A Space Mission for Cross‐Scale Coupling in the Earth's Magnetosphere

The Earth's magnetosphere occupies a huge volume in space. Past space missions have identified the basic structures and revealed several phenomena that release significant energy explosively. These activities are discovered through point‐wise measurements in space. Consequently, there is a severe lack of knowledge on the coupling between different activities. A space mission that can address this deficiency is proposed here, building on what previous space missions have revealed. A fleet of eight identical spacecraft in two sets of tetrahedral constellations will enable evaluation of how localized kinetic activities may lead to global changes and vice versa in the Earth's magnetosphere. This mission uses the full capability of a tetrahedral constellation to yield a quantitative determination of physical parameters that govern the mass, momentum, and energy flows between space disturbances at kinetic and global scales. It will also resolve the ambiguity in single‐point measurements to differentiate their temporal and spatial variations. Examples on how to use this mission to extract cross‐scale coupling of activities and tackle outstanding questions in magnetospheric research are discussed.


Introduction
Spacecraft measurements on space plasma are generally made on local parameters.These local measurements do not reveal how local disturbances can lead to macroscale changes in space or how macroscale changes may produce local disturbances.Past missions have indicated impulsive energetic processes such as current disruption (CD), which is a process that releases magnetic energy without invoking necessarily a magnetic neutral point (Lui, 1996;Takahashi et al., 1987), magnetic reconnection (Torbert et al., 2018), and turbulence (Ergun et al., 2020) in the Earth's magnetosphere.Therefore, it is a natural next step in advancing our understanding of magnetospheric dynamics to the next level by launching a space mission to evaluate quantitatively the physical parameters that govern the coupling between local and global processes.

Description of the Proposed Space Mission
Science relies on fundamental equations developed in several scientific principles.Space research is mature enough to know how to relate measured quantities directly to individual terms in these fundamental equations.For example, the gradient of physical parameters can be determined by four spacecraft arranged in a tetrahedral constellation.The required techniques have been documented in Paschmann and Daly (1998) and well demonstrated by the Cluster mission (Escoubet et al., 2001;Laakso et al., 2010).
Figure 1 shows the anticipated placement of the eight identical spacecraft for the proposed mission.They form two groups with four spacecraft in a tetrahedral constellation in each group.This arrangement allows one to evaluate the gradient or divergence of measured parameters, time derivative of a parameter distinct from spatial Abstract The Earth's magnetosphere occupies a huge volume in space.Past space missions have identified the basic structures and revealed several phenomena that release significant energy explosively.These activities are discovered through point-wise measurements in space.Consequently, there is a severe lack of knowledge on the coupling between different activities.A space mission that can address this deficiency is proposed here, building on what previous space missions have revealed.A fleet of eight identical spacecraft in two sets of tetrahedral constellations will enable evaluation of how localized kinetic activities may lead to global changes and vice versa in the Earth's magnetosphere.This mission uses the full capability of a tetrahedral constellation to yield a quantitative determination of physical parameters that govern the mass, momentum, and energy flows between space disturbances at kinetic and global scales.It will also resolve the ambiguity in single-point measurements to differentiate their temporal and spatial variations.Examples on how to use this mission to extract cross-scale coupling of activities and tackle outstanding questions in magnetospheric research are discussed.
Plain Language Summary Previous space missions focus on individual events that occur at the spacecraft location without addressing specifically how local activity and global activity are linked.This missing link in achieving the next level for understanding space disturbances is addressed by the proposed mission, which is a natural follow up from previous space missions.It uses eight identical spacecraft in two sets of tetrahedral constellation to evaluate quantitatively the physical parameters that govern the flow of mass, momentum, and energy between disturbances in various sizes.Deeper understanding of these phenomena in local or global scale will be gained with this mission for accurate forecasting and efficient mitigating their impacts that may affect our daily routines and lives.Examples to use the mission to extract the nature of coupling between disturbances at different scales and to solve outstanding research questions are also discussed.
For example, in energy equation, the time development of energy content, velocity moment of the particle distribution, the dot product of current density and electric field are parameters that can be evaluated by the tetrahedral constellation.Similarly, in momentum equation, the divergence of fluid flow energy weighted with velocity components, the divergence of pressure tensor weighted with velocity components, together with the dot product of current density and electric field are needed to perform the computation.All these parameters can be obtained from the tetrahedral constellation measurements.
The Cluster mission has provided an excellent basis for determining ion-scale disturbances (a few 100's-1,000's km).However, knowledge on the electron-scale disturbances was lacking.This leads to the follow up of the Magnetospheric MultiScale (MMS) mission designed to measure electron-scale activities.The spatial separations between the MMS spacecraft are small (few 10s km) and the temporal resolution of electron parameters is about a fraction of a second in order to capture the activities inside the electron diffusion region.
Immense knowledge on the ion-scale dynamics has been gained by the Cluster mission.The MMS mission has accomplished similar achievements in the electron-scale dynamics.However, information on the direct link between kinetic and global activities is not specifically addressed in these missions.To advance our knowledge on magnetospheric dynamics to the next level of comprehension requires filling this missing gap.A space mission is proposed here to accomplish this goal.It is composed of eight identical spacecraft arranged in two groups of cluster constellation, with one group embedded inside the second group as illustrated in Figure 1.
In this arrangement, the inner group has short spatial separations (a few 10's-100's km) between them to monitor space disturbances with small spatial scales.The outer group has larger spatial separations (∼0.5 Earth radius (R E ) to ∼3 R E ) between them to monitor space disturbances with larger spatial scales.The potential impact of the small-scale kinetic disturbances on global activities and vice versa can then be assessed based on this arrangement.
Required instruments are similar to the previous cluster-type missions, namely, the Cluster mission (Escoubet et al., 2001) and the Magnetospheric Multiscale mission (Burch et al., 2016).Measurements are magnetic field, electric field, and three-dimensional velocity distributions of ions and electrons.The scientific requirement for instruments in the inner group can be relaxed substantially from the MMS requirement.Since it is not the aim for the inner group spacecraft to investigate the electron diffusion region, the basic requirement becomes simply the detection of local disturbances.As indicated earlier, there are three major disturbances in the Earth's magnetosphere: current disruption (Lui, 1996;Takahashi et al., 1987), magnetic reconnection (Torbert et al., 2018), and turbulence (Ergun et al., 2020).A common feature among them is high levels of magnetic fluctuations.Therefore, the inner group cluster needs to capture this activity and coordinate with the outer group cluster to examine potential cross-scale coupling.Similarly, the outer group needs to capture global scale activity (e.g., substorm dipolarization) to investigate the potential link of dynamics inside the inner group.This cross-scale coupling mission may be used to resolve outstanding questions in magnetospheric research.As an illustration of this ability, some examples are discussed below.However, the discussions below are meant to illustrate the utilization of the new opportunities offered by the proposed mission.They should be replaced by more suitable procedures when they emerge.
The first example discusses whether or not a limited number of small-scale disturbances can lead to large-scale changes.The subject structure is a product of magnetic reconnection (MR).The second example examines also the potential link between small-scale and large-scale disturbances for a different phenomenon.The subject structure is current disruption (CD).The third example discusses a situation when a major magnetic field reconfiguration is detected by the outer cluster.The inner cluster is used to check accompanying small-scale changes.The fourth example discusses how observations from both clusters can be used to provide insightful clues on the related instability process that create the space disturbances.
An unresolved question is how substorm dipolarization can be achieved.It is advocated that dipolarizing flux bundles (DFBs) are the primary magnetic flux transporter for substorm dipolarization (Birn et al., 2019;Liu et al., 2014).A DFB is a small-scale magnetic flux tube lasting typically less than 1 min.According to their work, about 10 DFBs are sufficient to account for the magnetic flux needed in the near-Earth region.The reported work assumed that plasma flow would transport magnetic flux without verifying the validity of the frozen-in-condition, a necessary condition for the application of this fluid concept.However, Lui (2015) had examined the validity of the frozen-in condition for DFBs and found that the majority of them violate this condition.As a result, DFBs are very inefficient in magnetic flux transport.Consequently, at least 50 DFBs are needed to account for the desired magnetic flux transport.To determine which viewpoint is correct, the observation from the inner cluster can be used to detect the small-scale DFBs and the outer cluster can be used to examine whether or not the large-scale substorm dipolarization is established after the detection of about 10 DFBs by the inner cluster.If the majority of cases examined show that such dipolarization is indeed achieved with about 10 DFBs, this would imply that DFBs are efficient primary magnetic flux transporter.If the majority of cases do not show this expected result, then it implies that these small-scale disturbances do not produce large-scale changes.This procedure should be done for many cases in order to establish the statistical trend since small-scale disturbances may be missed, as discussed further below.
The potential coupling of large-scale effects due to small-scale activities from CD can be investigated with this mission.Large magnetic fluctuations that last for a few minutes only are produced by CD activity.The rather rare encounters of CD suggest that CD activity is a small-scale phenomenon.How current density changes during CD were revealed by observations from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission on 28 February 2009.The spacecraft was at the radial downstream distance of ∼8 R E .Two of the THEMIS spacecraft were at almost identical location on the XY-plane but were separated by ∼0.6 R E in the z-location.With the integral form of Ampere's law, it is shown that the current density can change its value by ∼70% in 0.25 s.This CD activity is unrelated to MR because the CD activity approached the spacecraft from the Earthward side as revealed by remote sensing from the ion sounding technique (Lui, 2013).The B z component was strongly positive at that time.If it were related to MR, then the B z component would be negative tailward of the MR site, contrary to the local observation of the B z component.If CD activity is detected by the inner cluster, the observation at the outer cluster can evaluate whether or not the small-scale short-duration CD activity can lead to a large-scale dipolarization.If the majority of cases examined show that large-scale dipolarization is indeed observed at the outer cluster, then it would serve as evidence that small scale CD activity can indeed produce large-scale changes.An artist's imaginary depiction of a potential turbulent site that this mission may encounter is shown in Figure 2. The turbulence site is speculated to have characteristics resembling current disruption and magnetic reconnection.More specifically, the magnetic field lines show very erratic geometry unlike that of dipolar field lines.Electric current within the disturbance may reverse its initial direction with much variability in its strength.Plasma flows may be ejected from the site accompanying the disturbance.
Substorm dipolarization in the near-Earth magnetosphere is a large-scale global magnetic field reconfiguration phenomenon.When the outer cluster detects this change, the inner cluster can be used to examine accompanying small-scale disturbances.Since small-scale disturbances may have limited spatial extent, it is essential to allow the possibility that the small-scale disturbances may be missed.If the majority of cases reveal the association between disturbances at the outer and inner clusters, then the potential link between large-scale and small-scale changes may be examined from the temporal sequence of events.If the majority of cases show that the inner cluster consistently shows the small-scale disturbances preceding the large-scale changes, then this may indicate that the large-scale disturbance is a consequence of small-scale disturbances.If the trend from the majority of cases is that is, large-scale disturbances consistently preceding the small-scale disturbances, then this may indicate that the large-scale disturbances provide the appropriate environment for small-scale disturbances to develop.
The role of plasma instabilities exciting space disturbances may also be investigated with this mission.If the inner cluster encounters turbulence and excited waves are produced, the cluster constellation can be used to determine the wave characteristics such as wavelength, wave frequency, wave period, and growth rate.The observed wave properties can be used to check potential plasma instabilities that produce the disturbance.The outer cluster can assess how widespread the excited waves can be detected to evaluate their global effects.There are several potential plasma instabilities related to space disturbances documented in a review paper (Lui, 2004).In particular, an instability that has been studied in detail and proposed to account for space activity responsible for the production of auroral beads is the cross-field current instability (CCI) (Lui et al., 1991).It has specific predictions on the nature of the excited waves.This instability can account for the characteristics of auroral beads (growth rate, wavelength, and period simultaneously) that form at a pre-substorm onset auroral arc (Lui, 2020).Therefore, the nature of excited waves detected by the mission can be used to compare with CCI predictions.The Earth's magnetic field can be measured directly from magnetometer, but the associated current density is not readily determined.For this reason, the current density distribution within the magnetosphere is poorly known.
The tetrahedral constellation provides a reliable means to determine current density with the curlometer procedure (Dunlop et al., 2002).This capability of this cross-scale coupling mission thus can survey the current density within the magnetosphere throughout the entire mission.The data collected can be used to build up an exhaustive list of current density at different levels of magnetospheric activity, including at different episodes of substorm and geomagnetic storms.The current density component aligned along the magnetic field, known as field-aligned current (FAC), can be extracted from the total current density.FACs provide the link between the current system in the magnetosphere and in the ionosphere.A survey of FACs may yield the opportunity to discover which space disturbances are linked to ionospheric disturbances.
Previous studies indicate that explosive energy release can often be detected at the downstream distance of ∼8 R E (Lui, 2013;Takahashi et al., 1987).This is the region where the magnetic field changes from dipolar-like to taillike configuration (Lui & Burrows, 1978).A suitable orbit for the cross-scale coupling mission is a highly elliptic one with apogee at this location.The high ellipticity provides a long dwell time around the apogee to maximize the probability of detecting an explosive energy release activity.
It is worth noting that the resulting findings from this cross-scale coupling mission will guide the community to advance our understanding of the magnetospheric dynamics to the next level of comprehension in space weather effects.With these potential advances, it will improve our prediction of the geospace weather forecasting and perhaps also gain better insight to devise means in mitigation of space weather hazards.
If phenomena of MR, CD, and turbulence are grouped together as space disturbances, then the innovative aspects on space disturbance research contained in the proposed mission are (a) determination of the similarities and differences between the three major space disturbances, (b) cross-scale coupling of each space disturbance at different scales, (c) association between space disturbances and instabilities that may reveal the underlying physical processes for their production, (d) global consequences of field-aligned currents generated by space disturbances at different scales and their link to ionospheric activities, and (e) the resulting findings that could impact space weather predictions and improve means to mitigate potential space weather hazards.

Summary
Previous space missions have provided firm foundation for investigation of small-scale and large-scale space disturbances individually.However, there is no space mission dedicated to close examining the link between them.The proposed cross-scale coupling mission will address this deficiency and enables a thorough quantitative investigation of the coupling between magnetospheric phenomena at different scales.Using the advance built on previous space missions, mass, momentum, and energy flows of explosive processes within the magnetosphere can be measured precisely based on fundamental physical equations.The potential for this mission to solve some outstanding questions in magnetospheric research and how coupling between space disturbances at different

Figure 1 .
Figure1.The placement of the eight identical spacecraft is illustrated in which four spacecraft form in one group.Each group is designed to possess a tetrahedral configuration.The inner group has short spatial separations between them to monitor space disturbances with small kinetic spatial scales.The outer group has larger spatial separations between them to monitor space disturbances with large global spatial scales.The potential impact of the small-scale kinetic disturbances to the large-scale global activities, and vice versa, can be assessed based on this arrangement.

Figure 2 .
Figure 2.An imaginary depiction of a turbulent site showing features of current reversal and significant variations in its strength locally.In addition, the speculated features consist of plasma flows accompany these changes much like CD and MR but are unorganized.