that are typically observed when a spacecraft is located antisunward of the X-line and traverses reconnection-generated field lines disconnected from the Sun (J. T. Gosling et al. 2005b). Briefly, Figure 1 demonstrates that from ∼06:25 until ∼10:00 UT, PSP detected closed magnetic field lines produced by reconnection at the HCS and simultaneously observed a sunward-flowing plasma jet and energetic protons up to approximately 400 keV from HCS reconnection sources located antisunward of PSP.

Figure 2 examines the temporal evolution of the proton PADs and their energy dependence from 06:20 to 07:00 UT. During this 40 min interval, PSP entered the HCS and detected abrupt onsets and flat-top profiles in the proton intensities (Figure 1(a)). During the onset-Period 1 from ∼06:20 to 06:25 UT (Figure 2(d))-the proton PADs peak at ∼120°PA and show an additional smaller peak near ∼45°, possibly because protons near these two PAs are reflected back into the exhaust from external regions with enhanced field strength, but those with PAs near 0°, 90°, and 180°are "lost" in magnetospheric-type loss cones (J. E. Borovsky et al. 2022).

During the initial portion of the flat-top intensity enhancement from 06:26 to 06:37 UT (Period 2; Figure 2(e)), the proton PADs between ∼90 and 400 keV exhibit strong (∼10:1 anisotropy) sunward flow with broad peaks over 0°-45°PAs, while those between ∼70 and 90 keV show peaks between 45°a nd 135°indicating the presence of a quasi-trapped proton population at these lower energies. Just before the magnetic field reverses polarity at 06:47 UT, the proton PADs at all energies up to 400 keV exhibit ∼30°-45°wide peaks centered at ∼90°(Period 3; Figure 2(f)). In this region, the field is relatively weak (∼250 nT), with a low B R and a dominant B N component (Figures 2(c) and 1(h)), which implies that the ∼67-400 keV protons with Larmor radii ranging between ∼150 and 370 km (J. R. Hörandel 2010) are ExB drifting and efficiently trapped perpendicular to the local magnetic field, and further that PSP is traversing regions close to their acceleration sites near the core of the reconnection exhaust. After the magnetic field polarity reverses at ∼06:47 UT, the proton PADs (Figure 2(g)) associated with the intensity modulations observed between ∼06:48 and 10:00 UT in Figure 1(a) show that the sunward-streaming energetic proton population is nearly uniformly distributed over ∼90°-180°PAs and extends upward of ∼400 keV. In summary, with the magnetic field pointing radially inward during Period 2 (Figures 2(c), (e)) and outward during Period 4 (Figures 2(c), (g)), the PADs of protons up to ∼400 keV during these two intervals exhibit strong sunward anisotropy, thereby providing direct, compelling evidence that these energetic protons originate from HCS reconnection sources located antisunward of PSP.

The differential intensity versus kinetic energy of protons from solar wind energies through the ST energy regime (Figure 3(a)) shows that the proton spectrum between ∼67 and 527 keV behaves as a power law of the form / dj dE E µ g -, where / dj dE is the differential intensity at energy E in MeV and γ ∼ 5.1 ± 0.12 is the fitted value of the spectral index. Additionally, the HCS solar wind proton spectrum shows the formation of a high-energy tail between 5 and 20 keV, which is well above the core Maxwellian distribution. Extrapolating the energetic proton spectrum to lower energies into the solar wind regime reveals the formation of a shoulder on the distribution, which might indicate the presence of local wave growth and scattering that interferes with the continuous acceleration to higher energies (J. L. Verniero et al. 2020;A. Fitzmaurice et al. 2024).

Simulations of Magnetic Reconnection

The magnetic energy released per particle controls the heating and energization of electrons and ions during reconnection. For a system with an asymmetry in the upstream conditions, this parameter is given by m i C Ah 2 , where C Ah is the hybrid Alfvén velocity for asymmetric magnetic reconnection, given by

where the subscripts 1 and 2 denote the magnetic field magnitude and density either side of the HCS (P. A. Cassak & M. A. Shay 2007; T. D. Phan et al. 2013Phan et al. , 2014;;M. A. Shay et al. 2014;M. Øieroset et al. 2023). In this HCS event, C Ah was ∼232 km s -1 , so m i C Ah 2 was ∼0.56 keV. Thus, it is surprising that the protons form power-law distributions that extend upwards of 400 keV, which is ∼10 3 times greater than the available magnetic energy per particle.

To establish that such extreme proton energization is possible in this event, and to better understand the underlying physical mechanisms, we carried out simulations with the kglobal model (H. Arnold et al. 2019Arnold et al. , 2021;;J. F. Drake et al. 2019), which has been upgraded to describe the energization of ions as well as electrons (Z. Yin et al. 2024aYin et al. , 2024b)). We carry out 2D simulations with a Harris-like equilibrium and upstream parameters based on direct PSP measurements outside of the reconnection exhaust. The antiparallel component of the magnetic field (determined using the minimum variance analysis of the magnetic field; B. U. Ö. Sonnerup & L. J. Cahill 1967) at the two edges of the HCS are given by B 1 = 560 and B 2 = 470 nT with corresponding densities of 1500 and 3000 cm -3 (T. Phan et al. 2024), respectively. The upstream proton and electron temperatures are 46 and 91 eV (not shown), respectively. The simulations are carried out with an initial current layer thickness of 0.01L and two different guide fields, corresponding to 0.2 and 0.3 of the reconnecting fields. Both these values are within the range of uncertainty in the guide field determination due to the long (3.7 hr) duration of the HCS crossing. The proton-to-electron mass ratio is 25, so the electrons are more massive than reality. However, it has been well established that the reconnection dynamics are insensitive to the electron mass (M. A. Shay & J. F. Drake 1998; M. Hesse et al. 1999;M. A. Shay et al. 2007). Magnetic reconnection is controlled by a hyperresistivity, as in earlier simulations with fluid ions (H. Arnold et al. 2021). The key characteristic of the model is that all kinetic scales have been eliminated so that direct simulation of reconnection dynamics in macroscale systems is now possible. All scales are normalized to the system scale length L, which is the periodicity length along the direction of the reconnecting magnetic field.

The simulations revealed that the HCS developed multiple reconnection sites, resulting in the formation of large numbers of flux ropes that merged dynamically during the evolution of the system (see Figures 4(a)-(e)). Reconnection proceeds with the growth of many small flux ropes that undergo mergers to drive electron and proton acceleration (J. F. Drake et al. 2006Drake et al. , 2013;;M. Oka et al. 2010). The feedback of energetic particles on the reconnection dynamics occurs predominantly through the pressure anisotropy. Because particle heating and acceleration occur predominantly through Fermi reflection (J. T. Dahlin et al. 2014;X. Li et al. 2019) and the pressuredriven macroscale parallel electric field, the pressure parallel to the ambient magnetic field greatly exceeds that in the perpendicular direction. Figure 4(f) shows the fire-hose parameter / ( )

-^late in time from the simulation in Figure 4(e). Negative values of α correspond to regions that are fire-hose unstable. The cores of islands are near marginal fire-hose stability so that the magnetic tension force that drives reconnection is strongly reduced. There, the plasma has undergone strong energization, and the energetic particles feedback on the dynamics of the flux ropes to suppress reconnection and island merger (J. F. Drake et al. 2006Drake et al. , 2013;;H. Arnold et al. 2021). The magnetic field B z increases substantially within the flux ropes compared with the corresponding upstream value due to plasma compression in the reconnecting current layer (Figure 4(g)). The enhanced values of B z reduce the magnetic shear during the flux rope merger compared with that across the HCS prior to reconnection (T. Phan et al. 2024).

Particle Acceleration in Merging Flux Ropes

Figure 4(h) shows the initial and late time distributions of electrons and protons, with the protons reaching ∼500 keV for the simulation with a guide field of 0.2. While the protons contain modestly more energy than the electrons at late times, Figure 3. Proton differential energy spectrum during the E14 HCS crossing and comparison with kglobal simulations. (a) Differential energy spectrum of ∼200 eV-527 keV protons from 06:20 to 10:00 UT. The solid line shows a power-law fit of the form dJ/dE α E -γ to the proton spectrum between 67 and 527 keV. The spectral index γ along with the measured proton energy range is shown. Note that this proton spectrum exhibits a notably harder or flatter profile and reaches energies nearly 5 times greater than that of the 30-100 keV proton spectrum (with γ values around 8) recorded by PSP in association with fast solar wind microstreams, which may be generated by interchange reconnection processes occurring near the Sun (S. D. Bale et al. 2023). (b) Proton spectra from kglobal simulations (H. Arnold et al. 2019;J. F. Drake et al. 2019;Z. Yin et al. 2024a) of reconnection at the HCS for two representative guide fields of 0.2 and 0.3 of the reconnecting magnetic field. Early and late times in the simulations are described in Figure 4. simulations show that both species are strongly energized. The strong energization of both electrons and protons results from the formation and merging of magnetic flux ropes in the reconnecting current layers. Electrons initially have a higher upstream temperature than the protons, but the protons reach higher energies up to ∼500 keV compared with the ∼100 keV energy attained by the electrons because of efficient Fermi reflection during the flux rope merger.

The power-law spectral indices of the energetic particles during reconnection are largely determined by the strength of the ambient guide field (H. Arnold et al. 2021). This is because an increasing guide field increases the effective radius of curvature of the reconnecting magnetic field, thereby reducing the effectiveness of the Fermi drive mechanism (J. The simulation with a guide field of 0.3 provides the best match to the observed proton power-law spectral index of approximately -5 shown in Figure 3(a). The simulation with a guide field of 0.2 has a slightly harder spectrum with a powerlaw index of approximately -4 with maximum proton energy of ∼500 keV, while that from the larger guide field is ∼200 keV. This reflects the weaker acceleration of particles during reconnection with a stronger guide field. In kglobal simulations, the upper energy limit of the power-law distribution is controlled by the size of the domain (H. Arnold et al. 2021;Z. Yin et al. 2024a); thus, a larger domain with a guide field of 0.3 is also anticipated to yield 500 keV protons. Briefly, the kglobal simulations reveal that protons up to ∼500 keV are produced in a spectrum of merging flux ropes (Figures 4(a)-(e)) during reconnection, even when the available magnetic energy per particle is only approximately 0.5 keV. That a small number of protons can gain such significant energy is a consequence of the rate of energy gain during Fermi reflection being proportional to the energy of the particles (J. F. Drake et al. 2006Drake et al. , 2013;;F. Guo et al. 2014;H. Arnold et al. 2021;Q. Zhang et al. 2021). Once a subset of particles gains sufficient energy, this population can rapidly outrun the bulk of the protons and gain significantly more energy than the average available per particle as reconnection proceeds.

Summary and Discussion

We have presented five key observational features that show that mechanisms associated with magnetic reconnection in the near-Sun HCS energized solar wind protons into extended power laws up to energies ≈1000 times greater than the available magnetic energy per particle. These observations are as follows: (1) the presence of a sunward-directed plasma jet from reconnection sources located antisunward of PSP (T. Phan et al. 2024); (2) the intensities of sunward-flowing protons up to ∼400 keV are greater than that of the antisunward-flowing population throughout the ∼3.7 hr HCS crossing, indicating that the energetic particle source regions are also located antisunward of PSP; (3) near the core of the HCS reconnection exhaust, the proton PADs up to ∼400 keV peak at ∼90°, indicating the presence of a stably trapped population of energetic protons as PSP traverses regions very close to their acceleration sites; (4) the intermittent presence of counterstreaming electron strahls indicates that reconnection processes occurring in the HCS antisunward ofPSP produced closed magnetic field lines with footpoints connected to the Sun (J. T. Gosling et al. 2006); and (5) the core solar wind proton distribution develops a shoulder that likely extends into the energetic proton regime upward of ∼400 keV, with the ∼67-527 keV proton spectrum behaving as a power-law with a spectral index of ∼5.1.

Observations and computer simulations of charged-particle acceleration during reconnection reveal that the three primary mechanisms responsible are Fermi acceleration in Alfvénic outflows and island mergers, betatron acceleration or magnetic pumping, and direct acceleration by the magnetic field-aligned electric field (J. F. Drake et al. 2006;J. Birn et al. 2012; J. T. Dahlin et al. 2014;F. Guo et al. 2019;X. Li et al. 2019;M. Oka et al. 2022). While wave-particle interactions and resonant acceleration may also be present, their contributions are expected to be less significant (R. E. Ergun et al. 2020a). Reconnection-generated turbulence or reconnection in a turbulent medium can also contribute to the acceleration processes in multiple stages (W. H. Matthaeus & S. L. Lamkin 1986; R. E. Ergun et al. 2020a;A. Lazarian et al. 2020). Indeed, observations in the Earth's magnetotail and supporting test-particle simulations indicate that reconnection-generated turbulence can create large-amplitude electric fields near the ion cyclotron frequency with local magnetic field depletions that can trap and accelerate electrons and ions to produce power-law distributions (R. E. Ergun et al. 2020aErgun et al. , 2020b)). In contrast, throughout the ∼3.7 hr HCS crossing (Figures 1(h), 2(c)) and especially when PSP detected the 400 keV trapped proton population in Period 3, the magnetic field remained relatively steady at ∼200 nT and exhibited few signatures of turbulence similar to those seen in the magnetotail (R. E. Ergun et al. 2020b). Instead, for this HCS encounter, large variations in the normal component of the magnetic field (B N in Figures 1(h), 2(c)) indicate that largescale magnetic islands or flux ropes are embedded within the exhaust. In addition, the identification of several subscale current sheets within the HCS reconnection exhaust points to merging flux ropes (T. Phan et al. 2024) that most likely play an important role in trapping and accelerating the energetic particles (J. F. Drake et al. 2006Drake et al. , 2013Drake et al. , 2019;;M. Oka et al. 2010;G. P. Zank et al. 2014;X. Li et al. 2017).

We explored particle energization during this reconnection event using the kglobal model (Z. Yin et al. 2024b). The proton distributions formed extended power laws with energies reaching approximately 500 and 200 keV with power-law slopes of -4 and -5 for the guide fields of 0.2 and 0.3, respectively. These simulations suggest that the trapping and acceleration of protons into power laws up to ≈400 keV in the near-Sun HCS reconnection exhaust are likely facilitated by merging magnetic islands (see T. Phan et al. 2024) with a guide field around ∼0.25 of the reconnecting magnetic field. These simulations reproduced the ∼1000-fold energization of protons and generated a power-law spectral index of around -5, which aligned well with the observations. Finally, our results have significant implications for particle energization in solar flares. It has long been hypothesized that nonthermal electrons and protons in flares carry comparable energy (A. G. Emslie et al. 2012). However, direct evidence for energetic protons in flares comes from observations of gamma-ray flares, which are relatively uncommon and only provide information on protons with energy above ∼1 MeV (R. P. Lin et al. 2003). Additionally, critical information about proton energies in flares below ∼1 MeV is lacking (E. Vogt & J.-C. Henoux 1999), even though in situ heliospheric measurements of various ion species following impulsive flare events reveal power-law spectra that extend down to ∼100's of keV (e.g., see G. M. Mason 2007). Reconnection events in the Earth's magnetotail reveal power-law spectra of both electrons and protons (R. E. Ergun et al. 2020b;M. Øieroset et al. 2023). However, the proton power laws extend only a single decade in energy, possibly due to demagnetization effects in the narrower current layers that characterize the magnetotail reconnection events. In this HCS reconnection event, however, the available magnetic energy per particle, m i C A 2 , is only ∼0.56 keV, while the proton power law extended above ∼400 keV, nearly 1000 times m i C A 2 . In a typical flare event, with B ∼ 50 G and n ∼ 5 × 10 9 cm 3 , the parameter m i C A 2 is around 10 keV. Thus, by analogy, we can expect solar flares to accelerate protons from 10's of keV up to ∼10 MeV. In summary, these definitive measurements of in situ particle energization in the near-Sun HCS provide fresh insights into magnetic reconnection processes that routinely dissipate the large magnetic field energy density in the near-Sun plasma environment and may be responsible for accelerating charged particles to near-relativistic speeds in solar flares (D. I. Pontin & E. R. Priest 2001;G. D. Fleishman et al. 2022), heating the Sun's atmosphere, and driving the solar wind (S. D. Bale et al. 2023).