Quantification of Cold-Ion Beams in a Magnetic Reconnection Jet

Cold (few eV) ions of ionospheric origin are widely observed in the lobe region of Earth’s magnetotail and can enter the ion jet region after magnetic reconnection is triggered in the magnetotail. Here, we investigate a magnetotail crossing with cold ions in one tailward and two earthward ion jets observed by the Magnetospheric Multiscale (MMS) constellation of spacecraft. Cold ions co-existing with hot plasma-sheet ions form types of ion velocity distribution functions (VDFs) in the three jets. In one earthward jet, MMS observe cold-ion beams with large velocities parallel to the magnetic fields, and we perform quantitative analysis on the ion VDFs in this jet. The cold ions, together with the hot ions, are reconnection outflow ions and are a minor population in terms of number density inside this jet. The average bulk speed of the cold-ion beams is approximately 38% larger than that of the hot plasma-sheet ions. The cold-ion beams inside the explored jet are about one order of magnitude colder than the hot plasma-sheet ions. These cold-ion beams could be accelerated by the Hall electric field in the cold ion diffusion region and the shrinking magnetic field lines through the Fermi effect.

1 Introduction

Cold (few eV) ions of ionospheric origin are widely present in the Earth’s magnetosphere (Chappell et al., 1980; Moore et al., 1997; Cully et al., 2003). In the lobes of the magnetosphere, spacecraft can be positively charged to several tens of volts due to photoelectron emissions. The positive potential prevents cold ions from reaching onboard ion instrument. With large-scale convective motion, for example, magnetopause fluctuation or plasma-sheet flapping, cold ions can be accelerated via the E×B drift to overcome the positive spacecraft potential (Sauvaud et al., 2004), and be detected by an ion instrument. Besides direct measurement with particle instruments, cold ions can also be inferred by a technique based on the wake signal of a charged spacecraft in a supersonic ion flow (Engwall et al., 2009; Li et al., 2013; André et al., 2015). Observational statistics show that cold ions dominate the plasma density in large regions of the nightside magnetosphere (e.g., lobe region) and polar regions (André and Cully, 2012). At times, the cold ions can also dominate in the dayside magnetosphere. Cold ions can play an important role in the solar wind-magnetosphere-ionosphere coupling system, including the terrestrial plasma escape and circulation and the magnetotail dynamics (Welling et al., 2015; Kistler and Mouikis, 2016; Yamauchi, 2019).

Magnetic reconnection is a fundamental and universal process to convert energy stored in the magnetic field into kinetic and thermal energies of charged particles (Priest and Forbes, 2007; Yamada et al., 2010). Magnetic reconnection is the major transport mechanism of mass, energy, and magnetic flux in the solar wind-magnetosphere coupling system, and is the predominant cause of the geomagnetic activity. In the past decade, the effects of cold ions on magnetic reconnection at the dayside magnetopause and in the magnetotail have been extensively analyzed via using in-situ measurements from multiple spacecraft missions (Wang et al., 2014; Toledo-Redondo et al., 2015; André et al., 2016; Li et al., 2017; Toledo-Redondo et al., 2021) and types of numerical simulation models (Aunai et al., 2011; Divin et al., 2016; Tenfjord et al., 2019; Dargent et al., 2019, 2020). At the dayside magnetopause, magnetic reconnection is typically asymmetric due to the large differences in plasma and magnetic field conditions between the magnetosheath and the magnetosphere. The gyroradii and the inertial lengths of the magnetosheath plasmas usually determine the two kinetic scales of the diffusion region, namely, ion and electron diffusion regions (Yamada et al., 2010). With the presence of cold-ion inflow from the magnetospheric side, cold ions bring a new diffusion region between the usual ion and electron diffusion regions (Toledo-Redondo et al., 2016a; Divin et al., 2016), and can push the reconnection jet towards the magnetosheath side (Cassak and Shay, 2007; Walsh et al., 2014). Li et al. (2017) present the first observation of the cold-ion outflows throughout the entire reconnection region via investigating the three-dimensional (3D) ion velocity distribution functions (VDFs). Cold-ion jets with high parallel velocities are formed on the magnetosheath side of the reconnection exhaust, and those cold ions remain relatively cold compared with the magnetosheath ions. Li et al. (2017) suggest that those fast cold-ion jets originate from the cold-ion inflow close to the X line, while the acceleration mechanism lacks detailed analysis.

In the magnetotail, the magnetic fields are oppositely directed on each side of the plasma sheet, and the plasma-sheet plasmas are hot with ion temperature of several to tens of keV. Magnetic reconnection is symmetric with homogeneous hot ion inflows from both sides. The plasma sheet boundary layer (PSBL) and lobe region always contain a certain amount of cold ions of ionospheric origin, which can affect the reconnection process in the magnetotail. One prominent feature is that cold ions create highly structured ion VDFs far from the Maxwellian shape. Among these distributions, counter-streaming cold-ion beams along the direction normal to the current sheet are frequently observed in the ion diffusion region both in observations and simulations (Fujimoto et al., 1996; Hoshino et al., 1998; Nagai et al., 1998; Shay et al., 1998; Wygant et al., 2005; Divin et al., 2016; Dai et al., 2021). The counter-streaming cold-ion beams are suggested to be accelerated by the Hall electric field along the normal direction at the separatrix, which is mostly along Z direction of Geocentric Solar Ecliptic (GSE) coordinates. The electric potential well across the separatrix is ${\mathrm{B}}_X^2$/2q_eN₀μ₀, where B_X and N₀ are the reconnection magnetic field and plasma number density in the inflow, q_e is the unit of charge and μ₀ is the magnetic permeability of free space (Wygant et al., 2005; Divin et al., 2016; Zaitsev et al., 2021). This electric potential can accelerate cold ions to the inflow Alfvén speed V_A = B_X/$\sqrt{{\mu }_0{m}_i{N}_0}$, when the width of the separatrix is comparable to the cold-ion gyroradius. Using a hybrid simulation model, Aunai et al. (2011) show that the angular aperture of the potential well and the bouncing motion between the separatries make the cold ions transfer the kinetic energy gained from the V_Z component to V_X.

Besides the acceleration by the Hall electric field in the ion diffusion region, the Fermi mechanism (slingshot effect) and the reconnection electric field can also be important for cold-ion acceleration in the reconnection exhaust. Several studies report counter-streaming cold-ion beams observed in bursty bulk flows (BBFs) and analyze acceleration mechanisms and ion anisotropic instabilities associated with these beams (Eastwood et al., 2015; Hietala et al., 2015; Birn et al., 2017; Runov et al., 2017; Xu et al., 2019). BBFs are widely interpreted as magnetic reconnection jets (Angelopoulos et al., 1992; Nagai et al., 1998; Birn et al., 2011) and can transport significant amount of magnetic fluxes and plasmas towards Earth (Baumjohann et al., 1990; Angelopoulos et al., 1992, 1994). Eastwood et al. (2015) find that counter-streaming beams are sourced from the thermal population in the preexisting plasma sheet and are accelerated by the reconnection electric field. Birn et al. (2017) show that the beam ions are from the low-energy lobe regions. These beams are firstly accelerated by the E×B drift motion and then by the slingshot effect of the earthward convecting BBF. A similar process is also described by Xu et al. (2019). In the previous studies, the counter-streaming cold-ion beams are mostly observed near the front edge of the reconnection jet, and quantitative studies analyzing the acceleration are primarily via numerical simulations. The existence and dynamics of the cold ions in an entire reconnection jet still lack quantitative analysis using in-situ observations. In this study, we perform a more comprehensive survey of ion VDFs in a magnetotail crossing by the Magnetospheric Multiscale (MMS) spacecraft. Various types of ion VDFs with cold-ion beams are observed inside a magnetic reconnection jet, and plasma partial moments of the cold ions are computed to investigate their dynamics through the reconnection process.

2 Observations

In-situ observations from NASA’s MMS mission (Burch et al., 2016) are utilized for this study. MMS was launched on March 13, 2015 and consists of four identical spacecraft designed to study the kinetic-scale physics of magnetic reconnection in the Earth’s magnetosphere. In this study, we use magnetic field data from the FluxGate Magnetometer (FGM) (Russell et al., 2016) and electric field data from the Electric Double Probe (EDP) (Ergun et al., 2016; Lindqvist et al., 2016). The ion data are from the Fast Plasma Investigation (FPI) (Pollock et al., 2016) sampled at 4.5 s for the fast mode and 0.15 s for the burst mode, and also, from the mass-resolved instrument Hot Plasma Composition Analyzer (HPCA) (Young et al., 2016) at 10 s resolution.

We investigate an MMS magnetotail crossing from 21:30:00 to 24:00:00 UT on July 06, 2017. The four spacecraft moved from [−24.6, −0.8, 5.2] R_E (Earth radii) to [−24.5, −1.4, 5.4] R_E (GSE) during this time interval. Owing to a small spacecraft separation ( ∼15 km), observations from the four spacecraft are nearly identical, and thus, we show results primarily from MMS1. An overview of the MMS1 observations is presented in Figure 1, and the data are in fast mode. The panels from top to bottom show 1) magnetic field B, 2) number densities of ions and electrons, 3) ion bulk velocities from FPI, 4) FPI ion omnidirectional differential energy flux, and 5) number densities of He⁺⁺ and O⁺ ions from HPCA. In Figure 1B, the number densities of H⁺ from HPCA, all ions from FPI and electrons from FPI are shown in black, blue and red, respectively. The three curves almost overlap with each other, indicating reliable number density results. The MMS fleet is initially located in the plasma sheet, characterized by weak magnetic field (Figure 1A) and high-density ( ∼0.5 cm⁻³) and hot ( ∼4,500 eV) ions. From 21:49:00 to 22:02:00 UT, MMS1 observes a strong tailward ion flow, with a peak V_X reaching -1,000 km s⁻¹. Such a strong ion flow indicates ongoing reconnection and that the spacecraft are located tailward of the reconnection X line. In this tailward ion jet, the B_X component is mostly positive, indicating that MMS cross the northern part of the ion jet.

FIGURE 1

FIGURE 1. MMS observation of the Earth’s magnetotail on July 06, 2017. MMS1 data of (A) magnetic field B, (B) number densities of hydrogen (H⁺, black) from HPCA, all ions (blue) and electrons (red) from FPI and electron number density derived from the Langmuir waves observed by EDP, (C) ion bulk velocity V_i from FPI, (D) FPI ion omnidirectional differential energy flux, (E) number densities of He⁺⁺ (black) and O⁺ (red) ions from HPCA. All vectors are presented in GSE coordinates, which are close to Geocentric Solar Magnetospheric (GSM) coordinates in this event. The horizontal green bars in the top of (A) denote the burst-mode time intervals, and detailed analysis of the ion VDFs in the two yellow-shaded intervals are presented in the following figures.

At 22:02:00 UT, we identify a separatrix of the reconnection exhaust, where B increases, plasma number density decreases, ion bulk velocity decreases, and energetic particles vanish (see Supplementary Figure S1 in Supplementary Material for more details). Then, MMS1 enters the lobe region until 22:34:00 UT. As shown by the ion energy flux in Figure 1D, cold ions of ionospheric origin, with ∼10 eV thermal energy, are present in the lobe region, while their total energy can reach 100 eV due to the E×B drift motion. In the lobe, the penetrating radiation leads to a nearly constant background from the lowest to the highest energy channels in the FPI ion measurement unit (Gershman et al., 2019), as seen by the green fluxes in Figure 1D. Thus, the FPI ion number density from the integral over the whole energy range is overestimated. Besides, the FPI electron measurement unit cannot provide reliable electron moment data in the lobe because of the low thermal energy and the photoelectron contamination (Gershman et al., 2019). So, we take the number density (0.03–0.05 cm⁻³) estimated from the waves at the electron plasma frequencies, as illustrated by the color-coded spectrum in Figure 1B. In the lobe, oxygen ions measured by HPCA have number densities about 0.0005–0.002 cm⁻³ (Figure 1E), and hydrogen is thus the primary ion species in terms of number density. From 22:13:04 to 22:13:15 UT, MMS cross a separatrix of the reconnection exhaust back and forth quickly (see Supplementary Figure S2 in Supplementary Material for details). Based on the observations during this time interval, Alm et al. (2018) analyzed the role of cold ions in the separatrix layer. They find that the cold ions account for ∼ 30% of the total ion number density and can significantly influence the Hall physics of reconnection. After 22:34:00 UT, MMS1 crosses back to the plasma sheet and sees two strong earthward ion jets, with aV_X peak reaching 860 km s⁻¹. O⁺ ions, as tracers of cold ionospheric ions, are continuously observed inside the plasma sheet shown in Figure 1, and have similar number densities with those in the lobe. Meanwhile, He⁺⁺ ions can be used as tracers of solar wind ions, and are also continuously observed in the plasma sheet. Thus, both the ionospheric and solar-wind ions are the ion sources of the plasma sheet in our event, even through the two sources are indistinguishable from the FPI ion energy flux panel (Figure 1D). We explore the 3D ion VDFs in the tailward and earthward reconnection jets and characterize different types of ion VDFs with cold-ion beams. In the following, we present results from the two time intervals indicated by the yellow-shaded bars in Figure 1.

Figures 2A–F present an overview of the tailward ion jet in the time interval indicated by the left yellow-shaded bar in Figure 1. Here, burst-mode data are used. In this jet, V_X varies between −1,240 km s⁻¹ and −430 km s⁻¹, and ions with distinct energy fluxes are all above 500 eV in the spacecraft frame (Figure 2D). Figure 2E shows the phase space density of the reduced ion VDF projected on to the magnetic field directions, and the black curve represents the parallel bulk velocity ${\mathbf{V}}_B^{all}$ of all ions. One can clearly see complicated structures in this reduced ion VDF panel. To categorize the ions in this tailward jet, we perform a systematic survey of all the ion VDFs in the time interval of Figure 2 and find three types of ion VDFs inside. Figures 2G–I show 2D reduced ion VDF examples in the V_E×B-V_B plane, as they clearly show the overall structures in the distribution functions. At times like 21:57:08 UT, ${\mathbf{V}}_B^{all}$ is close to the ion VDF peaks, denoting that there exists only a single energetic ion population of plasma-sheet origin (see Figure 2G). The hot population in Figure 2G has a temperature of 4.6 keV and follows E×B drift motion (green vertical dashed line), with negligible V_B. In GSE coordinates, it moves predominantly along -X direction. From 21:59:12 to 21:59:19 UT, MMS1 observes two distinct ion populations in the FPI ion energy flux plot (Figure 2D). One energetic population has energy above 8 keV and originates from the plasma sheet. The other population has energies below 5 keV. An example of the ion VDFs within this interval is presented in Figure 2I. At this time, the magnetic field is mostly along the +X direction (Figure 2A), and its magnitude is close to that in the lobe (see Figure 1). The electric field is dominated by the -Z component, indicating Hall electric field in the northern separatrix layer of the magnetotail reconnection in the magnetotail (Wygant et al., 2005; Eastwood et al., 2007). The two ion populations have the same E×B drift velocity. The hot population has a large negative V_B, and its bulk velocity is predominantly along the -X direction in GSE coordinates. The cold population has negligible V_B and moves along the -Y direction. Those cold ions can modify the balance of the Hall electric field at the separatrix, which has been extensively analyzed by previous studies using in-situ data (Toledo-Redondo et al., 2015; André et al., 2016; Alm et al., 2018) and numerical simulation models (Dargent et al., 2017; Toledo-Redondo et al., 2018).

FIGURE 2

FIGURE 2. Cold ions inside the tailward ion jet. (A) B. (B) N_i. (C) V_i. (D) FPI ion omnidirectional differential energy flux with ion temperature (white curve). (E) Reduced ion VDF integrated over the directions perpendicular to the magnetic field. The black solid curve shows the parallel ion bulk speed ${\mathrm{V}}_B^{all}$ of all ions, and the white dashed line denotes V_B = 0. (F) Electric field E. (G)–(I) Two-dimensional (2D) reduced ion VDFs in the V_ExB-V_B plane at times indicated by the three vertical lines in (A)–(F). In (G)–(I), the green dots represent the ion bulk velocities, and the vertical green dashed lines show the electric-field drift speeds (|E ×B/B²|). The GSE-X (black), Y (blue) and Z (red) directions normalized by 1,500 km s⁻¹ are projected in (G)–(I).

From 21:57:12 UT to 21:58:10 UT, MMS1 also observes two distinct populations in the reduced ion VDFs shown in Figure 2E, even though the two populations are not distinguishable from the FPI ion energy flux (Figure 2D). Figure 2H displays an example of the ion VDFs in this time interval. The properties of the hot population are similar to those shown in Figure 2I. The cold population follows E×B drift ( ∼630 km s⁻¹) motion and has a small ( ∼200 km s⁻¹) positive V_B. Its bulk velocity is predominantly along the -Z direction in GSE. These cold-ion beams may originate from the northern lobe. A small bulk speed ( ∼660 km s⁻¹) of this cold population suggests that those beams may be not from the cold-ion inflow close to the X line. They may experience an acceleration process as discussed previously by Birn et al. (2017). The cold ions are probably accelerated by the E×B drift motion when crossing a distant separatrix, and are further accelerated by the Fermi mechanism as the cold ions convect together with the shrinking magnetic field lines. Another prominent feature between the cold populations shown in Figures 2H,I is that the cold population in Figure 2H is clearly thermalized, and we discuss that in the following section. In the earthward ion jet between 22:36:00 UT and 22:47:00 UT, MMS observe similar features of the ion VDFs as those presented in Figure 2.

MMS see much more complicated features of cold-ion beams in the earthward ion jet between 23:43:23 UT and 23:47:53 UT (denoted by the right yellow-shaded bar in Figure 1). Figures 3A–F display a detailed overview of this ion jet using burst-mode data. MMS are originally located in the stagnant plasma sheet. When a dipolarization front (Nakamura et al., 2002; Runov et al., 2009; Fu et al., 2013) arrives at MMS at ∼23:43:34 UT, the plasma density drops from 0.31 cm⁻³ to 0.20 cm⁻³ and the magnetic field B_Z component increases from 5 to 13 nT. The earthward flow speed subsequently increases to its maximum values, with aV_X peak reaching 1,040 km s⁻¹. This kind of fast ion flow is frequently interpreted as an earthward bursty bulk flow (BBF) driven by magnetic reconnection with an X line located tailward of the spacecraft. In Figure 3, we use a yellow-shaded bar to highlight the BBF or the jet interval. The average N_i of the jet is approximately 0.29 cm⁻³, which is similar to that of the nearby plasma sheet. The average T_i is 3.8 keV, with a small temperature anisotropy (T_i‖/T_i⊥ ∼0.92). After a detailed survey of all the ion VDFs, we find four types of ion VDFs inside the jet shown in Figure 3: Type I consists of only a single hot plasma-sheet population (see an example shown by Figure 3H), Type II consists of a hot population and a cold population with a positive V_B (see Figure 3I), Type III consists of a hot population and a cold population with a negative V_B (see Figure 3J), and Type IV consists of a hot population with counter-streaming cold populations (see Figure 3K). We categorize all the ion VDFs of this earthward ion jet, and the results are presented by colored dots in Figure 3G. In Figures 3H–K, the green dots denote the projected ion bulk velocities in the V_E×B-V_B plane, and the green vertical dashed lines represent the E×B drift speeds. The small discrepancy between the two speeds is likely from the errors (0.5–1.0 mV m⁻¹) in electric field (Lindqvist et al., 2016) or could be caused by weak demagnetization of the ions. In GSE coordinates, all ions propagate earthward (illustrated by the black lines in Figures 3H–K). The large positive and negative V_B components of the cold ions correspond to the large positive and negative V_Z components (Figures 3I–K), respectively.

FIGURE 3

FIGURE 3. Four types of ion velocity distribution functions (VDFs) in the earthward ion jet. (A) B. The green horizontal bar denotes the ion jet interval. (B) N_i. (C) V_i. (D) FPI ion omnidirectional differential energy flux with ion temperature (white curve). (E) Reduced ion VDF integrated over the directions perpendicular to the magnetic field. The black solid curve shows the parallel ion bulk speed V_i‖, and the white dashed line denotes V_i‖ = 0. (F) Electric field E. (G) Ion VDF types inside the ion jet. (H)–(K) Examples of the four-type ion VDFs at times indicated by the four vertical lines in (A)–(G). (H)–(K) are in the same format with Figures 2G–I.

Previous studies like Eastwood et al. (2015) and Xu et al. (2019) explored the kinetic behavior of counter-streaming cold ions at the leading edges of the reconnection jets, with particular focus on the vicinity of dipolarization front. The cold-ion beams investigated in their works may originate from ions in the preexisting plasma sheet or the ionosphere and are swept up directly by a dipolarization front. In our study, we do not find the existence of isolated cold-ion beams in the region close to the dipolarization front, which could be due to the phase-space mixing by cold-ion thermalization. We find four types of ion VDFs widely distributed over the entire observed part of the jet. The cold-ion beams have total energies all above ∼3 keV and mix together with the plasma-sheet hot ions in the spectrogram of the differential energy flux (Figure 3D), and one can only distinguish cold ions in three-dimensional VDFs. This is different from the cold ions reported in Eastwood et al. (2015) and Xu et al. (2019), where the total energies of cold ions are lower than those of hot ions and one can easily see them in the spectrograms of the differential energy fluxes.

In the magnetotail, the B_X component can be used as a guide to determine the normal distance to the plasma-sheet neutral line (B_X = 0). Figure 4A shows the count profiles of the four types of ion VDFs along B_X. MMS spend most of the time in the southern exhaust, and most of the counts are therefore in the negative B_X region, where Type I and Type II VDFs clearly dominate. Figure 4B presents the occurrence rates of the four-type ion VDFs, and the gray shadow highlights the results with total counts over 50. Despite the large variation due to relatively low counts, one can conclude that the occurrence rate of Type I is nearly constant. The occurrence rate of Type II decreases gradually along B_X or from the southern to the northern sides of the neutral line. Conversely, the occurrence rate of Type III increases gradually along B_X. The occurrence rate of Type IV peaks at the neutral line. Therefore, the antiparallel beams are predominantly observed in the northern side of the neutral sheet, and the parallel beams are predominantly observed on the southern side. The majority of cold-ion beams were found to be approaching the neutral sheet, with a smaller subset of VDFs also showing cold ion populations moving away from the neutral sheet. This indicates that there is some mechanism that either prevents cold ions from crossing far into the opposite exhaust, that the cold-ion populations are no longer cold after the neutral sheet crossing (heating), or that they can not be distinguished from the hotter background.

FIGURE 4

FIGURE 4. Statistics of the four types of ion VDFs along B_X. (A) Counts profiles along B_X. The magenta curve shows the total counts, and the rest of the curves show the four types of VDFs. (B) Occurrence rates. The gray shadow highlights the interval with total counts over 50.

The distribution of VDFs shown in Figure 4B may be generated by several processes. First, MMS observe the northern (see Figure 1) and southern lobes on July 6,2,017 and see cold ions in both lobes. As an example shown in Figure 1D, the energy fluxes of the cold ions in the lobe are intermittent, indicating that the cold ions inflowing into the reconnection region could be patchy. Secondly, when cold ions enter the separatrices close to the X line (e.g., the cold-ion diffusion region), numerical simulations (Aunai et al., 2011; Divin et al., 2016) show that the cold ions bounce within an electrostatic potential well between the separatrices. The distribution feature in Figure 4B could be a statistical result of the bouncing motions of the cold ions inflowing from both lobes. Finally, as shown in Figure 3A, MMS see large-amplitude fluctuations in magnetic field, which may be convected from the upstream exhaust region or be driven by the ion temperature anisotropy associated with cold-ion beams (Hietala et al., 2015). Besides, the minimum curvature radii of the magnetic field lines in this event are comparable to the gyroradii of the cold ions (as shown by Figure 5H). Plasma waves and the curved magnetic field lines with small curvature radii can scatter and thermalize the cold ions when moving from one side of the neutral line to the other side, and thus, can mix them with the plasma-sheet hot ions. The distributions in Figure 4B could be combinational results of those three effects.

FIGURE 5

FIGURE 5. Partial moments of the cold-ion beams and the hot ions inside the earthward ion jet. Those ions are from the three types (Types II, III and IV) with cold ions. Types II, III and IV are colored in blue, red and green, respectively. The partial-moment results of the hot, parallel cold and anti-parallel cold ions are marked by circles, upward-pointing triangles and downward-pointing triangles, respectively. (A) B. (B) N_i of all ions (black curve) and cold and hot ions from partial moments. (C) Ion bulk speed V. (D)–(F) Three components of the ion bulk velocities V_i. The black curves are the average bulk velocities. (G) T_i. (H) Adiabatic parameter defined by κ² = $\frac{R_B}{{\rho }_{ci}}$ (Büchner and Zelenyi, 1989), where R_B is magnetic field curvature radius and ρ_ci is the gyroradius of the 320 eV cold ions. (I)–(K) Scatter plots of the measured E from EDP and the convection electric field (-V_i×B) of hot and cold ions from selected data points. The black dashed lines denote slope = 1, and the red dashed lines are the linear fits of the partial-moment results. (L)–(M) Scatter plots of the ion bulk velocity of the selected points. The crosses present the averages and the standard deviations, and the black lines show the normalized magnetic fields.

3 Quantification of Cold-Ion Beams in the Earthward Jet

In order to study the dynamics of the cold-ion beams inside the jet, we utilize the same technique as used in Li et al. (2017) (see supporting information of that paper and Supplementary Figure S3 in Supplementary Material for more details) to compute partial moments of the hot and cold populations. First, we select data points of the three types of ion VDFs with cold ions with most coverage of the variant magnetic field conditions. Then, we separate the cold and hot populations for each ion VDF in three-dimensional velocity space and compute their partial moments, including number density, bulk velocity and ion temperature. The results are presented in Figure 5, and the average results with standard deviations are listed in Table 1. In Figures 5B–G, L,M, the partial-moment results of the three-type VDFs (Types II, III and IV) with cold ions are labeled in blue, red and green, respectively. The hot ions from all three types are marked by circles. The parallel cold-ion beams from Types II and IV VDFs are marked by the upward-pointing triangles, while the anti-parallel beams from Types III and IV are marked by the downward-pointing triangles. The black lines in Figures 5L,M denote the magnetic fields of the selected data points for the partial-moment calculations. Figures 5I–K show the comparison between the measured electric field from EDP and the convection electric field (-V_i×B) of the hot and cold ions from our partial-moment calculations. A good consistency of the three components means that the ions in the investigated jet are mainly frozen-in with the magnetic field lines. Also, it demonstrates a relatively good reliability of our partial-moment calculation via separating multiple populations from one VDF.

TABLE 1

TABLE 1. Average partial moments of the hot and cold ions of the selected data points shown in Figure 5

As presented in Table 1, the average number density ( ∼0.04 cm⁻³) of the cold-ion beams is comparable to that of the cold ions in the lobe and approximately 13% of that of the hot ions inside the jet. Even though the cold ions have large peak VDFs in velocity space, they are still minor populations in this investigated event. As shown by the circles in Figure 5C, the bulk velocities of the hot ions from the partial-moment calculations are close to the average bulk velocities (black curve) of all ions. This is consistent with the partial-moment number density results. All of the hot ions convect earthward, and their speed ${\mathrm{V}}_i^H$ ( ∼760 km s⁻¹) is close to the E×B drift speed. As shown in Figures 5C–F; Table 1, all the cold-ion beams move earthward, meaning that all those ions are outflow ions of reconnection. The parallel cold ions have large positive V_Z component ( ∼710 km s⁻¹), and the anti-parallel ones have large negative V_Z component ( ∼-660 km s⁻¹). The bulk speed ( ∼1,050 km s⁻¹) of the cold-ion beams is approximately 38% larger than that of the hot ions, which is predominantly contributed by the V_Z or parallel component.

It is difficult to know the acceleration process from the observational aspect. Here, we find a similarity between the velocity patterns in Figures 5L,M and previous numerical results (Aunai et al., 2011; Divin et al., 2016) and suggest that the cold ions inside this investigated jet may come from the region close to the X line. Cold ions are demagnetized while crossing the separatrices close to the X line (Toledo-Redondo et al., 2016a; Divin et al., 2016), and are accelerated primarily by the Hall electric field, while the beams can remain relatively cold. The cold-ion beams may bounce for several times within the Hall electrostatic potential well, and get significant V_Z and V_X components. Then, the accelerated cold-ion beams could be further accelerated by the shrinking magnetic field lines due to the Fermi effect. One can find a characteristic example of such acceleration process from Figure 5 of Divin et al. (2016). This process could be responsible for the 38% extra speed at the MMS observation location.

Using Cluster data, Toledo-Redondo et al. (2016b) showed that cold ions can be heated by the large electric field gradient when crossing a separatrix boundary. Graham et al. (2017) analyzed a magnetopause reconnection event with cold ions and found lower-hybrid waves at the separatrix driven by the ion-ion streaming instability between the cold ions and the magnetosheath ions. The lower-hybrid waves can contribute to the cold-ion heating. Norgren et al. (2021) showed that the cold ions can be heated through a combination of thermalization at the separatrices and pitch angle scattering in the curved magnetic field around the neutral plane. Here, we calculate the temperature ( ∼320 eV) of the cold-ion beams inside the reconnection jet, which corresponds to about 6% of the total energy in the spacecraft frame. The cold-ion beams are approximately one order of magnitude colder than the hot ions, while the cold-ion beams are thermalized compared to the cold ions ( ∼10 eV) in the lobe. The large electric-field gradient at the separatrix and the scattering effect by the kinetic waves (see Supplementary Figure S4 in Supplementary Material for more details) and small magnetic-field curvature radii (Figure 5H) may all contribute to the heating of the observed cold ions from the lobe into the ion jet. However, one should note that the temperature results have a large uncertainty from our partial-moment calculation. As shown in Figures 3; Supplementary Figures S3, the thermal parts of the hot and cold populations usually overlap with each other. We cut major parts of the cold-ion VDFs empirically by eye. The results of the number density and bulk velocity are relatively reliable, but the ambient treatment of the VDF boundaries brings large errors to the temperature. The temperature results can be improved by fitting the cold-ion VDFs in the three-dimensional velocity space, which will be tried in our future works.

4 Conclusion

We investigated an MMS magnetotail crossing from 21:30:00 UT to 24:00:00 UT on July 06, 2017 with cold ions and ongoing magnetic reconnection and present quantitative analysis of the cold ions inside a reconnection ion jet. In this event, MMS cross one tailward and two earthward ion jets, and we explored the three-dimensional ion VDFs and find types of ion VDFs with cold-ion beams. MMS observe hot ions of plasma-sheet origin throughout the tailward jet and the first earthward ion jet, and cold ions with small V_B show up in part of the jet crossing. At the separatrix, MMS observe E×B drifting cold ions with negligible V_B. The second earthward ion jet is lead by a dipolarization front, and we find four types of ion VDFs inside: Type I consists of only a single hot plasma-sheet population, Type II consists of a hot population and a cold population with a positive V_B, Type III consists of a hot population and a cold population with a negative V_B, and Type IV consists of a hot population with counter-streaming cold populations. Our analysis focuses on those VDFs with cold-ion beams. The occurrence rate of Type II VDFs decreases gradually from the southern to the northern sides of the neutral line. Conversely, the occurrence rate of Type III VDFs increase gradually from south to the north. The occurrence rate of Type IV peaks at the neutral line. This distribution of VDFs could be formed by the patchy cold-ion inflow, the bouncing motions within the divergent Hall electrostatic potential well, and the scattering effect due to plasma waves and the curved magnetic field lines with small curvature radii.

We adopted the same technique as used in Li et al. (2017) to compute the partial moments of the hot and cold populations of Types II, III and IV VDFs. The average number density of the cold-ion beams is approximately 13% of that of the hot ions, meaning that the cold ions are a minor population in this investigated event. All the hot and cold ions are outflow ions towards Earth. The average bulk speed of the cold-ion beams is approximately 38% larger than that of the hot plasma-sheet ions. This extra speed is predominantly along the magnetic field direction. Those cold-ion beams could come from the cold-ion diffusion region and be initially accelerated by the Hall electric field. Then, the accelerated cold-ion beams could be further accelerated by the shrinking field lines through the Fermi effect. The cold-ion beams are still one order of magnitude colder than the hot ions, while the electric field with large gradient at the separatrix and the scattering effect by the waves and highly curved magnetic field lines may thermalize those cold ions from the lobe into the ion jet.

Data Availability Statement

All data used in this work are available at the MMS Data Center (https://lasp.colorado.edu/mms/sdc/public/). Data analysis was performed using the IRFU-MATLAB package (https://github.com/irfu/irfu-matlab).

Author Contributions

WL, YL, and BT carried out the data analysis and interpretation. YL wrote the first-version article, and WL revised it. CN, JH, CW, and QZ contributed to the data interpretation and article preparation. JB led the design and operation of the MMS mission. The remaining co-authors contributed to the data analysis under the framework of an ISSI international team.

Funding

This work was supported by NNSFC Grant No. 41731070, 41974170, and 41974196, the Chinese Academy of Sciences (QYZDJSSW-JSC028, XDA15052500, XDA17010301 and XDB41000000), and the Specialized Research Fund for State Key Laboratories of China. WYL was also supported by the Youth Innovation Promotion Association (2018177), and the Young Elite Scientists Sponsorship Program by CAST and the Open Research Program of Key Laboratory of Geospace Environment CAS. CN received support from the Research Council of Norway under contract 300865.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

We thank the MMS team and instrument principal investigators for data access and support. We acknowledge support from the International Space Science Institute (ISSI) international team Cold plasma of ionospheric origin in the Earth’s magnetosphere.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fspas.2021.745264/full#supplementary-material

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