Magnetic reconnection is a fundamental plasma process converting magnetic energy into other forms, including particle thermalization and energization and electromagnetic waves. Such potentially dramatic processes most often occur at the interfaces between sharply differing magnetic topologies in collisionless plasmas, whether in the laboratory, in the Earth’s magnetotail or dayside magnetopause, or in structures preceding solar or stellar flares (Hesse and Cassak, 2020; Toledo-Redondo et al., 2021).

The detailed mechanisms of energy conversion in reconnection, and how these respond to specific magnetic configurations, plasma parameters, and constituent particles, are not yet fully understood. When reconnection occurs at Earth’s dayside magnetopause, distinct plasma regimes feed into the diffusion region: the magnetosheath and magnetosphere. The magnetosheath consists of solar wind plasma (H+ and He++) that has been heated by passage through Earth’s bow shock. It is cooler and denser and has a weaker magnetic field than the magnetosphere, which can contain He+ and O+ from ionospheric sources. Because the plasma properties and composition of the magnetosheath and magnetosphere are so different, reconnection between them is inherently asymmetric. This asymmetry must be accounted for when estimating the plasma temperature, Alfvén speed, and available magnetic energy per ion-electron pair in the combined inflow region (Phan et al., 2014, hereafter referred to as PH2014).

Additionally, the composition of the magnetosphere is highly variable, depending on solar cycle and magnetic activity (Fuselier, 2020; Toledo-Redondo et al., 2016; Yau et al., 1985; Young, Balsiger, and Geiss, 1982). GOES 1 and 2 observations of H+, He+, He++, O+, and O++ were compared with F10.7 and Kp to investigate the dependence of ion composition on solar cycle and geomagnetic activity, respectively (Young, Balsiger, and Geiss, 1982). Strong correlations with F10.7 were found for He+, O++, and O+, whereas Kp was strongly correlated only with O+ (Young, Balsiger, and Geiss, 1982). Solar cycle and seasonal dependence of upflowing O+ from the ionosphere was supported by Yau et al. (1985). Occurrence of upflowing O+ was greater at solar maximum and in summer, which was attributed to correlation of the O+ scale height with solar EUV flux and to the fact that solar maximum resulted in higher altitudes of the O+ source (Yau et al., 1985).

Observations have established that magnetopause reconnection can be slowed when plasmaspheric plume material is present. In a comparison of two THEMIS spacecraft crossing the magnetopause, Walsh et al. (2014) noted that the reconnection exhaust was slower when the plume was observed nearby. Borovsky et al. (2013) published estimated reconnection rate reductions observed with ionospheric populations such as the plasmaspheric plume and warm plasma cloak at the dayside magnetopause; ion composition measurements were unavailable. Recent observational studies have utilized ion composition measurements to quantify the impact of heavy ions on the dayside magnetopause reconnection rate (Fuselier et al., 2017; 2019a; 2019b; 2021), providing evidence that the reconnection rate is only modestly affected even when a relatively large number of heavy ions is present. In a series of statistical investigations using ion composition measurements from the Hot Plasma Composition Analyzer (HPCA) instrument on board the Magnetospheric Multiscale (MMS) mission, Fuselier et al. estimated the reconnection rate in events exhibiting high concentrations of either He+ from the plasmaspheric drainage plume or O+ from the warm plasma cloak (Fuselier et al., 2017, Fuselier et al., 2019b, Fuselier et al., 2021). They found that reductions of more than 20% in the reconnection rate were rare. A case study in which high concentrations of counterstreaming O+ were observed in association with a prolonged period of northward IMF predicted that the resulting reconnection rate would decrease by 32% due to the presence of the heavy O+ ions, but the authors noted that such an effect would be transient (Fuselier et al., 2019a). Kolsto et al. (2020) analyzed the reconnection rate in a 2.5D particle-in-cell simulation with varying symmetric and asymmetric distributions of O+. They found that increased O+ density reduced the reconnection rate, but that this effect was greater if the O+ was symmetrically rather than asymmetrically distributed. Importantly, the simulations did not reach steady-state, and the O+ remained demagnetized (Kolsto et al., 2020).

An observational study of composition dependence in reconnection exhausts in Earth’s magnetotail determined that ion enthalpy accounted for the bulk of the energy, consistent with earlier studies (e.g., Eastwood et al., 2013), and that O+ could contribute significantly to enthalpy (Tyler et al., 2016). These events were observed using data from the four-satellite Cluster mission; significant differences were identified in H+ enthalpy fluxes during proton-scale satellite separations, suggesting that proton energization was highly localized. Similarly, H+ and O+ enthalpy fluxes often exhibited strikingly different characteristics within reconnection exhausts, possibly due to different acceleration processes acting over their corresponding length scales.

By analyzing the motion of test particle ions in simulated reconnection fields, Drake et al. (2009a) determined that demagnetized ions entering the magnetosphere exhaust would be accelerated by essentially the same mechanism as pickup ions in the solar wind. Solar wind reconnection observations from Wind and ACE followed the predicted heating relation but with a lower scaling factor (Drake et al., 2009a). In a related study investigating reconnection with guide fields, ion heating was found to be mass dependent when a significant guide field was present: heating was suppressed for ions below a critical mass-to-charge ratio of m i / m p Z i = 10 β 0 x / 2 / π where m i is the ion mass, m p is the proton mass, Z i is the ion charge in units of electron charge, and β 0 x is the plasma β corresponding to the background reconnecting magnetic field (Drake et al., 2009b). An analysis of asymmetrical reconnection in THEMIS magnetopause crossings published in PH2014 found the same scaling coefficient of the observed ion heating as Drake et al. (2009a). In both studies, the ion heating Δ T i varied with available magnetic energy per ion-electron pair m i V A L , i n f l o w 2 as Δ T i = 0.13 m i V A L , i n f l o w 2 (Drake et al., 2009a; PH2014). Recently, the heating of cold magnetospheric ions was investigated using 2.5D PIC simulations, with cold and hot ion species of the same mass and charge (Song et al., 2023). The initial magnetic field configuration was antiparallel (no guide field), and multiple simulations with different ratios of cold to hot ions in the magnetospheric region were performed. Cold ions, when present, were heated by stochastic processes and claimed a significant share of the energy released from magnetic fields (Song et al., 2023).

Our study was designed to elucidate the relative heating of heavy ions in reconnection at Earth’s dayside magnetopause. Following the method of PH2014, we compare the heating of H+ and He++ in the reconnection exhaust, relative to the inflow magnetic energy per ion-electron pair. In section 2, we discuss the datasets. In section 3, we describe the methods. In section 4, we discuss the results of our analysis, and in section 5 we present our conclusions.

The data for this study was collected by the Magnetospheric Multiscale (MMS) mission, an Earth-orbiting constellation (Burch et al., 2016). The equilibrium spacing of the four satellites is comparable to characteristic electron scales in the local plasma; thus, ion observations vary little between spacecraft near the dayside magnetopause, and we utilize data from a single spacecraft, MMS1.

Magnetic field measurements are provided by the Fluxgate Magnetometer (FGM; Russell et al., 2016; Torbert et al., 2016). Particle distributions and moments are available at high cadences from the Fast Particle Investigation (FPI), with complete electron and ion distributions available every 4.5 s in Fast Survey mode (Pollock et al., 2016). The Hot Plasma Composition Analyzer (HPCA) provides distributions and moments for hydrogen (H+) and helium (He++) ions, among others, every 10 s (Young et al., 2016). We use Fast Survey mode for the FPI and HPCA particle data because the higher-resolution Burst data is not available for all of our selected events. We use solar wind parameters from the OMNI dataset available via NASA’s CDAWeb.

We obtained 111 magnetopause reconnection observations from the MMS1 database of Paschmann et al. (2018). Prospective events were selected only if the magnetosphere, magnetopause, and magnetosheath regions could be clearly identified, with a time gap of no more than 60 s separating adjacent plasma regions. We also required that every event have at least one plasma measurement within the magnetosheath and magnetosphere regions and three within the magnetopause. Because FPI and HPCA operate with different cadences from each other, not all events satisfying these requirements for FPI were also acceptable from the perspective of HPCA. From the original 111 events, we chose 21 suitable for FPI (10 for HPCA). An additional 6 FPI (5 HPCA) reconnection events found in adjacent crossings were also included. The study of He+ rich events from Fuselier (2020) provided one more event for both instruments. Our final database consisted of 28 events for FPI (16 for HPCA).

For every event, we rotated the magnetic field and particle velocity vectors from Geocentric Solar Ecliptic (GSE) coordinates into an LMN coordinate system determined by Minimum Variance Analysis (MVA) of the magnetic field vector through the magnetopause transition. The L component corresponds to the maximum variance, M corresponds to intermediate variance, and N corresponds to minimum variance, or the normal to the discontinuity, which is assumed to be planar.

As described above, each event in our study had to have clearly identifiable plasma regions. An example is shown in Figure 1, where each region’s boundaries are indicated by pairs of vertical lines: blue, green, and red for the magnetosphere, magnetopause, and magnetosheath, respectively. The magnetosheath can be identified by its weaker, and more variable, magnetic field, with negative B L (typically ∼ GSE z), higher density, lower temperatures, and broadened distributions of ions and electrons (here centered around 1 keV and 100 eV, respectively) after the narrow solar wind beam has been heated by the bow shock. In contrast, the magnetosphere has higher magnetic field magnitude (dominated by + B L ), lower particle densities, higher electron and ion temperatures, and comparatively stagnant particle velocities. Often, as in Figure 1, both a cold ionospheric population and a hot population (sometimes beyond the energy range of FPI) are observed.

The brief transition through the magnetopause is distinguished by a rapid shift from − B L to + B L , accompanied by a drop in particle densities, and usually high-velocity ion outflows as ions accelerated by reconnection processes escape the diffusion region. Figure 1 also illustrates the variability in composition. Note that O+ and He+ densities in the magnetosheath are inaccurate due to contamination by high H+ fluxes (Fuselier et al., 2021); consequently, we omit O+ and He+ from our analysis.

In addition to the well-defined regions described above, when choosing events for this study, we imposed the following requirements:

Magnetic local time (MLT) must be between 8 and 16.

A statistical overview of our database is presented in Figure 2. Figure 2a shows the radial distance and magnetic local time (MLT) position of all crossings, while Figure 2b,c shows the IMF Bz and the solar wind dynamic pressure, respectively, as a function of each crossing’s radial distance. Radial distances are shown in units of Earth radii (RE). The event in Figure 1 is identified by a red dot in each panel of Figure 2. Our events occur between radial distances of 8 RE and ∼12 RE. IMF B Z values were between −8 nT and +3 nT, with most events between −5 nT and 0 nT. As expected, solar wind dynamic pressure was inversely correlated with radial distance: the highest solar wind pressures (>3 nPa) occurred for the smallest radial distances.

We calculated the effective inflow temperature, asymmetric Alfvén speed, and magnetic energy per proton-electron pair following the equations of PH2014, but in two ways. First, we used the ion data from FPI, which does not distinguish between individual species, in order to compute total properties for the plasma and produce a database directly comparable to PH2014. This method cannot account for the effect of heavy ions on the mass density. Second, we performed the same calculations after combining HPCA moments from individual species to obtain a collective plasma measurement that does take the species masses into account. (See the equations in Table 1). Measurements for He+ and O+ were so sparse within our dataset, and likely often reflected contamination by H+, that we neglected their contributions.

In the equations of Table 1, the s subscript indicates either of the HPCA ion species used (H+ or He++) while the a l l subscript labels a collective quantity representing both species; m , n , and T are the mass, number density, and temperature, respectively; angular brackets indicate an average taken over the specified time range, where the subscripts s p , s h , i n , and o u t refer to the magnetosphere, magnetosheath, inflow (magnetosphere and magnetosheath combined), and outflow (i.e., magnetopause) regions, respectively; and B L is the maximum-variance component of the magnetic field. Average temperatures for individual species were scaled by their density such that T s i = n s T s i n s i where subscript i indicates the magnetosphere, outflow (i.e., magnetopause), or magnetosheath region. Although we show two different methods of computing a collective inflow temperature in Table 1, we found that they yielded similar results (compare Figures 3b,d).

Two potential sources of error in this statistical study have been identified: (1) if the spacecraft is too far from the X-line, the magnetic shear and the value of B L used in our computations (see Table 1) may not adequately represent the parameters at the X-line; and (2) the ion distributions (all species) are often not simple Maxwellians well modeled by a single temperature. Eight candidate events (of which five were retained in the final database) were examined in detail to assess the probable impact of these considerations on the results of this statistical study. For only one of these events were the local measured shear and B L significantly smaller than the model of Fuselier et al. (2019b), suggesting that distance from the X-line does not impact our results.

The ion distributions within the magnetosheath, magnetopause, and associated boundary layers are often very complex, and differ between ion species. For some of the eight events examined in detail, one or more species was well modeled by a single Maxwellian; often, however, two or more components would be required to fit the distribution. Use of a single temperature is justified because our study is based on an MHD treatment of the plasma. In addition, we are following the approach of PH2014.

Figure 3 shows the statistics of our MMS events and comparison with the THEMIS results of PH2014. In each panel, the x-axis represents available magnetic energy per ion-electron pair (see equations in Table 1), while the y-axis shows the temperature difference Δ T . Figure 3a reproduces Figure 2g from the THEMIS study by PH2014, with the inclusion of a shaded box to indicate the approximate plot area of Figures 3b–e. The magnetic energy per ion-electron pair for Figures 3b–f is computed with MMS FPI ion data, which is similar to the ion measurements on THEMIS. Negative values of the temperature differences are seen in all panels. The red line in each panel represents a linear fit to the data, Δ T i = 0.13 m i V A L , a s y m 2 , where Δ T i is the change in total ion temperature, m i is the proton mass, and V A L , a s y m is the asymmetrical Alfvén speed (PH2014). The blue, dashed lines in Figures 3b–f are Least Squares (LSQ) fits, surrounded by light blue shading to indicate the 95% confidence intervals, while a red dot indicates the event shown in Figure 1.

In Figure 3a (Figure 2g from PH2014), the available magnetic energy spans a wide range up to nearly 4000 eV, with the bulk of the data below ∼2000 eV. Note that PH2014 included another version of this panel (see their Figure 2h) showing a subset of their events where the average outflow density exceeded the average magnetosheath density, which they interpreted as containing heated plasmaspheric plume material too low in energy to be measurable in the magnetosphere. None of the events in our database had average outflow density greater than the magnetosheath density.

Figure 3c highlights the temperature changes for the MMS FPI ion data and is the most comparable to Figure 3a. However, there are important differences between the two panels. First, the energy range of Figure 3c (maximum <2000 eV) is lower than that of Figure 3a by a factor of two. We have indicated the approximate energy range of Figures 3b–e with a shaded box in Figure 3a. Second, the temperature differences of Figure 3c exhibit slightly greater scatter than those of Figure 3a, in particular showing more events with negative temperature differences. Most temperature differences are clustered between −30 eV and +200 eV, with a few outliers approaching −100 eV. In Figure 3a, the temperature differences for data within the shaded box range between about −20 eV and +250 eV. Seven events (out of 28) in Figure 3c have temperature differences below zero, whereas two events in Figure 3a have a small negative difference. The LSQ fit for the FPI ion data is lower than the empirical relation reported by PH2014. Based on the 95% confidence interval, the difference between the two fit lines is statistically significant.

Figures 3b,d show the temperature differences obtained when the inflow temperature is calculated for the combined HPCA species, using the two methods described in Section 3 and shown in Table 1: the first (V1) is in Figure 3b, while the second (V2) is in Figure 3d. The results from these methods are so similar that it can be difficult to see the differences between them. Both methods yield three temperature differences below zero. In Figures 3b,d, although the corresponding LSQ fits are somewhat lower than the empirical relation of PH2014, the difference is not statistically significant, as can be seen by the fact that the PH2014 relation falls within the 95% confidence interval of each LSQ fit. The empirical relation was determined from THEMIS data, where information about the ion composition was unavailable (PH2014).

Figures 3e,f show temperature differences for the HPCA species individually: H+ and He++, respectively. In Figure 3e, the temperature differences computed for HPCA H+ measurements span a similar range of values as in Figure 3c, which is to be expected since H+ is the dominant ion species. The LSQ fit line for H+ is lower than the fit line of PH2014, which lies outside the bounds of the 95% confidence interval. In Figure 3f, the HPCA He++ show greater scatter compared to the H+ data (Figure 3e) and FPI ions (Figure 3c), and the range of temperature differences represented (≲800 eV) is larger than for HPCA H+ (≲200 eV) by a factor of about four. Two temperature differences are negative. The LSQ fit for He++ is higher than the PH2014 fit, but the corresponding 95% confidence interval is large enough to contain the empirical scaling relation from PH2014.

It is interesting that the collective HPCA fits are statistically comparable to PH2014, whereas the FPI ions and HPCA H+ fits are statistically lower. The LSQ fit for He++ exceeds the scaling relationship of PH2014, but the difference is only marginally significant. This suggests that heavy ions are more heated than H+, although decisive conclusions cannot be offered due to small number of events and large scatter.

The critical mass-to-charge ratio of Drake et al. (2009b) was derived specifically in the context of reconnection in the presence of a large guide field. A threshold to distinguish large guide fields was not stated, but observations with magnetic shear angle at or above 120° were treated as low guide field by Drake et al. (2009a). In PH2014, magnetic shear angles below 90° (above 165°) are considered high (low) guide field. In our database, only two events (used for both FPI and HPCA analysis) had shear angles below 90°, and only seven events for FPI, including four events used for both FPI and HPCA, had shear angle less than 120°. The critical mass-to-charge ratio in the magnetopause for all cases exceeds the mass-to-charge ratios of both H+ and He++. The heating mechanism constraint of Drake et al. (2009b), therefore, is unlikely to explain the negative temperature changes that we observe in our results. The negative temperature differences are more likely due to the fact that temperatures were determined using the assumption of Maxwellian distributions, whereas the actual distributions may be more complex.

We have compared the observed ion heating to the available magnetic energy per ion-electron pair in a set of MMS magnetopause crossings, with 28 events for FPI and a subset of 16 for HPCA. We compared the MMS observations to the results of PH2014, whose THEMIS observations (reproduced in Figure 3a) obeyed the relation Δ T i = 0.13 m i V A L , a s y m 2 , where Δ T i is the change in total ion temperature, m i is the proton mass, and V A L , a s y m is the asymmetrical Alfvén speed. However, ion composition measurements are not available from THEMIS. We used HPCA measurements to assess possible composition dependence. Due to the small number of events, it is not possible to reach definitive conclusions about composition-dependent differences in ion heating. Although the number of events in our database was small, the range of inflow magnetic energies more limited, and the scatter high, the LSQ fits of FPI ions (Figure 3c) and HPCA H+ (Figure 3e) were lower than the PH2014 fit. The scaling seen for the HPCA collective data (Figures 3b,d) was consistent with PH2014. Although marginally significant, the LSQ fit for He++ (Figure 3f) exceeded the PH2014 scaling. These results support the idea that observed heating may be higher overall when the contributions of heavier ions are explicitly included.

Although the simulations and observations of Drake et al. (2009a) were symmetric, PH2014 found the same linear scaling between available magnetic energy and observed temperature change (albeit with a lower than predicted scaling factor) in asymmetric magnetopause reconnection events. Scattering due to instabilities and waves in the exhaust could reduce the observed ion heating compared to the prediction (Drake et al., 2009a). Further research utilizing larger datasets is needed to determine whether the scaling of the temperature change of heavier ion species, such as He++, with the available magnetic energy is larger than that for H+, as predicted by Drake et al. (2009a) and other studies (Oka et al., 2023; Fiksel et al., 2009; Kolsto et al., 2020; Yoon and Bellan, 2019).