# FLANK MAGNETOSPHERE: DYNAMICS AND TURBULENT PATHWAY TO/FROM THE MAGNETOTAIL

Principal Author:

**Kyoung-Joo Hwang**, Southwest Research Institute, San Antonio, TX

Co-authors:

**Chih-Ping Wang**, University of California, Los Angeles, Los Angeles, CA

**Katariina Nykyri**, Embry-Riddle Aeronautical University, Daytona Beach, FL

**Jim Burch**, Southwest Research Institute, San Antonio, TX

**Jerry Goldstein**, Southwest Research Institute, San Antonio, TX

**Kyunghwan Dokgo**, Southwest Research Institute, San Antonio, TX

**Hiroshi Hasegawa**, Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan

**Takuma Nakamura**, Austrian Academy of Sciences ÖAW, Space Research Institute, Graz, Austria

**Mikhail Sitnov**, Applied Physics Laboratory, Johns Hopkins University, Laurel, MD

**Xuanye Ma**, Embry-Riddle Aeronautical University, Daytona Beach, FL

**Yu Lin**, Auburn University, Auburn, AL

**Xueyi Wang**, Auburn University, Auburn, AL

## SYNOPSIS

About sixty years ago Dungey (1961) and Axford and Hines (1961) proposed two different models of the solar wind (SW)-magnetosphere interaction. The former was based on the concept of magnetic reconnection under large magnetic field shear. The latter was on quasi-viscous interaction in the boundary layer powered by large flow velocity shear. Since then, two most important physical processes that lead and regulate the SW-Earth's magnetosphere coupling are thought to be magnetic reconnection and the Kelvin-Helmholtz instability (KHI). Understanding the former has been greatly advanced via the MMS mission with its high-resolution measurements, while the latter still leaves room for enhanced understanding. Kelvin-Helmholtz waves (KHWs) or their nonlinearly-developed form, i.e., Kelvin-Helmholtz vortices (KHVs) developed along the flank-side magnetopause grow in size down the tail and, thus, the impact of the latter can become important at the mid-tail X-line or beyond.

Our goal is to resolve the long-standing Dungey vs. Axford-Hines dichotomy via simultaneous measurements of dayside reconnection (two polar-orbiting satellites) and flank-side diffusive process (two equator-orbiting satellites at dawn and dusk flanks, respectively). Another equator-orbiting satellite simultaneously probing the near-midnight plasma sheet, for the first time, enables us to address causality between unstable central magnetotail current sheets and flank-side dynamics (Figure 1). In this white paper we focus on these long-lasting and unexplored problems on Heliophysics research with brief suggestions of a mission concept optimized for answering those science questions.
<figure><img src="image_1.png" /></figure>

**Figure 1.** The mission determines the relative importance and effectiveness of KHWs for plasma heating, acceleration and transport, in comparison to dayside subsolar and cusp reconnection and associated diamagnetic cavities. Three equator-orbiting spacecraft (S1-3) on an elliptical orbit with an apogee of ~35 $R_E$ and two polar-orbiting spacecraft (S4, 5) on a circular orbit with an altitude of ~7.5-10 $R_E$ resolve the long-standing Dungey vs. Axford-Hines dichotomy in terms of various solar wind and IMF conditions.

# 1. Background and Unknowns

The KHI condition in the MHD regime predicts that the condition becomes easily satisfied at the dawn flank than the dusk under typical Parker-Spiral IMF (interplanetary magnetic field) (Hasegawa, 1975; Nykyri, 2013). Under the same IMF condition, the kinetic physics also predicts the dawn-side magnetosheath to be more turbulent, which can act as seed fluctuations for KHI or lead a stronger growth of KHI on the dawn side than the dusk (Omidi et al., 2009; Nykyri et al., 2017; Nakamura et al., 2020). This may explain the dawn-dusk asymmetry of the ion mixing layer (Hasegawa et al., 2003; Wing et al., 2005), evidencing the role of KHWs in the SW entry. While there have been some case (Moore et al, 2016) and statistical studies (Moore et al., 2017) that suggest that the source of this asymmetry is related to KHI-driven enhanced ion-scale wave generation, we yet lack a systematic framework quantifying the relative importance and effectiveness of KHWs for plasma heating, acceleration and transport, in comparison to dayside subsolar and cusp reconnection and associated diamagnetic cavities. In particular, it is crucial to understand their roles in terms of various SW/IMF conditions, as well as related to memory of magnetosphere-system.

The mechanism via which KHWs can transfer the solar wind plasma into the magnetosphere includes 1) diffusive transport through the turbulent decay of KHVs (Matsumoto & Hoshino, 2004; Faganello, 2008; Matsumoto & Seki, 2010; Cowee et al., 2010) (Figure 2a) and 2) in-plane and/or mid-latitude vortex-induced reconnection (Nakamura et al., 2017; Faganello et al., 2012; Eriksson et al., 2016; Vernisse et al. 2016; Hwang et al., 2020; 2021) (Figure 2b). Regarding 1), previous simulations (Nykyri and Otto, 2001; Nakamura and Daughton, 2014) show that KHWs cause efficient transport with a diffusion coefficient of $10^{9-10} m^2/s$. A pre-existing LLBL (low-latitude boundary layer) can form via high-latitude reconnection during northward IMF and promote the
diffusion with the coefficient of $10^{10-11}$ m$^2$/s (Nakamura et al., 2017). Regarding 2), vortex-induced reconnection or secondary tearing/KH/RT (Rayleigh-Taylor) instabilities can occur along the KHV boundary. Nakamura and Daughton (2014) showed that vortex-induced reconnection causes a rapid mixing while the secondary KHI and RTI cause a gradual transport deeper into the magnetosphere. Reconnection can also occur out of the shear plane, due to a 3-D twist of magnetospheric and magnetosheath fields induced by KHVs. The mid-latitude double reconnection also creates the flux tube with reduced entropy, which facilitates a rapid inward motion of the flux tube deeply into the magnetosphere (Ma et al., 2017). Which process is dominant in which evolution phase/location of the flank dynamics under which external conditions and how deep into the magnetosphere KHWs can transport mixed plasmas are an open question.

<figure><img src="image_2.png" /><figcaption>**Figure 2.** Solar wind plasma transport into the magnetosphere induced by KHWs via diffusive transport as predicted from 3-D fully kinetic simulations using VPIC code (Nakamura et al., 2017) (a), and in-plane (b, upper) and mid-latitude (b, lower) reconnection.</figcaption></figure>

Not only the KHWs/KHVs affect the SW transport across the flank, but they also drive the global magnetosphere. Simulations and observations (Merkin et al., 2013; Li et al., 2012; Wang et al., 2017; Ling et al., 2018) have indicated that as KHWs propagate down the tail beyond $X = -20$ R$_E$, the wavelength of the KHVs grows larger to ~10 R$_E$, the north-south width of KHVs expands with a certain $k_z$ component, and the plasma flow and magnetic fluctuations associated with KHWs penetrate inward to as deep as the midnight region (Figure 3). As the magnetospheric magnetic fields become weaker with increasing downtail distances, the tail current sheet beyond $X \le -20$ R$_E$ can be easily disturbed by such KH-driven fluctuations. Two-point observations by ARTEMIS together with MHD simulations suggest that the inward-propagating fluctuations engaged with the KHWs drive an asymmetry in the central (near-midnight) current sheet between above and below the current sheet, which causes current sheet flapping in both the kink and sausage modes (in a
time scale of a few minutes with a Y-scale of ~2-3 $R_E$). The localized thinning or thickening of the current sheet associated with the sausage mode may play a role in controlling the onset of magnetotail reconnection. This KHWs/KHVs driving is different from other mechanisms proposed for the current sheet flapping, such as double gradients (Erkaev et al., 2008), ion drift-kink instability (Daughton, 1998), ballooning/interchange instability (Golovchanskaya and Malsev, 2005), firehose instability (Wang et al., 2020), and nonadiabatic ions (Wei et al., 2015). It is also different from the current sheet flapping externally driven by the SW/IMF perturbations (Forsyth et al., 2009; Wang et al., 2019).

On the other hand, the evolution of KHWs is regulated by the width of the KH-unstable band due to the stabilization effect of the lobe magnetic field (Hashimoto and Fujimoto, 2006). Moreover, the current sheet flapping that is excited internally and propagates from the midnight region toward flanks may disturb the existing KHWs/KHVs. The temporal and spatial scales and propagation of the current sheet flapping associated with different drivers/mechanisms can be different. These studies indicate causality between flank-side KHWs/KHVs and central current sheet behavior, which has been never explored.

KHWs provide a place for not only solar wind transport but also energetic (> 30keV) particle transport (Figure 4). Sorathia et al. (2017) showed that energetic particles can be entrained in tailward KHWs at dawn/dusk flanks penetrating the magnetosheath depending on their energy and species. Furthermore, dayside reconnection leads to the formation of cusp diamagnetic cavities (Nykyri et al., 2011a,b; Adamson et al., 2011, 2012), which can be filled with energetic particles via local acceleration. These trapped particles can leak out via either IMF orientation changes or high-latitude KHWs (Hwang et al., 2012; Ma et al., 2016). Thus, KHWs can play roles in the leakage of energetic particle into the magnetosheath or transport within the KHVs down the tail flanks and into the plasma sheet. However, we lack the observational framework about the importance and efficiency of magnetopause KHWs in such roles.

<figure><img src="image_3.png" /></figure>

**Figure 3.** Illustration of KHWs externally driving current sheet fluctuations as predicted in a global hybrid (top, ANGIE3D code (Lin et al., 2014; 2017)) and global MHD (bottom, LFM code (Merkin et al., 2013)) simulation and/or being, in turn, affected by such current sheet disturbances. Simultaneous observations of the KH activity at the dawn/dusk flank (S1 and S2) and the current sheet thickness and behavior at a location inside the magnetosphere (S3) provide an important causal relationship between the flank and midnight current sheet dynamics.
<figure><img src="image_4.png" /><figcaption>**Figure 4.** Paths of energetic particles originated from the near-Earth midnight sector (see a light green wedge in panel a; Sorathia et al., 2017): H⁺ (top low), O⁺ (middle), and e⁻ are separated into two streams, one moving inward toward trapped drift orbits and the other moving along the magnetopause flanks penetrating the magnetosheath. Formation of the diamagnetic cavities for southward and duskward IMF (b, Nykyri et al., 2021a): the yellow ovals show the expected location of two “traditional” diamagnetic cavities, while a “non-traditional” cavity (at/around M1/M2) created at southern dusk sector via component reconnection.</figcaption></figure>

**2. Science Questions**

Our goal is to fill the gaps in our understanding of the Earth's magnetosphere that have resulted from neglecting one of the two fundamental physical processes occurring over the entire surface of the magnetopause, i.e., KHI. We also consider the dynamics and effects of the flank magnetopause fluctuations caused by foreshock transients and FTEs (flux transfer events). We achieve this goal by answering **three science questions**:

**Q1.** What are the roles and importance of flank dynamics in the solar wind transport?

* Q1.1: How importantly do *flank dynamics* (Kelvin-Helmholtz waves/vortices, fluctuations caused by foreshock transients and FTEs) transfer the solar wind plasma into the magnetosphere? In particular, compared to dayside reconnection in terms of SW conditions including varying IMF orientation? Is there a dawn-dusk asymmetry?

* Q1.2: How deep do KHWs/flank dynamics transport solar wind or mixed plasmas into the magnetosphere beyond the boundary layer? What is the transport path? Is there a dawn-dusk asymmetry?

**Q2.** Is there a causal relationship between flank dynamics and central tail current sheet dynamics?

* Q2.1: Can flank dynamics/conditions serve triggers of the marginally stable current sheet in the central magnetotail plasma sheet? How do flank dynamics drive the current sheet into an unstable state? E.g., via KHW-driven solar wind entry, modifying tail reconnection inflow conditions and/or current sheet thickness/orientation?

* Q2.2: Whether or not and how does the current sheet behavior affect the flank dynamics?
**Q3.** What roles do flank dynamics play in the energetic particle escape or transport?

* Q3.1: How far and how effectively do flankside and high-latitude KHWs transport energetic particles?

* Q3.2: Which particle species in what energy ranges effectively transport or escape via KHWs at flanks and high-latitude magnetopause? Is there a dawn-dusk asymmetry?

Answering **Q1** enables us to ultimately resolve the long-standing Axford-Hines/Dungey dichotomy. Answering **Q2** impacts our understanding of the drivers of the unstable central current sheet and its self-consistent behavior via communications with flank dynamics. Answering **Q3**, when combined with answering **Q1**, completes our understanding of roles and impact of flank dynamics as a channel for two-way transport.

# 3. Technical Approach and Methodology

## 3.1. Observational Approach

Our approach is to fly five satellites consisting of three equator-orbiting spacecraft (S1-3) on an elliptical orbit with an apogee (perigee) of ~35 (~1) $R_E$ and two polar-orbiting spacecraft (S4, 5) in the near noon-midnight meridian on a circular orbit with an altitude of ~7.5-10 $R_E$ to optimize simultaneous observations of the dayside magnetopause and the flankside magnetopause as well as maximize simultaneous observations of the dawn and dusk flanks and the central plasma sheet (Figure 1). This mission can be categorized as NASA's MIDEX program ($250-300M).

**Instrument Requirements** All five spacecraft are equipped with the same suite of instruments: the fluxgate magnetometer, the electric field detector, the ion and electron electrostatic analyzer, and the solid state telescope to measure the magnetic field, the electric field, thermal (< 30 keV) plasmas, and energetic particles, respectively. In-situ data of the magnetic field configuration and thermal plasma features enable the identification of reconnecting current sheets and KHWs/KHVs (**Q1-2**). The energetic particle detector is required to achieve answering **Q3**. Two of the most important waves for the interaction between the magnetosheath and the magnetosphere (Nakamura, 2021) or for an efficient plasma mixing observed near the edge of KHVs (Nakamura et al., 2022) are Kinetic Alfvén waves (KAWs) and Lower-hybrid drift waves (LHDWs). To identify these waves and their roles and effects in answering **Q1-3**, the wave electric- and magnetic-field measurements are required. Table 1 shows detailed requirements for each instrument.

<table><caption>**Table 1.** Performance requirements of instruments onboard all five spacecraft to answer Q1-3</caption><thead><tr><th></th><th>Particle</th><th>Magnetic field</th><th>Electric field</th></tr></thead><tbody><tr><th>Instrument</th><td>Thermal plasma:<br>Electrostatic Analyzer<br>Energetic particles:<br>Solid State Telescope</td><td>DC: Flux Gate<br>Magnetometer<br>AC: Search Coil<br>Magnetometer</td><td>DC: Spin-plane Double<br>Probe<br>AC: Axial Double<br>Probes</td></tr><tr><th>Range</th><td>10 eV to 30 keV<br>25 keV to 0.5 MeV<br>for both ion and electron</td><td>DC: 25000 nT<br>AC: 1 Hz to 4 kHz<br>(frequency range)</td><td>DC: ±300 mV/m<br>AC: 1 Hz to 32 kHz<br>(frequency range)</td></tr><tr><th>Accuracy</th><td>Angular res.: 15°</td><td>0.1 nT</td><td>0.5 mV/m</td></tr><tr><th>Fast mode</th><td>1 sample per 4.5 s</td><td>DC: 32 samples per 1 s</td><td>DC: 32 samples per 1 s</td></tr><tr><th>Burst mode</th><td>1 sample per 100 ms</td><td>AC: 8k sample per 1 s</td><td>AC: 64k sample per 1 s</td></tr></tbody></table>
**Mission Design** The orbit of S1-3 needs encompass the region about -30 $R_E \le X \le -40 R_E$, where multiple current sheet activities in the midnight region and KHWs/KHVs at dawn/dusk flanks occur. While S1 and S2 identify the activity of KHWs/KHVs and its characteristics at the dawn and the dusk, respectively, S3 monitors the motion and shape of the central current sheet. Y-directional separations between S1/2 and S3 varying from ~10 $R_E$ to ~20 $R_E$ allow for the study of causality between flank-magnetopause KHWs and near-midnight current sheets. To study the simultaneous formation of diamagnetic cavities both at northern and southern hemisphere, we need at least two polar-orbiting spacecraft (S4, 5) with synchronized orbital phases such as when one passes through dusk-sector of the northern cusp, one passes through southern hemisphere dawn-sector high-altitude (~7.5 to 10 $R_E$) cusp. For strong IMF $B_y < 0$ ($B_y > 0$) we can have both diamagnetic cavity creation and KHI occurring both at north and south hemisphere simultaneously. Dipole tilt will then decide on which hemisphere the effect will be the strongest. This pair of S4 and S5 also enables simultaneous detection of subsolar and high-latitude reconnection.

**Launch** By taking advantage of a lunar swing-by trajectory, all mission orbits can all be reached from a single launch. The launch would be to an orbit very similar to the SwRI IBEX mission, which is in a low-inclination orbit with a ~47 (~8) $R_E$ apogee (perigee). After systems check-out, the polar orbiter (S4, 5) boosts its apogee for a lunar swing-by or series of swing-bys to maximize its inclination (final inclination >70°). Total delta-V for the polar orbiter would be ~0.8 km/s, including a small allowance for station-keeping. The comparison between Geotail and MMS datasets indicates that the equatorial spacecraft (S1-3) *with the inclination of 10-15°* may maximize the number of the nightside current sheet crossings. S1-3 would be locked into their lunar-resonant (3:1) orbit and would not require orbit maintenance.

**Duration/Operation** This orbit with orbital periods of ~9 (S1-3) and ~1.4 (S4, 5) days guarantees ample statistics (> 50 dayside reconnection events (Webster et al., 2018; Lenouvel et al., 2021); ~20 KHI events (Henry et al, 2017)) for the (at least) 2-year operation to be properly organized in terms of SW conditions. An extended period will augment our statistics. Although the success of the mission is relatively insensitive to the phase of the solar cycle, the primary mission (phase E) is most desirably coordinated during solar maximum or the declining phase since dayside reconnection may play a larger role at solar maximum, which facilitates the investigation of the relative contributions of dayside reconnection and flankside KHI.

While compilation and comparison with the data obtained from the currently operating near-Earth (Geotail, Cluster, THEMIS, MMS) and distant-tail (ARTEMIS) missions can give us an important indication of the diffusive transport and the causality in terms of the evolutionary phases of KHWs, a future mission focusing on the investigation of the region, -30 $R_E \le X \le -40 R_E$ will greatly fill the gap highlighted in our white paper. All five-point observations by S1-5 provide comparative means of Dungey and Axford-Hines hypothesis as well as sequential links or correlations between the midnight current sheet and flank dynamics.

## 3.2 Modeling Approach

In-situ data integrated can be incorporated with predictions by global simulations. Statistics obtained from S1-5 and modeling approach enable us to fully unravel **Q1-3**. To address **Q1-3** that involve processes in multi-scales and interaction between multi-regions, advances in global modeling is required. Ultimately, we need a global model that includes all the processes from
MHD down to electron kinetic scales so that we can determine the weight of each process in KHI, the competition of KHW with other magnetopause processes (Q1), and the impact of KHW/KHV on other magnetosphere regions (Q2, 3). Additionally, fully kinetic particle-in-cell (PIC) and hybrid (kinetic ions and fluid electrons) simulations with non-periodic boundary condition along the z-direction (perpendicular to the KH vortex plane) are needed. Systematic comparison between MHD/Hall MHD with test particle simulation, hybrid simulation, and fully kinetic PIC simulation can help better understand the major heating and acceleration mechanisms in the KHI, covering electron kinetic- to MHD-scales. New theory and tools (e.g., information theory) can help us better understand the multiscale energy coupling process during the KHI.

In the near-term future (10 years) we can expect (1) inclusion of the M-I coupling processes down to kinetic scales, which supports the data interpretation associated with the feedback from/to the ionosphere such as KHV-generated field-aligned current and ion outflow (Petrinec et al., 2022; Hwang et al. 2022). It is feasible to couple the global hybrid code with an ionosphere/thermosphere model to simulate the feedback from/to KHW/KHV. We, then, expect (2) coupling the realistic global modeling with a local realistic PIC simulation for fully ion and electron kinetics. By imputing realistic parameters from the global modeling to local fully kinetic PIC simulations, it is feasible to treat both global and local variations under realistic conditions in the fully kinetic regime. The present-day and next-generation peta-to-exa scale resources allow us to perform such realistic PIC simulations with a few 100's $d_i$-size simulation boxes, which correspond to the sizes treating local processes including KHI and reconnection. Based on these numerical efforts, in the next decades (around the same time as the launch of the mission) zetta-scale resources, which would allow us to treat at least 10 times larger simulation domains in all 3D directions than the peta-to-exa scale resources, would eventually enable to perform global PIC simulations of the whole Earth's magnetosphere.

**Data Interpretation Support** Quantitative comparison with these realistic global modeling resolving ion and electron kinetics would support our globally scattered five satellite mission, interpolating the multi-point observation data. In particular, global simulations are performed with various steady and varying/various driver conditions such as the IMF, solar wind velocity, and density. The input conditions in the solar wind and ionosphere will be selected on the basis of the observation events. Runs for the total 12 bins of the IMF orientation (§3.1) help to shed light on the conditions and roles of KHI, foreshock waves, and magnetic reconnection in the global transport. For the same purpose, simulations will be performed with different solar wind speeds and/or Alfvén Mach numbers. The locations of the tail and its boundaries, including the magnetopause and tail current sheet, are highly variable depending on upstream and foreshock conditions. Thus, global simulations can infer the location of S1-3 relative to those boundaries, in addition to giving information on likely/most-dominant processes in those regions.

**Mission Design Support** Global simulations support not only answering Q1-3 for the coupled physics from the dayside to the nightside magnetosphere but also the mission design and operation requirements. Global models can demonstrate the optimal orbit inclination that maximizes the plasma sheet residence times or the number of current sheet crossings (§3.1). Considering that we lack of reliable empirical model for the mid-tail region, the result also provides simplified mission operations, e.g., by anticipating regions of interest (ROIs), which are transferred to mission operations such as science mode turn-on/off.
## References

Adamson, E., A. Otto, and K. Nykyri (2011), 3-D mesoscale MHD simulations of a cusp-like magnetic configuration: method and first results, *Annales Geophysicae*, 29, 759-770, doi:10.5194/angeo-29-759-2011.

Adamson, E., A. Otto, and K. Nykyri (2012), 3-D mesoscale MHD simulations of magnetospheric cusp-like configurations: cusp diamagnetic cavities and boundary structure, *Annales Geophysicae*, 30, 325-341, doi:10.5194/angeo-30-325-2012.

Axford, W. I., and Hines, C. O. (1961), A unifying theory of high-latitude geophysical phenomena and geomagnetic storms. *Canadian Journal of Physics*, **39**, 1433. https://doi.org/10.1139/p61-172.

Burkholder, B. L., Nykyri, K., & Ma, X. (2021a). Magnetospheric multiscale statistics of high energy electrons trapped in diamagnetic cavities. *Journal of Geophysical Research: Space Physics*, 126, e2020JA028341. https://doi.org/10.1029/2020JA028341.

Burkholder, B. L., Nykyri, K., Ma, X., Sorathia, K., Michael, A., Otto, A., & Merkin, V. (2021). The structure of the cusp diamagnetic cavity and test particle energization in the GAMERA global MHD simulation. *Journal of Geophysical Research: Space Physics*, 126, e2021JA029738. https://doi.org/10.1029/2021JA029738.

Cowee, M. M., D. Winske, and S. P. Gary (2010). Hybrid simulations of plasma transport by Kelvin-Helmholtz instability at the magnetopause: Density variations and magnetic shear, J. Geophys. Res., 115, A06214, doi:10.1029/2009JA015011.

Dungey, J. W. (1961). Interplanetary magnetic field and the auroral zones. *Phys. Rev. Lett.* 6, 47-48. doi:10.1103/PhysRevLett.6.47.

Daughton, W. (1998), Kinetic theory of the drift kink instability in a current sheet, *J. Geophys. Res.*, **103**(A12), 29,429-29,443, doi:10.1029/1998JA900028.

Eriksson, S., B. Lavraud, F. D. Wilder, et al. (2016). Magnetospheric Multiscale observations of magnetic reconnection associated with Kelvin-Helmholtz waves, Geophys. Res. Lett., 43, 5606-5615, doi:10.1002/2016GL068783.

Erkaev, N. V., Semenov, V. S., and Biernat, H. K. (2008). Magnetic double gradient mechanism for flapping oscillations of a current sheet. *Geophysical Research Letters*, **35**, L02111. https://doi.org/10.1029/2007GL032277.

Faganello, M., F. Califano, and F. Pegoraro (2008). Numerical evidence of undriven, fast reconnection in the solar-wind interaction with Earth's magnetosphere: Formation of electromagnetic coherent structures, Phys. Rev. Lett., 101, 105001. https://doi.org/10.1103/PhysRevLett.101.105001

Faganello, M., F. Califano, F. Pegoraro, and T. Andreussi (2012). Double mid-latitude dynamical reconnection at the magnetopause: An efficient mechanism allowing solar wind to enter the Earth's magnetosphere, Europhys. Lett., 100(6), 69001, doi:10.1209/0295-5075/100/69001.

Forsyth, C., Lester, M., Fear, R. C., Lucek, E., Dandouras, I., Fazakerley, A. N., et al. (2009). Solar wind and substorm excitation of the wavy current sheet. *Annales de Geophysique*, **27**(6), 2457-2474. https://doi.org/10.5194/angeo-27-2457-2009.

Golovchanskaya, I., and Y. Maltsev (2005), On the identification of plasma sheet flapping waves observed by cluster, *Geophys. Res. Lett.*, **32**, L02102, doi:10.1029/2004GL021552.

Hasegawa, H., M. Fujimoto, K. Maezawa, Y. Saito, and T. Mukai (2003), Geotail observations of the dayside outer boundary region: IMF control and dawn-dusk asymmetry, J. Geophys. Res., 108(A4), 1163, doi:10.1029/2002JA009667.

Hashimoto, C., and M. Fujimoto (2006), Kelvin-Helmholtz instability in an unstable layer of finite
thickness, Adv. Space Res., 37, 527-531. https://doi.org/10.1016/j.asr.2005.06.020

Henry, Z. W., Nykyri, K., Moore, T. W., Dimmock, A. P., & Ma, X. (2017). On the dawn-dusk asymmetry of the Kelvin-Helmholtz instability between 2007 and 2013. *Journal of Geophysical Research: Space Physics*, 122, 11,888–11,900. https://doi.org/10.1002/2017JA024548.

Hwang, K.-J., M. L. Goldstein, M. M. Kuznetsova, Y. Wang, A. F. Viñas, and D. G. Sibeck (2012), The first in situ observation of kelvin-helmholtz waves at high-latitude magnetopause during strongly dawnward interplanetary magnetic field conditions, *Journal of Geophysical Research: Space Physics*, 117(A8), doi:10.1029/2011JA017256, a08233.

Hwang, K.-J., Dokgo, K., Choi, E., Burch, J. L., Sibeck, D. G., Giles, B. L., et al. (2020), Magnetic reconnection inside a flux rope induced by Kelvin-Helmholtz vortices. *Journal of Geophysical Research: Space Physics*, 125, e2019JA027665. https://doi.org/10.1029/2019JA027665.

Hwang, K.-J., Burch, J. L., Russell, C. T., Choi, E., Dokgo, K., Fear, R. C., Fuselier, S. A., Petrinec, S. M., Sibeck, D. G., Hasegawa, H., et al. (2021), Microscale processes determining macroscale evolution of magnetic flux tubes along Earth's magnetopause, *Astrophys. J.*, 914, 26, https://doi.org/10.3847/1538-4357/abf8b1.

Hwang, K.-J., Weygand, J. M., Sibeck, D. G., Burch, J. L., Goldstein, M. L., Escoubet, C. P., Choi, E., Dokgo, K., Giles, B. L., Pollock, C. J., Gershman, D. J., Russell, C. T., Strangeway, R. J., and Torbert, R. B. (2022), Kelvin-Helmholtz Vortices as an Interplay of Magnetosphere-Ionosphere Coupling. *Front. Astron. Space Sci.* 9:895514. doi: 10.3389/fspas.2022.895514.

Ma, X., A. Otto, P. A. Delamere, and H. Zhang (2016), Interaction between reconnection and kelvin-helmholtz at the high-latitude magnetopause, *Advances in Space Research*, 58(2), 231–239, https://doi.org/10.1016/j.asr.2016.02.025.

Michael, A. T., Sorathia, K. A., Merkin, V. G., Nykyri, K., Burkholder, B., Ma, X., et al. (2021). Modeling Kelvin-Helmholtz instability at the high-latitude boundary layer in a global magnetosphere simulation. *Geophysical Research Letters*, 48, e2021GL094002. https://doi.org/10.1029/2021GL094002

Li, W. Y., X. C. Guo, and C. Wang (2012), Spatial distribution of Kelvin-Helmholtz instability at low-latitude boundary layer under different solar wind speed conditions, *J. Geophys. Res.*, 117, A08230, doi:10.1029/2012JA017780.

Lin, Y., Wang, X. Y., Lu, S., Perez, J. D., and Lu, Q. (2014), Investigation of storm time magnetotail and ion injection using three-dimensional global hybrid simulation, *J. Geophys. Res. Space Physics*, 119, 7413–7432, doi:10.1002/2014JA020005.

Lin, Y., Wing, S., Johnson, J. R., Wang, X. Y., Perez, J. D., and Cheng, L. (2017), Formation and transport of entropy structures in the magnetotail simulated with a 3-D global hybrid code, *Geophys. Res. Lett.*, 44, 5892–5899, doi:10.1002/2017GL073957.

Ling, Y., Shi, Q., Shen, X.-C., Tian, A. [TSE], Li, W., Tang, B., et al. (2018). Observations of Kelvin-Helmholtz waves in the Earth's magnetotail near the lunar orbit. *Journal of Geophysical Research: Space Physics*, 123, 3836–3847. https://doi.org/10.1029/2018JA025183

Lenouvel, Q., Génot, V., Garnier, P., Toledo-Redondo, S., Lavraud, B., Aunai, N., et al. (2021). Identification of electron diffusion regions with a machine learning approach on MMS data at the Earth's magnetopause. *Earth and Space Science*, 8, e2020EA001530. https://doi.org/10.1029/2020EA001530

Matsumoto, Y., and M. Hoshino (2004). Onset of turbulence induced by a Kelvin-Helmholtz vortex, *Geophys. Res. Lett.*, 31, L02807, doi:10.1029/2003GL018195.

Matsumoto, Y., and K. Seki (2010). Formation of a broad plasma turbulent layer by forward and
inverse energy cascades of the Kelvin-Helmholtz instability, J. Geophys. Res., 115, A10231, doi:10.1029/2009JA014637.

Merkin, V. G., J. G. Lyon, and S. G. Claudepierre (2013), Kelvin-Helmholtz instability of the magnetospheric boundary in a three-dimensional global MHD simulation during northward IMF conditions, J. Geophys. Res. Space Physics, 118, doi:10.1002/jgra.50520.

Moore, T. W, Nykyri, K, Dimmock, A. P. (2016), Cross-scale energy transport in space plasmas, Nature Physics, Volume 12, Issue 12, pp. 1164-1169, 10.1038/nphys3869, https://doi.org/10.1038/nphys3869

Moore T. W, Nykyri, K., and Dimmock, A. P. (2017), Ion-Scale Wave Properties and Enhanced Ion Heating across the Low-Latitude Boundary Layer during Kelvin-Helmholtz Instability, J. Geophys. Res., 122, doi:10.1002/2017JA024591.

Nakamura, T. K. M., and W. Daughton (2014), Turbulent plasma transport across the Earth's low-latitude boundary layer, Geophys. Res. Lett., 41, doi:10.1002/2014GL061952.

Nakamura, T. K. M., H. Hasegawa, W. Daughton, S. Eriksson, W. Y. Li, and R. Nakamura (2017), Turbulent mass transfer caused by vortex induced reconnection in collisionless magnetospheric plasmas, Nature Communications, 8, 1582, doi:10.1038/s41467-017-01579-0.

Nakamura, T. K. M., Stawarz, J. E., Hasegawa, H., Narita, Y., Franci, L., Wilder, F. D. et al. (2020), Effects of fluctuating magnetic field on the growth of the Kelvin-Helmholtz instability at the Earth's magnetopause. Journal of Geophysical Research: Space Physics, 125, e2019JA027515. https://doi.org/10.1029/2019JA027515.

Nakamura, T. K. M., (2021), the Earth's low-latitude boundary layer, Chapter 12 in Magnetospheres in the Solar System (eds. R. Maggiolo, N. André, H. Hasegawa, D.T. Welling, Y. Zhang and L.J. Paxton), Wiley, https://doi.org/10.1002/9781119815624.ch12

Nakamura, T. K. M., K. A. Blasl, H. Hasegawa, T. Umeda, Y. -H. Liu, S. A. Peery, F. Plaschke, R. Nakamura, J. C. Holmes, J. E. Stawarz and W. D. Nystrom (2022), Multi-scale evolution of Kelvin-Helmholtz waves at the Earth's magnetopause during southward IMF periods, Physics of Plasmas 29, 012901, doi:10.1063/5.0067391

Nykyri, K., and A. Otto (2001). Plasma transport at the magnetospheric boundary due to reconnection in Kelvin-Helmholtz vortices, Geophys. Res. Lett., 28, 3565-3568, https://doi.org/10.1029/2001GL013239.

Nykyri, K., A. Otto, E. Adamson, E. Dougal, and J. Mumme (2011a), Cluster observations of a cusp diamagnetic cavity: Structure, size, and dynamics, Journal of Geophysical Research (Space Physics), 116, A03228, doi:10.1029/2010JA015897.

Nykyri, K., A. Otto, E. Adamson, and A. Tjulin (2011b), On the origin of fluctuations in the cusp diamagnetic cavity, Journal of Geophysical Research (Space Physics), 116, A06208, doi:10.1029/2010JA015888.

Nykyri, K., A. Otto, E. Adamson, E. Kronberg, and P. Daly (2012), On the origin of high-energy particles in the cusp diamagnetic cavity, Journal of Atmospheric and Solar-Terrestrial Physics, 87, 70-81, doi:10.1016/j.jastp.2011.08.012.

Nykyri, K. (2013), Impact of MHD shock physics on magnetosheath asymmetry and Kelvin-Helmholtz instability, J. Geophys. Res. Space Physics, 118, 5068-5081, doi:10.1002/jgra.50499.

Nykyri, K., X., Ma, Dimmock, A., Foullon, C., Otto, A., and Osmane, A. (2017), Influence of velocity fluctuations on the Kelvin-Helmholtz instability and its associated mass transport, *J. Geophys. Res. Space Physics*, 122, 9489–9512, doi:10.1002/2017JA024374.
Nykyri, K., Chu, C., Ma, X., Fuselier, S. A., and Rice, R. (2019). First MMS Observation of Energetic Particles Trapped in High-Latitude Magnetic Field Depressions. *Journal of Geophysical Research: Space Physics*, 124(1). https://doi.org/10.1029/2018JA026131

Nykyri, K., Ma, X., Burkholder, B., Rice, R., Johnson, J. R., Kim, E.-K., et al. (2021). MMS observations of the multiscale wave structures and parallel electron heating in the vicinity of the southern exterior cusp. *Journal of Geophysical Research: Space Physics*, 126, e2019JA027698. https://doi.org/10.1029/2019JA027698.

Nykyri, K., Johnson, J., Kronberg, E., Turner, D., Wing, S., Cohen, I., et al. (2021). Magnetospheric multiscale observations of the source region of energetic electron microinjections along the duskside, high-latitude magnetopause boundary layer. *Geophysical Research Letters*, 48, e2021GL092466. https://doi.org/10.1029/2021GL092466.

Omidi, N., D. G. Sibeck, and X. Blanco-Cano (2009), Foreshock compressional boundary, J. Geophys. Res., 114, A08205, doi:10.1029/2008JA013950.

Petrinec, S. M., Wing, S., Johnson, J. R., and Zhang, Y. (2022) Multi-Spacecraft Observations of Fluctuations Occurring Along the Dusk Flank Magnetopause, and Testing the Connection to an Observed Ionospheric Bead. Front. Astron. Space Sci. 9:827612. doi: 10.3389/fspas.2022.827612.

Sorathia, K., Merkin, V. G., Ukhorskiy, A. Y., Allen, R. C., Nykyri, K., & Wing, S. (2019). Solar wind ion entry into the magnetosphere during northward IMF. *Journal of Geophysical Research: Space Physics*, 124, 5461–5481. https://doi.org/10.1029/2019JA026728.

Vernisse, Y., B. Lavraud, S. Eriksson, et al. (2016). Signatures of complex magnetic topologies from multiple reconnection sites induced by Kelvin-Helmholtz instability, J. Geophys. Res. Space Physics, 121, 9926-9939, doi:10.1002/2016JA023051.

Wang, C.-P., V. G. Merkin, and [SEP]V. Angelopoulos (2017), Mesoscale perturbations in midtail lobe/mantle during steady northward IMF: ARTEMIS observation and MHD simulation, [SEP], J. Geophys. Res. Space Physics, 122, doi:10.1002/2017JA024305.

Wang, C.-P., Liu, Y.-H., Xing, X., Runov, A., Artemyev, A., & Zhang, X. (2020). An event study of simultaneous earthward and tailward reconnection exhaust flows in the Earth's midtail. *Journal of Geophysical Research: Space Physics*, 125, e2019JA027406. https://doi.org/10.1029/2019JA027406.

Wang, G. Q., Zhang, T. L., Wu, M. Y., Schmid, D., Cao, J. B., & Volwerk, M. (2019). Solar wind directional change triggering flapping motions of the current sheet: MMS observations. *Geophysical Research Letters*, 46, 64–70. https://doi.org/10.1029/2018GL080023.

Webster, J. M., Burch, J. L., Reiff, P. H., Daou, A. G., Genestreti, K. J., Graham, D. B., et al. (2018). Magnetospheric Multiscale dayside reconnection electron diffusion region events. *Journal of Geophysical Research: Space Physics*, 123, 4858–4878. https://doi.org/10.1029/2018JA025245.

Wei, X. H., Cai, C. L., Cao, J. B., Rème, H., Dandouras, I., & Parks, G. K. (2015). Flapping motions of the magnetotail current sheet excited by nonadiabatic ions. *Geophysical Research Letters*, 42, 4731–4735. https://doi.org/10.1002/2015GL064459.

Wing, S., J. R. Johnson, P. T. Newell, and C.-I. Meng (2005), Dawn-dusk asymmetries, ion spectra, and sources in the northward interplanetary magnetic field plasma sheet, J. Geophys. Res., 110, A08205, doi:10.1029/2005JA011086.