Successive Energy Conversion at a Stepwise Dipolarization Front

Plasma jets, i.e., fast plasma flows (speed V > 150 km s⁻¹), are widely observed in space. In Earth's magnetotail, jets are traditionally dubbed bursty bulk flows (BBFs) due to their bursty (∼10 minute), finite-scale nature revealed by spacecraft observations (e.g., Baumjohann et al. 1989; Angelopoulos et al. 1992; Cao et al. 2006). It has been well documented that magnetospheric activities, such as aurora substorms, are closely related to the BBFs (e.g., Cao et al. 2010; Birn et al. 2013; Yu et al. 2017; Sitnov et al. 2019), which serve as "high-speed trains" responsible for the transport of mass, energy, and flux in the nightside magnetosphere (e.g., Cao et al. 2013, 2019; Liu et al. 2014). Inside these large-scale flows (several Earth radii R_E along the dawn–dusk direction), kinetic-scale electromagnetic structures have been commonly detected. In particular, ion-scale flow leading boundaries characterized by a sharp increase of northward magnetic field B_z (in geocentric solar magnetospheric (GSM) coordinates), usually termed as jet fronts or dipolarization fronts (DFs; e.g., Nakamura et al. 2002; Runov et al. 2009), are of intense interest because they are the primary regions hosting the interaction between the BBFs and the ambient plasmas.

DFs are typically generated along with the BBFs inside magnetic reconnection diffusion region (hence, they are also called reconnection fronts; e.g., Sitnov et al. 2009; Liu et al. 2019a), and they have been widely observed in the magnetotail, extending from X_GSM ≈ −30 to ∼−8 R_E (e.g., Schmid et al. 2011; Fu et al. 2012a; Liu et al. 2013). Multipoint observation had revealed that DFs can propagate along with the BBFs toward Earth as coherent structures over a long distance more than 10 R_E (Runov et al. 2009). During the DFs' earthward propagation, intense particle and wave activity have been observed, such as particle heating and acceleration (e.g., Birn et al. 2013; Zhou et al. 2013, 2018; Duan et al. 2014; Runov et al. 2015; Gabrielse et al. 2016; Lu et al. 2016, 2020; Liu et al. 2017a), pitch angle evolution (e.g., Fu et al. 2012b; Liu et al. 2017b), and wave–particle interactions (e.g., Zhou et al. 2009; Khotyaintsev et al. 2011; Huang et al. 2012; Balikhin et al. 2014; Hwang et al. 2014; Divin et al. 2015; Liu et al. 2019b, 2021; Chen et al. 2022). These plasma activities are manifestations of ongoing energy transfer associated with the DFs, which have hitherto been extensively studied by observations and simulations (e.g., Huang et al. 2015; Khotyaintsev et al. 2017; Yao et al. 2017; Liu et al. 2018a, 2018b, 2022b, 2022a; Lu et al. 2018; Zhong et al. 2019; Wang et al. 2020; Shu et al. 2022), revealing that DFs are important sites not only for local reconnection dynamics but also for the global energy transport in the magnetotail (e.g., Angelopoulos et al. 2013; Liu et al. 2022c).

DF-driven energy conversion processes revealed by previous studies are typically isolated, and hence it is difficult to compare local energy conversion from case to case. So far, it remains elusive how the DF-driven energy conversion develops and what controls the local energy partition. In this study, we report, for the first time, successive energy conversion driven by multiple current layers in a stepwise DF in the magnetotail, via high-cadence measurements provided by NASA's MMS mission (Burch et al. 2015). The multiple current layers are closely connected and cause gradual variations in particles and electromagnetic fields, and therefore a successive increase of energy conversion rates within the DF in the satellite frame. The present observation provides a unique opportunity to study the evolution of energy conversion within the DFs, revealing that both ion and electron currents can contribute to energy conversion and energy partition between the two species is controlled by lower hybrid drift instability developed within the front region.

Unprecedently high resolution data collected by the MMS mission, including data from the Fluxgate Magnetometer (Russell et al. 2014) and the Electric Double Probe (Ergun et al. 2014a; Lindqvist et al. 2014) for electromagnetic fields and data from the Fast Plasma Investigation instrument (Pollock et al. 2016) for particles, are exploited and presented in the GSM coordinates. The event of interest was observed by MMS on 2017 August 1, from 09:01:06 to 09:01:16 UT, when MMS was located at [−22.8, 8.92, 2.47] R_E . Separation of the spacecraft tetrahedron is close to 12 km (∼3 local electron inertial lengths d_e ), hence allowing us to study local energy transfer at the electron scale.

Figure 1 shows the overview of the event. During the whole interval, a steady earthward ion flow with speed close to 400 km s⁻¹ was observed (Figure 1(d)), suggesting passage of a moderate ion jet. A DF, characterized by a clear B_z increase (from ∼1 to ∼14 nT; Figure 1(a)) and density drop (from ∼0.9 to 0.3 cm⁻³; Figure 1(b)), was detected between 09:01:09.0 and 09:01:12.6 UT. Different from traditional DFs featuring a quasi-monotonous B_z increase (e.g., Runov et al. 2015), the observed DF exhibits a stepwise B_z increase and hosts three current layers (CLs), named hereafter CL1, CL2, and CL3. The first current layer (CL1) was detected between 09:01:09.0 and 09:01:09.6 UT (marked by two black dashed lines), manifested by a clear B_z increase (from ∼1 to ∼6 nT; Figure 1(a)) and density drop (from ∼0.9 to 0.8 cm⁻³; Figure 1(b)). During the CL1 crossing, both ion and electron temperatures stay approximately steady (Figures 1(e) and (f)), indicating the absence of particle heating. The electric field increases from ∼0.9 to ∼1.9 mV m⁻¹ across CL1, primarily in the E_y component, with both E_x and E_z close to zero (Figure 1(g)). No clear enhancement of magnetic and electric wave power is observed associated with the front (Figures 1(h) and (i)). The CL1 propagation velocity V_CL1 estimated based on the timing analysis is 375 × [0.93, −0.16, 0.33] km s⁻¹, and based on the CL1 duration (∼0.6 s), the front thickness, defined as the distance between B_z ,_min (minimum B_z ) and B_z ,_max (maximum B_z ) during the CL interval, is calculated as ∼230 km, close to 1 d_i (d_i is the ion inertial length estimated based on plasma density prior to CL1). The second CL (CL2), characterized by a dramatic B_z increase (from ∼3 to ∼9 nT; Figure 1(a)) and density drop (from ∼0.8 to 0.6 cm⁻³; Figure 1(b)), was observed between 09:01:10.5 and 09:01:11.0 UT (flanked by two red dashed lines), right behind CL1. During the CL2 interval, the electron perpendicular temperature still keeps steady, while the electron parallel temperature clearly rises (T_e,∥: ∼440 → 550 eV), establishing strong parallel temperature anisotropy behind CL2. Both ion parallel and perpendicular temperature increase across CL2 (T_i : ∼1800 → ∼2400 eV). Electric fields are further amplified at CL2, reaching up to ∼4 mV m⁻¹ in E_y , with E_x also showing a local peak near ∼1 mV m⁻¹. In addition, electric fields at CL2 fluctuate more than at CL1, exhibiting a clear increase in electric wave power near the lower hybrid frequency (Figure 1(i)). The CL2 propagation velocity V_CL2 estimated based on the timing analysis is 378 × [0.92, −0.14, 0.37] km s⁻¹, and considering the CL2 period (∼0.5 s), the front thickness is calculated as ∼190 km, close to 0.8 d_i . The third CL (CL3), characterized by a dramatic B_z increase (from ∼9 to ∼14 nT; Figure 1(a)) and density drop (from ∼0.6 to 0.3 cm⁻³; Figure 1(b)), was observed from 09:01:12.0 to 09:01:12.6 UT (indicated by two blue dashed lines), right after CL2. During the CL3 interval, the electron parallel and perpendicular temperatures both increase (T_e,⊥: ∼460 → ∼650 eV; T_e,∥: ∼590 → ∼750 eV). The ion parallel and perpendicular temperatures also increase up to ∼3000 eV during the CL3 crossing. Electric fields at CL3 fluctuate more and are stronger, approaching ∼5 mV m⁻¹ in E_y , with E_x showing a local peak near ∼6 mV m⁻¹. In addition, more intense wave activity near the lower hybrid frequency is observed at CL3. The CL3 propagation velocity V_{CL 3} estimated based on the timing analysis is 437 × [0.92, 0.01, 0.39] km s⁻¹, and based on the CL3 period (∼0.6 s), the front thickness is calculated as ∼190 km, close to 1.1 d_i . Overall, these CLs are very close and similar in terms of magnetic field variations, length scales, and propagation velocities, but they host distinct particle and wave activities: CL3 hosts the most intense activity, i.e., the strongest electrostatic fluctuations and particle temperature increase; CL2 has relatively weaker activity; while CL1 is basically quiet.

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The differences in the particle and wave activities at these CLs may suggest distinct energy transfer driven by currents and electric fields developed therein. To investigate local energy conversion, a local coordinates system is established via minimum variance analysis of the B field, yielding L = [−0.47, −0.03, 0.88], N = [0.87, −0.21, 0.45], and M = N × L. The obtained normal direction N is close to the CLs' propagation directions estimated from the timing analysis. Currents and electric fields in the local coordinates are displayed in Figure 2. Here the current density is estimated by two different methods, Curlometer (Dunlop et al. 1988) and direct calculation using particle moments from the Fast Plasma Investigation instrument. As can be seen in Figures 2(c)–(f), the two methods yield similar results, indicating the reliability of the particle moments. The current density at CL1 is mainly carried by −J_M , i.e., the tangential component (approximately along the dawn–dusk direction), reaching up to ∼−45 nA m⁻² (Figure 2(c)), consistent with the typical current direction at CLs (e.g., Liu et al. 2013). At CL2, the current density is also dominated by −J_M , approaching −52 nA m⁻²; while the J_L component, which is an approximately field-aligned current, also contributes to an important portion, peaking near 20 nA m⁻² (Figure 2(e)). The current density at CL3, however, is primarily carried by J_L , which reaches up to 40 nA m⁻², larger than J_M , which peaks near −33 nA m⁻². Hence, along the M-direction, CL2 hosts the strongest current, while the field-aligned current reaches its maximum at CL3.

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Electric fields at these CLs are primarily along the M and N directions, with the E_L component staying basically steady during the whole interval (Figure 2(f)). Associated with these CLs, the E_M component shows a persistent, stepwise enhancement, from ∼0 to −1.5 mV m⁻¹ at CL1, to −2.5 mV m⁻¹ at CL2, and further to −4.3 mV m⁻¹ at CL3. The E_N component, however, exhibits rather localized variations: from −0.6 to −0.3 mV m⁻¹ at CL1, from −0.6 to 0.4 mV m⁻¹ at CL2, and from −2 to 2 mV m⁻¹ at CL3. We examine the electric fields in the context of a two-fluid magnetohydrodynamics framework, by comparing the measured electric field E with terms in the generalized Ohm's law. Figures 2(g) and (h) show the comparison between the measured electric field with ion convection and Hall terms. One can see that during the whole interval, E_M is approximately balanced by the ion convection term (Figure 2(g)), indicating that E_M is basically the convectional electric field (or motional electric field) carried by the dipolarizing ion jet. The localized E_N component at the CLs, however, clearly deviates from the ion convection term and roughly follow the variation of the Hall term (Figure 2(h)), suggesting that ions are demagnetized with electrons approximately remaining magnetized. Electric fields in the ion frame are further compared with the Hall term in Figures 2(i) and (j), where one can see that the nonideal electric fields, manifested mainly along the N direction, are indeed balanced by the Hall electric fields (here the electron pressure gradient term is insignificant and thus not considered).

We now focus on the energy exchange between the electromagnetic fields and particles by calculating E•J_total,i,e terms (i.e., total energy conversion, ion energy conversion, and electron energy conversion) in the spacecraft frame, as displayed in Figure 3. Note that energy conversion is frame dependent; hence, its value will vary in different reference frames (e.g., Khotyaintsev et al. 2017; Liu et al. 2022b). Nevertheless, in the context of magnetospheric dynamics, energy conversion is typically investigated in the satellite frame (e.g., Angelopoulos et al. 2013; Huang et al. 2015; Zhong et al. 2019; Liu et al. 2022a), since magnetospheric dynamics, e.g., global energy transport, is well considered in the satellite frame. Therefore, we also investigate energy conversion and the associated partition in this frame. The total energy conversion term E•J_total (J_total is calculated via the Curlometer method), ion energy conversion term E•J_i , and electron energy conversion term E•J_e . are shown in Figure 2(b). In addition, the spatial integrals of these terms across the CLs are also calculated (∫E•J_total,i,e •dx, where dx is the distance across the fronts) and are presented in Figure 3(c). One can see that intense, localized energy conversion happens at these CLs, with E•J_total > 0, indicating magnetic field energy being transferred into particle energy. At CL1, E•J_total peaks near 50 pW m⁻³, comparable to typical values (∼40 pW m⁻³) of the energy conversion rate revealed by previous statistical studies (e.g., Huang et al. 2015; Zhong et al. 2019; Wang et al. 2020). At CL2, it reaches up to a much higher magnitude, close to 130 pW m⁻³. At CL3, it achieves its maximum during the whole interval, ∼200 pW m⁻³. As such, the spatial integral of the total energy conversion exhibits a stepwise enhancement in association with these CLs, with a local increment close to ∼4 μW m⁻² at CL1, ∼12 μW m⁻² at CL1, and ∼30 μW m⁻² at CL3 (Figure 3(c)). Figures 3(d)–(f) present energy conversion in the LMN coordinates. One can see that the total energy conversion terms at these CLs, although differing in magnitude, are all primarily provided by the E_M •J_M terms (Figure 3(e)), with the E_L •J_L and E_N •J_N terms being close to zero (Figures 3(d) and (f)).

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Energy partition at these CLs exhibits quite interesting features. At CL1, electron energy conversion dominates and exhibits a similar profile to the E•J_total term (except a localized derivation in the front trailing edge), with an increase of ∫E•J_e being close to 3.7 μW m⁻². Electron energy conversion at CL1 is mainly provided by the E_N •J_N term (Figure 3(f)), indicating ongoing electron acceleration along the front normal direction. Ion energy conversion at CL1 is contributed by both E_N •J_N and E_M • J_M terms, but the two terms are in the opposite sense, thus yielding negligible ion energy conversion rates. At CL2, ion and electron energy conversion terms are comparable, with E•J_i peaking near 90 pW m⁻³ and E•J_e peaking near 70 pW m⁻³, and ∫E•J_i is increased by ∼7 μW m⁻², also close to the increment (∼5 μW m⁻²) of ∫E•J_e . Electron energy conversion at CL2 is also mainly provided by the E_N •J_N term, while ion energy conversion at CL2 is primarily contributed by the E_M • J_M term. At CL3, the ion energy conversion term clearly dominates and is comparable to the total energy conversion term, and ∫E•J_i is increased by ∼28 μW m⁻², providing a predominant contribution to the increment of ∫E•J_total. Electron energy conversion at CL3 is provided by both the E_N •J_N and E_M • J_M terms, and ion energy conversion is provided by the E_M • J_M term. Overall, energy conversion is controlled by the electron current at CL1, equally contributed by ion and electron currents at CL2 and dominated by ion currents at CL3. Energy conversion in the electron rest frame ${{\boldsymbol{J}}}_{\mathrm{total}}\bullet {{\boldsymbol{E}}}^{{\prime} }\ ({{\boldsymbol{E}}}^{{\prime} }={\boldsymbol{E}}+{{\boldsymbol{V}}}_{{\boldsymbol{e}}}\,\times \,{\boldsymbol{B}})$ is also calculated and presented in Figures 3(g) and (h). The ${{\boldsymbol{J}}}_{\mathrm{total}}\bullet {{\boldsymbol{E}}}^{{\prime} }$ term also shows a local increase at these CLs and is dominated by energy generators, approaching ∼−17 pW m⁻³ at CL1, ∼−20 pW m⁻³ at CL1, and ∼−56 pW m⁻³ at CL3 (Figure 3(h)), suggesting that particles were losing energy in the electron rest frame. The locally enhanced energy generators have also been observed at DFs in previous studies (e.g., Yao et al. 2017). The spatial integral of ${{\boldsymbol{J}}}_{\mathrm{total}}\bullet {{\boldsymbol{E}}}^{{\prime} }$ exhibits a stepwise decrease, with a local drop close to ∼0.5 μW m⁻² at CL1, ∼1.5 μW m⁻² at CL1, and ∼3.6 μW m⁻² at CL3 (Figure 3(h)). Hence, energy conversion in the electron rest frame operates in the opposite direction with much weaker rates compared with energy conversion in the spacecraft frame.

We further calculate the temporal variation rate of the magnetic field energy density (∂E_B /∂t) based on Faraday's law:

$$\begin{eqnarray}&&\displaystyle \frac{\partial {E}_{B}}{\partial t}=\displaystyle \frac{{\boldsymbol{B}}}{{\mu }_{0}}\,\bullet \,\displaystyle \frac{\partial {\boldsymbol{B}}}{\partial t}=-\tfrac{{\boldsymbol{B}}}{{\mu }_{0}}\,\bullet \,{\rm{\nabla }}\times {\boldsymbol{E}},\end{eqnarray} \tag{ 1 }$$

where E_B , E , B , and μ₀ represent magnetic field energy density, electric field, magnetic field, and magnetic permeability in empty space, respectively. The results are presented in Figures 3(h) and (j). At CL1, ∂E_B /∂t is basically close to zero (Figure 3(i)), and the spatial integral of ∂E_B /∂t (∫∂E_B /∂t) remains approximately steady during the front interval (Figure 3(j)), indicating that the local magnetic field energy remains unchanged. Hence, CL1 is a steady front. ∂E_B /∂t at CL2 clearly rises but fluctuates with positive and negative values, and ∫∂E_B /∂t shows negligible variations across the front. Therefore, like CL1, CL2 also remains steady in terms of magnetic field energy variation. At CL3, ∂E_B /∂t varies more dramatically and fluctuates with localized positive and negative values, with its positive value, which peaks near ∼2300 pW m⁻³, relatively larger than its negative value, which drops down to ∼−1700 pW m⁻³ (Figure 3(h)). ∫∂E_B /∂t increases quasi-monotonically across CL3 (from ∼−10 to ∼90 μW m⁻²; Figure 3(j)), suggesting that CL3 is a growing front, different from the two preceding CLs.

In this study, we report the first observation of successive energy conversion driven by multiple current layers in a stepwise DF in the midtail (X_GSM ∼ −23 R_E ), via high-cadence measurements from the MMS mission. Note that multiple DF layers had been detected by previous spacecraft missions, such as Cluster (Hwang et al. 2011) and THEMIS satellites (Zhou et al. 2009). Different from the previous observations where multiple DFs were embedded inside variable plasma flows (i.e., flow speed varies dramatically) and well separated (e.g., Birn et al. 2019; Gabrielse et al. 2016; Merkin et al. 2019), the sequential current layers reported in the present study are inside a steady ion flow with an approximately constant speed (∼400 km s⁻¹) and closely connected, leading to gradual variations in particles and electromagnetic fields, such as a magnetic field B_z increase, electric field increase, and density drop in a stepwise fashion. Such induced changes thus favor the development of a successive increase of energy conversion rates at these DFs. The closely related CLs may be reminiscent of substructures generated by some kinetic instabilities previously reported at DFs, such as lower hybrid drift instability (LHDI; e.g., Liu et al. 2018b; Pan et al. 2018) or ballooning/interchange (Pritchett 2015). However, these instabilities typically generate wavy structures in the front tangential plane (approximately along the dawn–dusk direction), inconsistent with the stepwise structures that are distributed primarily along the front normal direction (approximately the Earth–Sun direction). Instead, since DFs have been traditionally suggested as reconnection ejecta (e.g., Sitnov et al. 2009; Liu et al. 2019a), the observed CL chain indicates that magnetic reconnection in the midtail may proceed progressively.

Albeit the multiple CLs are adjacent, they host distinct particle and wave activities, indicating development of local dynamics during the CLs' global propagation. The first CL (CL1) is basically quiet, without particle temperature increase and wave emissions observed across the front. The second CL (CL2) is relatively more dynamical, hosting an electron parallel temperature increase, ion temperature increase (in parallel and perpendicular directions), and electrostatic waves. The third CL (CL3) hosts the strongest particle and wave activities, in terms of particle temperature increase and wave intensity. Such a difference in the CL dynamics is also manifested in the magnetic field energy variation, showing that the magnetic field energy remains steady at CL1, weakly fluctuates at CL2, and dramatically increases at CL3. This indicates magnetic field accumulation at CL3, even though CL3 hosts the strongest energy loads. Hence, the energy source for ongoing energy conversion at these CLs is the incoming Poynting flux, consistent with the suggestion by recent kinetic simulations (Shu et al. 2022). The magnetic field energy variation is also in line with the electron perpendicular heating feature across these CLs (absent at CL1 and CL2 but present at CL3). Note that an increase of parallel temperature is usually indicative of Fermi acceleration, which has well been suggested to operate during the CLs' earthward propagation and is essentially related to the global change of magnetic field lines (e.g., Birn et al. 2013). Since these CLs are closely located, Fermi acceleration should yield the same energy variations therein. Hence, the difference in the parallel temperature increase at these CLs should be ascribed to local heating, which may be ascribed to the development of LHDI, which is sensitive to the plasma density gradient and local plasma β (β is the ratio of plasma thermal pressure to magnetic pressure; e.g., Davidson et al. 1977). The plasma density gradient along the N direction increases from CL1 to CL3 (0.0004 → 0.0011 → 0.0016 cm⁻³·km⁻¹), and β decreases from CL1 to CL3 (242 → 4.2 → 1.6). As such, the LHDI growth rate should theoretically increase from CL1 to CL3, consistent with the observed wave intensity at these CLs (we have also calculated the local LHDI dispersion relation and found positive growth rates; not shown). The observed electron parallel heating at CL2 and CL3 is also consistent with wave heating by the LHDI through Landau resonance (e.g., Divin et al. 2015). Note that here we do not focus on LHDI itself since it is not within the scope of this study.

The LHDI also plays an important role in the energy conversion at the CLs, particularly in the energy partition between the ions and electrons. Energy conversion is dominated by electrons at CL1, equally contributed by electrons and ions at CL2, but controlled by ions at CL3. Hence, LHDI seems to reduce the relative role played by electrons in the energy conversion at these CLs. The underlying reason may be explained as follows: the electric fields induced by LHDI are mainly along the N direction and balanced by the Hall electric field. Therefore, when LHDI develops at the CLs, ions that mainly move along the N direction will obtain energy, while electrons, in contrast, will not obtain any energy since electrons basically remain magnetized. This suggests that electrons dominate the energy budget at quiet CLs, while ions control energy transfer at turbulent CLs. Note that the total energy conversion is driven by a motional electric field that gradually rises due to a stepwise B_z increase in the steady ion jet, yielding the dominant E_M • J_M term, consistent with previous studies suggesting that the duskward electric field is responsible for DF-driven energy conversion (e.g., Hamrin et al. 2014; Li et al. 2016). Note that the locally enhanced energy conversion is not related to nonlocal plasma transport across the DF, since it is driven by intense electric fields and currents right at the front. In terms of particle motion, it can be linked to the well-documented ion reflection and acceleration at DFs or to particle penetration driven by various drift due to gradients in electromagnetic fields.

In summary, we present, for the first time, observations of successive energy conversion driven by multiple CLs in a stepwise DF in the midtail (as illustrated in Figure 4). The multiple CLs are adjacent and lead to gradual changes of particles and electromagnetic fields, giving rise to intense, successive increase of energy conversion rates within these CLs, with electromagnetic field energy being transformed into particle energy. The successive energy conversion is driven by motional electric fields. Ion and electron currents both contribute to the total energy conversion, and the partition is modulated by wave electric fields driven by LHDI. The LHDI also affects the variation of magnetic field energy at the CLs and causes both electron parallel and perpendicular heating. Hence, LHDI can play an important role in DF-driven energy conversion in the tail.

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We greatly thank the entire MMS team for making the high-cadence data available. The present study is supported by the National Natural Science Foundation of China (grants 41821003 and 42104164). The data used in the present study are collected by the NASA MMS mission and publicly available at https://lasp.colorado.edu/mms/sdc/public/about/browse-wrapper/.