Ion‐Scale Magnetic Flux Ropes and Loops in Earth's Magnetotail: An Automated, Comprehensive Survey of MMS Data Between 2017 and 2022

Magnetic reconnection is a critically important process in defining the dynamics and energy transport within plasma environments. In near‐Earth space we may track where and when reconnection occurs by identifying associated coherent magnetic structures. On a global scale these structures facilitate the flow of mass and magnetic flux into, within, and out of the magnetospheric system, whilst contributing to local plasma heating. In the Earth's magnetotail there are two similar structures we identify in this work: magnetic flux ropes and loops. We present a robust, automated and model independent method by which encounters with such structures may be identified using the Magnetospheric Multiscale (MMS) mission. The magnetic structures are first identified through their magnetic field signatures at a single spacecraft (MMS1), including checks on the local minimum variance coordinate system. Next, the local curvature of the magnetic field is evaluated with all four MMS spacecraft. Finally, the plasma conditions are checked to ensure that the interpretation is fully self‐consistent. We evaluate the data obtained by MMS between 2017 and 2022. In total we find 181 self‐consistent magnetic flux ropes and 263 magnetic loops, which fit an exponentially decaying size distribution with a scale size comparable to the ion gyroradius (∼0.23 RE/1,400 km). If we remove the requirements on the plasma properties of the structure, we locate 648 potential magnetic flux ropes and 1,073 magnetic loops. The magnetic structures are preferentially observed in the pre‐midnight region of the magnetotail, with most identifications occurring beyond 20 RE. All catalogs are provided to the community.


Introduction
Magnetic reconnection is a fundamental plasma process that re-configures magnetic fields, transferring energy from the magnetic field to the kinetic and thermal energy of the local particle population (Zweibel & Yamada, 2009).The ion and electron diffusion regions, where the local plasma decouples from the magnetic field during magnetic reconnection, are relatively small compared to the volumes of space surveyed during the orbit of scientific spacecraft.This makes direct observations of the reconnection diffusion regions rare and fortuitous (e.g., Burch, Torbert, et al., 2016;Eastwood et al., 2010;Lenouvel et al., 2021;Øieroset et al., 2001).Nonetheless, we can often infer that reconnection has occurred through encounters with coherent, transient magnetic structures that are generated during the process.In two dimensions, reconnection at two adjacent points will generate magnetic islands (or loops) in between the reconnection sites (e.g., Hones, 1976;Schindler, 1974).Generalizing to three dimensions, loops will only be generated if the magnetic fields are quasi 2D, that is, they lie in a plane with no perpendicular magnetic field component.If the reconnecting magnetic fields have a shear, or guide field, then flux ropes are generated: cylindrical structures with nested helical magnetic fields (e.g., Hughes & Sibeck, 1987;Lepping et al., 1990;Moldwin & Hughes, 1991;Sibeck et al., 1984;Sun et al., 2019).Magnetic islands, loops or flux ropes are sometimes termed "plasmoids" within the Earth's magnetotail (see review by Eastwood & Kiehas, 2015).
Nonetheless, these studies require large statistical catalogs to ensure that the diverse and dynamic magnetospheric system is sufficiently sampled by the spacecraft.However, performing such surveys by eye is a time consuming and potentially inconsistent endeavor.Even an experienced observer's judgment may change over the course of a survey, and therefore many methods have been developed to identify reconnection-related coherent structures in the last 10 years.These methods attempt to reduce the variation in event selections, ensuring that any bias is consistent over the interval of the survey.Some methods are semi-automated, requiring manual confirmation where expert users remove false positive identifications (e.g., Smith et al., 2016;Sun et al., 2016;Vogt et al., 2014).Most often these methods target the distinctive magnetic signatures of plasmoids and flux ropes (e.g., Huang et al., 2018;Sarkango et al., 2022), with recent machine learning methods showing some promise (e.g., Garton, Jackman, Smith, Yeakel, et al., 2021).Some methods have reduced the need for manual inspection, but often this higher degree of automation has been achieved through comparison to analytical models (e.g., Smith, Slavin, Jackman, Fear, et al., 2017).This implicitly limits the type of structure that will be identified, for example, to those that are "force-free" (Lundquist, 1950).Such structures will only represent a fraction of those encountered by the spacecraft, leading to an underestimation of the true population, and correspondingly the mass and energy transport associated with such coherent magnetic structures.Further, it will limit the observations to those structures that have had time to evolve toward a low-energy state (Priest, 1990), likely excluding recently formed flux ropes that are still actively evolving.This has lead to alternative methods that do not rely upon such models but instead rely on complementary observations of the plasma and electric field, and use multi-spacecraft methods (e.g., Bergstedt et al., 2020).
In this work, we present a model-independent, robust method of identifying encounters with magnetotail plasmoids (flux ropes and magnetic loops) using the MMS spacecraft.The method presented has been designed to select for features common to flux ropes and loops, while requiring as few manual empirical thresholds as possible.We use several steps, utilizing the full capabilities of the MMS mission, while providing a framework by which such structures could be identified using data from other missions that are more limited (e.g., consisting of a single spacecraft or obtaining low time resolution plasma data).We present catalogs of magnetic flux ropes and loops, identified with the method between 2017 and 2022.

Data
We use data obtained by the Magnetospheric Multiscale (MMS) Mission (Burch, Moore, et al., 2016) in the magnetotail of the Earth.The magnetic field measurements are provided by the flux gate magnetometers (Russell et al., 2016).Whilst we mostly rely on magnetic field data, for an additional level of affirmation we also check the plasma conditions local to candidate flux ropes, measurements provided by the fast plasma investigation (FPI) (Pollock et al., 2016).Three dimensional plasma moments are used at the burst mode data rate (with a resolution of 0.15 s).Data are predominantly used in the GSM (Geocentric Solar Magnetospheric) coordinate system, where the origin is defined as the center of the Earth.In this right handed system XGSM is oriented toward the Sun, ŶGSM is the cross product of XGSM with the Earth's magnetic dipole axis.ẐGSM then completes the set as the cross product between the XGSM and ŶGSM .
In this study, we survey intervals between 2017 and 2022 during which the MMS spacecraft were deemed to be within the magnetotail plasma sheet.Our plasma sheet criteria require the plasma β to exceed 0.5, and for MMS to be located where X GSM < 10 R E and |Y GSM | < 15 R E .To calculate the plasma β, we used fast-mode ion and electron moments with a time resolution of 4.5 s from FPI and survey-mode magnetic field with time resolutions ranging from 0.0625 to 0.125 s from FGM.We combine plasma sheet intervals that occurred with a time gap of less than 5 min.

Key Characteristics of Magnetic Flux Ropes and Loops
In this study we target two similar but distinct magnetic structures associated with magnetotail reconnection: magnetic flux ropes and magnetic loops.We therefore must develop operational definitions of both structures.To a first order, in the magnetotail these constitute cylindrical structures that are generated and travel within the magnetotail current sheet, that is, approximately within the X GSM -Y GSM plane, with their axial direction often approximately aligned with ŶGSM (e.g., Slavin, Lepping, et al., 2003).The motion of these structures is typically in the ± XGSM direction, as they are ejected away from the site of reconnection.Often the motion of the spacecraft is negligible compared to the velocity of these structures toward or away from the Earth.As these structures travel over a spacecraft it will primarily observe a deflection in the north-south component of the magnetic field (i.e., B GSM Z ).The orientation of this deflection depends the order in which the hemispheres of the structure pass over the spacecraft.If the structure is moving toward the Earth, then the spacecraft will observe a negative to positive change in B GSM Z .Alternatively, if the structure is moving away from the Earth then the spacecraft will record a positive to negative deflection of B GSM Z .With multiple, closely separated spacecraft it is possible to observe the curvature of the magnetic field change (i.e., C GSM X ), with the same orientation as the change in B GSM Z .Previous studies have employed identification criteria based on the magnetic curvature using Cluster (Shen et al., 2007;Zhang et al., 2013) and MMS (Sun et al., 2019).
Magnetic loops, as the name suggests, are a series of nested cylindrical loop-like fields.At the center of these loops a region of very low magnetic field strength can be found, sometimes called an o-line (Hones, 1979;Zong et al., 2004).Within this region the beta of the plasma should increase, representing the decreased magnetic field strength and larger plasma pressure required to maintain pressure balance, assuming the structure is in quasiequilibrium.However, we note that these structures may not be in steady-state, particularly if encountered early in their lifetime prior to equilibrium being reached (e.g., Drake et al., 2006).The contraction of such loops has been suggested to be key in energizing electrons (e.g., Chen et al., 2007).
Meanwhile, magnetic flux ropes are a series of nested helical fields, with a strong axial core field.The commonly applied Lundquist (1950) "force-free" model solutions describe a stable, low energy configuration of flux ropes (Priest, 1990), where no pressure gradients are present (∇P = 0).Here, magnetic pressure is balanced by magnetic curvature.In this model the field is entirely axial at the center, and entirely azimuthal at the edge of the flux rope (e.g., Lepping et al., 1990).A spacecraft encountering a magnetic flux rope will typically observed an increase in the magnetic field strength at the center, associated with a peak in the magnetic field strength in the axial direction (often close to BGSM

Y
), corresponding to a decrease in plasma beta at the center.
The specific magnetic signature that a spacecraft will record during an encounter with a magnetic flux rope or magnetic loop will depend strongly on the relative trajectory of the spacecraft and magnetic structure.Nonetheless, given the typical configuration of the magnetotail the descriptions above should still hold true.We direct the interested reader to several studies (e.g., Borg et al., 2012;Di Braccio et al., 2015;Jackman et al., 2014), who provide excellent schematics detailing how the magnetic signature recorded is dependent upon the relative orientation of the spacecraft encounter with the reconnection related structures.

Method
We provide an overview of the method in Figure 1, which will be described in detail below.The first steps (in green) simply require magnetic field data from a single spacecraft.The second stage (orange) requires magnetic field data from all four MMS spacecraft in order to calculate and assess the local magnetic curvature.The final stage requires plasma moments from a single spacecraft.These three stages of identification ensure rigorous and reliable identifications.The framework also enables the use of catalogs from intermediate steps, should some data be unavailable (e.g., without high resolution plasma data).Where thresholds or limits on derived parameters have been required, these have been selected empirically through the examination of magnetic structures identified in previous studies (e.g., Sun et al., 2019), and the aim to minimize false positive identifications.

Single Spacecraft Magnetic Field Evaluation
An example flux rope that is selected by this process is shown in Figure 2. The starting point by which the magnetic flux ropes and loops are found is through the identification of a bipolar B GSM Z signature.This first step is an adapted version of that first applied by (Smith, Slavin, Jackman, Fear, et al., 2017).First, the method checks for times when the sign of the B GSM Z component of the magnetic field changes sign.From this epoch B GSM Z = 0) the algorithm looks 15 s ahead and behind in order to locate potential maxima and minima of B GSM Z that may form a coherent deflection through zero.
The maxima and minima are identified in data that has been down-sampled from 20 to 2 Hz.This serves two purposes: (a) it effectively low pass filters the data ensuring the B GSM Z maxima and minima are relatively Green boxes are completed using data from a single spacecraft (MM1), orange require all four spacecraft while yellow require the availability of plasma moment data.Four catalogs are produced, two for magnetic flux ropes (A1 and A2), and two for magnetic loops (B1 and B2).consequential; (b) it significantly reduces the computational cost of the process, while losing only a few smaller events.All combinations of maxima and minima (within ±15 s) are then evaluated to find the pair that best describe the deflection.Between each pair a linear fit is evaluated, and the r 2 (coefficient of determination) calculated.We then select the pair (defined to be at t = 0, N), for which r 2 ≥ 0.95 and We compare ΔB GSM Z to the standard deviation of B GSM Z within the ±30 s interval that is considered for the deflection: requiring that ΔB GSM Z > σ Bz (the standard deviation of B GSM Z ).In effect, checking that the deflection is locally "significant."In Figure 2c we can see that this process has successfully defined the limits of the bipolar B GSM Z deflection, indicated with vertical dashed lines.
Once the B GSM Z deflection has been identified we check the <|B GSM X |> within the interval.We remove any intervals for which the <|B GSM X | > > 20 nT (e.g., Coxon et al., 2016).This is intended to remove identifications close to the magnetotail lobe that may be related to traveling compression regions (TCRs), signatures of the lobe wrapping around the plasmoid-related plasma sheet bulge (Imber et al., 2011;Jasinski et al., 2022;Slavin et al., 2005;Slavin, Owen, et al., 2003), or those where only the outer part of the structure are encountered by MMS (e.g., Di Braccio et al. (2015), Figure 2).
Next, a continuous wavelet transform (CWT) is applied to |B GSM Y | and |B|.As in Smith, Slavin, Jackman, Fear, et al. (2017), we use large positive or negative values of the CWT coefficient to select where peaks (flux ropes) or reductions (loops) lie in the data.We use a Ricker/Marr wavelet to perform this search (Daubechies, 1992).This wavelet is characterized by a large central peak, making it ideally suited for peak detection (e.g., Du et al., 2006).In Figures 2b and 2d we show these locations with vertical dashed green lines.We require that the bipolar signature overlaps with peaks (for flux ropes) or decreases (for loops) in order for the bipolar deflection to be selected.
We note that while the CWT checks for peaks with a range of temporal scales (i.e., narrow/fast and broad/slow peaks) in a single interval it will select the "largest" of these as defined by the CWT coefficient.This can result in broad (yet bifurcated) peaks being selected, when by eye it may be better represented by two adjacent peaks (e.g., Figure 2d at ∼15:38:56).Due to the range of spatial scales examined we place a further requirement, that the |B| at the center of the magnetic structure is greater (for flux ropes) or less than (for loops) the mean |B| in the interval defined by the bipolar deflection.This is particularly important for those potential structures that have long durations: small duration peaks/decreases at any point in the interval would incorrectly validate unsuitable structures.
The final step using single spacecraft magnetic field data is to check the properties of the three-dimensional structure.Here we use minimum variance analysis (MVA; Sonnerup and Cahill (1967)), rotating the magnetic field signature into a local coordinate system using the nature of the three dimensional changes.Encounters with magnetic flux ropes and loops are expected to generate a distinct MVA result, displaying a clear rotation of the field (e.g., Sibeck et al., 1984;Slavin et al., 1989;Smith, Slavin, Jackman, Fear, et al., 2017;Xiao et al., 2004).
MVA provides three orthogonal eigenvectors, corresponding to the maximum ( êmax ) , intermediate ( êint ) and minimum variance ( êmin ) directions, with three associated eigenvalues (λ max , λ int , λ min ).These eigenvalues are most useful when used in comparison with each other, for example, the ratios of the maximum to intermediate (λ max /λ int ) and intermediate to minimum (λ int /λ min ) eigenvalues.These eigenvalue ratios provide a measure of the distinctiveness of the relative eigenvector determinations (i.e., the anisotropy of the magnetic field fluctuations).Low ratios suggest that the axes are degenerate, while large ratios suggest that the axes can be regarded as distinct (Khabrov & Sonnerup, 1998;Lepping & Behannon, 1980;Sonnerup & Scheible, 1998).Studies have often placed empirical constraints on the minimum acceptable eigenvalue ratios for magnetic structures, from theoretical (Lepping & Behannon, 1980) or empirical perspectives (e.g., Briggs et al., 2011;Di Braccio et al., 2015;Smith, Slavin, Jackman, Fear, et al., 2017).
In this work we calculate the MVA results for an interval equal to twice the proposed event duration, indicated in Figure 2 with the vertical green dot-dashed lines.We place an empirically defined limit of λ int /λ min ≥ 3, to ensure that the minimum variance axis is able to be well defined.For flux ropes we further require that λ max /λ int is less than 10, in order to ensure that the maximum and intermediate directions are comparable.

Multi-Spacecraft Magnetic Field Evaluation
Unlike surveys in the past, often at other planetary bodies (e.g., Di Braccio et al., 2015;Imber et al., 2011;Sarkango et al., 2022;Sun et al., 2016), we have access to multiple spacecraft and can therefore examine the local magnetic field with more fidelity than is possible with a single point of observation.Fundamentally, flux ropes and magnetic loops are coherent, self-contained structures.For this to be true, the magnetic field should wrap around the structure -ignoring for the moment any magnetic connectivity into the planet or solar wind.Given our assumptions as to the orientation of the structures detailed above, we should see a change in the local magnetic curvature over the course of the structure: C GSM X should exhibit a bipolar signature, with an orientation that corresponds to the change in B GSM Z .We may calculate the magnetic curvature: With the curvature radius (R C ) being the inverse of C. Figure 2e shows the magnetic curvature C GSM X ) , evaluated from the four MMS spacecraft in that interval.We can see that there is a change from positive to negative C GSM X through the candidate flux rope structure.We can also see that C GSM X is a relatively noisy measurement, therefore to automatically evaluate the curvature we compare the average C GSM X obtained in the first and last parts of the structure.For candidates less than 1 s in duration we use the first and second halves of the signature, while for those with a duration greater than 1 s we use the first and last thirds of the magnetic signature.
The curvature radius is shown in Figure 2f, for flux ropes we check that the local R C at the center of the structure is not less than half the average R C at the edge of the flux rope.For magnetic loops, we check that the local R C is less than 1.7 times the average at the start and end of the proposed magnetic loop.
We define those structures who pass the above criteria as "magnetically confirmed," and provide these catalogs as "A1" and "B1" for magnetic flux ropes and magnetic loops respectively (Figure 1).

Single Spacecraft Plasma Moment Evaluation
Finally, we check the plasma measurements that correspond to the "magnetically confirmed" structures.The first check we make is to confirm that the sign of the mean V GSM X recorded during the magnetic signature is consistent with the interpretation from the orientation of the magnetic field change (i.e., B GSM Z and C GSM X ). Figure 3 shows an example magnetic loop, inferred to be traveling toward the Earth.
For magnetic loops, as in Figure 3, we then confirm that the perpendicular ion beta (β ⊥ ) is greater than one in the center of the structure, and that this is larger than the average β ⊥ at the start and the end of the signature.Similarly, for magnetic flux rope candidates we confirm that the central β ⊥ is less than 10, and that it is less than the average β ⊥ at start and end of the magnetic signature.Candidate structures that pass these criteria are defined as "plasma confirmed" magnetic flux ropes and loops, and provided in catalogs "A2" and "B2," respectively (Figure 1).

Results
The method described above has been applied to MMS tail plasma sheet encounters between 2017 and 2022.In these years the method identifies 648 and 1,073 "magnetically confirmed" magnetic flux ropes and loops (catalogs A1 and B1 in Figure 1), respectively.The full method meanwhile selects a subset of 181 and 263 "plasma confirmed" magnetic flux ropes and loops (catalogs A2 and B2 in Figure 1).These catalogs are provided to the community (Smith et al., 2023).While the main goal of this study is to present the method and resulting catalogs, we now briefly analyze the identifications statistically to evaluate key properties of the catalogs.
First, we note that there is a factor of approximately five between the "magnetically confirmed" structures and the "plasma confirmed" subset.Our first consideration is that the plasma checks require burst mode data to be available.This is not always the case, and will contribute significantly to the factor of five difference.There may also be a considerable number of plasmoids that do not conform to the plasma portion of our operational definition, or represent distinct phenomena that are nonetheless identified by our initial method (e.g., Bergstedt et al., 2020).Our operational plasma-based definition of a magnetic flux rope or loop is relatively simple, simply requiring that the sign of the plasma velocity is consistent with the orientation inferred through the magnetic field change, and that the plasma beta acts to balance the changing magnetic field within the structure, assuming quasiequilibrium.Therefore, some flux rope/loop-like structures may in fact move in the opposite direction to that which may be expected, or there may be a number of structures present in the magnetotail that are not well approximated by quasi-equilibrium, perhaps encountered shortly after their generation.
Figure 4 details the spatial distribution of the identified plasmoids in the magnetotail.We clearly see a strong asymmetry across the magnetotail, with the vast majority of identifications occurring on the dusk-side of the magnetotail (i.e., pre-midnight) and between 20 and 25 R E from the Earth.These results are consistent with the asymmetries observed in other studies of magnetotail reconnection and related structures (e.g., Gabrielse et al., 2014;Imber et al., 2011;Liu et al., 2013;Slavin et al., 2005;Walsh et al., 2014).The opposite asymmetries have been found by large scale surveys of flux ropes within Mercury's magnetotail (Smith, Slavin, Jackman, Poh, & Fear, 2017;Sun et al., 2016).Liu et al. (2019) linked these asymmetries to the relative widths of the magnetotail of Earth and Mercury.In this model, reconnection initiates pre-midnight in the thinner dusk-side current sheets (Artemyev et al., 2011;Poh et al., 2017;Rong et al., 2011;Walsh et al., 2014), however the dawnward drift of electrons, which transport reconnected magnetic flux, leads to a further thinning of the current sheet on the dawnside of the reconnection region and therefore preferential conditions for magnetic reconnection to continue.This effect is more prominent in Mercury's small magnetosphere, where flux rope occurrence is pushed into the midnight to dawn region.Interestingly, we also see more magnetic loops than magnetic flux ropes.However, more work is needed to determine if this is a product of the slightly different selection criteria employed (by necessity), or a fundamental property of Earth's magnetotail.
Figure 5 investigates the properties of the identified structures, in particular the duration of the spacecraft encounters, defined through the bipolar B GSM Z signature and the velocity of structures.We find that the majority of plasmoid encounters last less than 10 s, with a peak around 2 5 s.Interestingly, we see relatively fewer events with durations of 20 s or longer, events that may be more easily spotted in lower resolution data, and were previously found in manual surveys (cf.Slavin, Lepping, et al., 2003).We note that there is a defined upper limit of 30 s to the flux rope duration that the method will find, and further postulate that larger events may appear to be more perturbed (relative to the data resolution), and may correspond less well to the assumptions made within our operational definitions and their implementation.Nonetheless, similar size distributions have been observed in numerical models of reconnection (Fermo et al., 2010(Fermo et al., , 2011)), with a preference for the generation of small-scale structures that then merge through coalescence.A characteristic decaying exponential size distribution from both modeling (Fermo et al., 2011) and observations (Akhavan-Tafti et al., 2018) can be combined the preferential selection of "mid-size" flux ropes to explain the characteristic shape of the size distributions (Smith, Jackman, Frohmaier, Fear, et al., 2018): with a rapid increase to a peak occurrence that then decays exponentially.We suggest that our identifications include "young" flux ropes, and contain a population that we would be unlikely to include if we were to restrict ourselves to more mature force-free structures (Priest, 1990).
Combining the peak-to-peak duration (Figures 5a and 5b) with the average absolute V GSM X within the structures allows an estimation of the structures' cross-section.We find that the vast majority of structures are smaller than 1 R E (with a peak around ∼0.1 0.2 R E , or 600 1200 km), comparable to the magnetotail proton gyro-radius.Similarly sized flux ropes have been linked with so-called secondary reconnection within thin reconnecting current sheets (e.g., Daughton et al., 2006;Dong et al., 2017;Drake et al., 2006;Eastwood et al., 2016;Hasegawa et al., 2022Hasegawa et al., , 2023;;Lu et al., 2020;Sun et al., 2019).Our observations of significant numbers of these ion scale structures suggest that secondary reconnection is indeed a frequent occurrence, and may play a crucial role in the dynamics of Earth's magnetotail current sheet.
However, we note that our cross-sections will represent an underestimate of the mean radius of the plasmoids, due to the variable relative path of the spacecraft through the structures (Akhavan-Tafti et al., 2018).For both types of structure the characteristic scale size of these encounter cross sections is found to be ∼0.23 R E (1465 km), comparable to the thickness of the thin current sheet at the end of the growth phase of a substorm (e.g., Bakrania et al., 2022;Sergeev et al., 1988).
Inspecting Figures 5e and 5f we see that these structures travel with velocities ranging from less than 100 kms 1 to nearly 1,000 kms 1 .Most commonly the structures travel at a few hundred kms 1 .Interestingly, while we see an approximately even split of flux ropes moving in each direction, we see a greater number of magnetic loops moving planetward -suggesting that magnetic loops are preferentially created deeper in the magnetotail before traveling over MMS.Further work is required to investigate this imbalance.These catalogs provide a rich vein from which to understand magnetic reconnection and its associated coherent structures.

Assumptions
Our operational definition of magnetic flux ropes and loops, alongside the practical choices made during the implementation of the method, mean that there are assumptions that should be noted during any practical use of the catalogs.We will discuss several of the most significant here.within the magnetic structures.The distributions of cross section are fit to decaying exponentials using a maximum likelihood method, with the best-fit shown in blue, and the corresponding scale size of the cross section of the spacecraft trajectory through the structure (r 0 ) provided in the legend.
First, the initial identification of magnetic field deflections to start the method uses down sampled magnetic field data, at a cadence of 2 Hz.As described above, this serves two purposes: (a) it ensures that the start and end of the B GSM Z deflection are relatively consequential, and (b) it reduces the computational cost of the method significantly (approximately an order of magnitude faster).The chosen down sampling rate was determined empirically to ensure that known magnetic structures in the literature were able to be recovered (e.g., Sun et al., 2019).However, combined with other practical choices made during the implementation, it imposes a minimum event duration of 0.5 s, and likely reduces the sensitivity of the method to very short events (i.e.<2 s): the deflection must be greater than a defined size based on the local standard deviation of the field.In a similar fashion, the use of multispacecraft techniques here imposes a minimum structure size, the magnetic curvature change must be clear or the candidate structure will be rejected.Nonetheless, as the method is robust and consistent, is it possible to examine these biases by flying virtual spacecraft through model structures and evaluating their fractional recovery by the method (Smith, Jackman, Frohmaier, Fear, et al., 2018).However, this does mean there could be a population of very small structures that will not-by definition-be identified.
Second, in several steps we evaluate the properties of the central point within the candidate structures, both against fixed thresholds but also in comparison to the rest of the structure.We define the central point as the center of the interval defined by the magnetic B GSM Z deflection.However, this presupposes that the correct duration has been identified.If this has been incorrectly defined, or the structure is not symmetric in time (e.g., it is expanding/ contracting) then this point will not correspond to the center.These criteria are likely to work best for relatively small magnetic structures (i.e., ∼10 s or less), for which the assumptions will have a reduced impact.Very long duration structures (relative to the data cadence), are likely to be less well described by this method.This is particularly true for measurements that are highly variable, the magnetic curvature and curvature radius (Figures 2e and 2f), for example, We also note, though we do not explicitly compare to a model, for example, the force-free flux rope model (Lepping et al., 1990;Priest, 1990), some of the parameters and thresholds set are based upon known examples that can be well approximated by such models.We have attempted to minimize this by setting thresholds on parameters, such as the definition of the MVA system, through an iterative process with manual confirmation.However, these limits are similar to those suggested to locate force-free structures (e.g., Di Braccio et al., 2015;Smith, Slavin, Jackman, Fear, et al., 2017;Sun et al., 2016).Force-free structures will form a key subset of the identified flux ropes, but one that can be removed to isolate structures that do not conform to such strict assumptions.

Future Use
The method has been specifically designed such that it uses the full capabilities of the MMS mission (Burch, Moore, et al., 2016), including multiple spacecraft and high time resolution magnetic field and plasma data.However, we have decades of measurements from other missions, at other bodies in the solar system, which do not have the same level of capabilities.For this reason the method has been built in such a way that the initial steps only require magnetic field data, in this way some of the process is applicable to other environments -though the identifications may require further, potentially manual, confirmation.In these environments, it may be necessary or desirable to compare the selections to empirical models (cf.Smith, Slavin, Jackman, Fear, et al., 2017;Sarkango et al., 2022).We note that more complex techniques such as Grad-Shafranov reconstruction have highlighted the limitations of such models (e.g., Hasegawa et al., 2007).
Large statistical catalogs are key to understand the global dynamics of the magnetosphere, for example, to estimate where and when reconnection may occur (e.g., Garton, Jackman, & Smith, 2021;Slavin, Lepping, et al., 2003;Smith et al., 2016;Smith, Slavin, Jackman, Poh, & Fear, 2017;Sun et al., 2016;Vogt et al., 2014), and allow the inference of suppressive effects (Liu et al., 2019).The consistent identification process also enables further modeling efforts, accounting for both when such structures are present and when they are absent (e.g., Smith, Jackman, Frohmaier, Coxon, et al., 2018).When combined with analytical models, such robust selection methods have been shown to enable the evaluation of selection biases (Smith, Jackman, Frohmaier, Fear, et al., 2018), probing where the method will systematically partially recover, or not be able to identify structures.Such studies are crucial to understand where and when reconnection may occur-without such knowledge understanding when magnetotail reconnection (and magnetospheric substorms) will occur remains a significant challenge (Maimaiti et al., 2019).
Magnetic flux ropes and magnetic loops are important for the transport of particle flux.It has been proposed that plasmoids play a significant role in carrying plasma away from planets such as Jupiter (e.g., Cowley et al., 2015;Vogt et al., 2010), Saturn (e.g., Jackman et al., 2014;Smith et al., 2016), andUranus (e.g., DiBraccio &Gershman, 2019).Moreover, on the dayside magnetopause, FTEs have been shown to transport a significant amount of solar wind particles into the magnetosphere of planets such as Mercury and Earth.
While the ensemble of identifications is crucial for understanding the formation, global contribution and dynamics of the structures, it is also fundamentally important to understand the physics within such magnetic structures, determining their contribution to plasma heating (e.g., Drake et al., 2006;Sun et al., 2022) and their evolution (e.g., Akhavan-Tafti et al., 2019).

Summary
We have presented a robust, automated method by which spacecraft encounters with magnetotail magnetic flux ropes and magnetic loops may be identified.The method uses a series of stages to confirm that the three dimensional structures meet the expectations of the desired coherent structures, without direct comparison to analytical models.We have constructed the method using the full capabilities of the MMS spacecraft and mission, but structured it such that parts would be possible with only a single observing platform, or with only low resolution plasma measurements available.We summarize the methods as follows for flux ropes (and magnetic loops): • Confirm |B| increase (decrease) at the center.

Multi-Spacecraft Magnetic Field
• Confirm bipolar C GSM X with correct orientation.• Check relative R C at the center of the structure, compared to the edges.

Single Spacecraft Plasma Moments
• Check sign of <V GSM X >.
• Confirm central ion β ⊥ less (greater) than the average of the start and end β ⊥ .
The outputs of steps two and three above are provided as catalogs of potential flux ropes and magnetic loops.In total this method identifies 648 "magnetically confirmed" and 181 "plasma confirmed" flux ropes between 2017 and 2022 (inclusive).In the same period we identify 1,073 and 263 magnetic loops, for each category respectively.Most identifications are located pre-midnight in the magnetotail, approximately 20-25 R E from the Earth.Encounters with the vast majority of the structures last less than 10 s, with cross-sections smaller than 0.5 R E , comparable to the local ion gyro-radius.The structures typically move with velocities in the Earth-Sun direction of between 100 and 1,000 kms 1 , most frequently around 200 kms 1 .We have discussed the assumptions made by the method, and the future uses of such robust, statistical samples.

Figure 1 .
Figure1.A flow chart outlining the automated selection process.Green boxes are completed using data from a single spacecraft (MM1), orange require all four spacecraft while yellow require the availability of plasma moment data.Four catalogs are produced, two for magnetic flux ropes (A1 and A2), and two for magnetic loops (B1 and B2).

Figure 2 .
Figure 2. Magnetic field data around a candidate magnetic flux rope in July 2017.The three magnetic field components in the GSM system are shown in panels (a, b and c), while d displays the total magnetic field strength.The X GSM component of the magnetic curvature is shown in panel (e).The vertical dashed blue lines show the identified start and end of the bipolar deflection in B GSM Z , while the dot-dashed green lines indicate the MVA window at twice the duration of the event.The vertical green bars in panels b and d represent locations where the CWT method has identified peaks in |B GSM Y | or |B|, respectively.The orange line and crosses in panel c represent the down-sampled magnetic field data from which the maxima and minima are identified.The red and green in panel e represent the first and second halves of the candidate event, while the horizontal dashed lines show the mean of these intervals.

Figure 3 .
Figure 3. Magnetic field data around a candidate magnetic loop in July 2017.The three magnetic field components in the GSM system are shown in panels a, b and c, while d displays the total magnetic field strength.The vertical dashed blue lines show the identified start, middle and end of the bipolar deflection in B GSM Z .The X GSM component of the plasma velocity is shown in panel (e), while the ion density and perpendicular ion β are shown in panels (f and g).The horizontal dashed line in panel g shows the average ion β ⊥ at the start and end of the defined structure.

Figure 4 .
Figure 4.The spatial distribution of identified magnetic structures in the X GSM Y GSM plane of the magnetotail.All four separate catalogs are represented: (a) magnetically confirmed flux ropes, (b) magnetically confirmed magnetic loops, (c) plasma and magnetically confirmed flux ropes and (d) plasma and magnetically confirmed magnetic loops.

Figure 5 .
Figure 5.The properties of the identified magnetic structures: left, (a, c, e) magnetic flux ropes, and right (b, d, f) magnetic loops.The top row (a, b) displays a histogram of the duration defined by the bipolar B GSM Z signature.The middle row (c, d) shows the inferred cross section, defined by the duration of the encounter and the average |V GSM X |, while the bottom row (e, f) shows the average V GSM X