MAVEN Survey of Magnetic Flux Rope Properties in the Martian Ionosphere: Comparison With Three Types of Formation Mechanisms

Flux ropes are a magnetic field phenomenon characterized by a filament of twisted, helical magnetic field around an axial core. They form in the Martian ionosphere via three distinct mechanisms: Boundary wave instabilities (BWI), external reconnection (ER) between the interplanetary magnetic field and the crustal anomalies, and internal reconnection (IR) of the crustal anomalies themselves. We have identified 121 magnetic flux ropes (FR) from 1900 orbits using plasma and magnetic field measurements measured by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, and separate FR into categories based on formation mechanism by analyzing electron signatures. We find evidence for flux ropes formed via BWI, ER, and IR mechanisms which comprise 9%, 34%, and 57% of our data‐set, respectively. FR formed via different mechanisms exhibit differences in location and force‐free radius, indicating the formation mechanism of a FR impacts their influence on the Martian plasma environment.

Multiple X-line reconnection also occurs to form FRs in the cross-tail current sheet where magnetic fields are oppositely oriented in the two lobes (e.g., DiBraccio et al., 2015;Elphic et al., 1986;Slavin et al., 2003). On the dayside of planets with intrinsic magnetic fields, a high shear between the dipole magnetic field and the IMF along the magnetopause may result in single X-line reconnection or multiple X-line reconnection, the latter forming at least two magnetic FRs. After their formation on the dayside of the planet, these FRs subsequently carry magnetic flux and plasma to the nightside.
FRs have also been observed at Venus, Mars, and Titan where global intrinsic planetary magnetic fields are absent (e.g., Cloutier et al., 1999;Luhmann & Elphic, 1985;Martin et al., 2020;Penz et al., 2004;Wolff et al., 1980). These FRs must form through different processes than those observed at planets with a global, intrinsic magnetic dipole. At Venus, the IMF flux tubes penetrate into ionosphere and drape around the planet, and the barrier between the fast moving tailward flows of the magnetosheath and the slower moving ionospheric plasma (i.e., the ionopause) is subject to the development of large amplitude boundary wave instabilities. Simulation results have suggested that boundary wave instabilities such as Kelvin-Helmholtz (KH) may become non-linear and lead to FR formation at the ionopause of Venus (e.g., Terada et al., 2002;Möstl et al., 2011). These FRs were observed to be small-scale structures (∼10 km in radius) and are evidence for the twisting of draped IMF flux tubes at the ionopause of Venus (Luhmann & Elphic, 1985).
FRs in the Martian induced magnetosphere are of particular interest due to the localized magnetic anomalies preserved by the crust of the planet . In the southern hemisphere, the crustal anomalies are strong (∼100-1,000 nT at the surface) and protrude into space creating "mini-magnetospheres" similar to the IMF-planetary interactions along the dayside magnetopause of magnetized planets. In the northern hemisphere, the crustal anomalies are much weaker, and do not inhibit the IMF flux tubes from penetrating deep into the ionosphere, creating a plasma environment similar to that at Venus. Together, these two hemispheres comprise a unique hybrid magnetosphere at Mars. FRs play two major roles at Mars: (a) The rapid reconfiguration of planetary crustal magnetic fields and the acceleration of charged particles, and (b) atmospheric mass loss as planetary particles travel through their helical wraps and escape down the magnetotail (e.g., Brain et al., 2010;Hara et al., 2014Hara et al., , 2017. Magnetic FRs have been observed in the Martian ionosphere by the Mars Global Surveyor (MGS) (e.g., Briggs et al., 2011;Cloutier et al., 1999;Hara et al., 2014;Morgan et al., 2011;Soobiah et al., 2014;Vignes et al., 2004) and the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecrafts (e.g., Hara et al., 2017). The hybrid nature of Mars' magnetosphere suggests that these FRs may be created in processes similar to Venusian FRs formed by ionopause instabilities, or perhaps by a process unique to the Martian plasma environment. Brain et al. (2010) first reported the MGS observation of an FR forming as a result of crustal field detachment due to magnetic reconnection. Using the plasma analysis capabilities of MAVEN, Hara et al. (2017) also provided a detailed analysis of a similar event and demonstrated that this single ionospheric FR contained multiple planetary ions including H + , O + , O 2 + , and likely CO 2 There is evidence that FRs at Mars may form via at least of the following three distinct mechanisms: 1. The development of boundary wave instabilities (BWI), most probably KH, on the boundary between the fast tailward flows in the magnetosheath and the slowly moving ionospheric plasma. KH waves have been detected at Mars (Ruhunusiri et al., 2016), and if these boundary waves steepen sufficiently, the IMF flux tubes frozen into the magnetosheath plasma may become trapped and twisted (Russell et al., 1990;Wei et al., 2010;Wolff et al., 1980), leading to FR formation as illustrated in Figure 1a. 2. Multiple X-line external reconnection (ER) between the draped IMF and a crustal anomaly can form FRs in a manner similar to FR formation on the dayside magnetopause of intrinsically magnetized planets (Hara et al., 2014(Hara et al., , 2017Soobiah et al., 2014), illustrated in Figure 1b. 3. Single X-line internal reconnection (IR) of the crustal anomalies themselves (e.g., Beharrell & Wild, 2012;Brain et al., 2010;Hara et al., 2014;Morgan et al., 2011). As the solar wind plasma flows around Mars, the ram pressure may stretch-out the crustal anomalies as they respond to maintain pressure balance, leading to single X-line reconnection between the field lines of the anomalies resulting in FR formation illustrated in Figure 1c.
Observations of FRs in the Martian ionosphere provide direct evidence for boundary wave instabilities or crustal field magnetic reconnection; however, there has been no comprehensive study of ionospheric FRs using the measurement capabilities of MAVEN to investigate their formation mechanisms. The work presented here conducts an extensive survey of FRs in the ionosphere of Mars. We use plasma data measured by MAVEN to estimate the magnetic topology of the FRs, providing evidence for three distinct formation mechanisms at Mars. Further analysis of the constituents, density, and velocity of the plasma contained within the FRs increases our understanding of their role in the fascinating topic of atmospheric mass loss at Mars.
BOWERS ET AL.

10.1029/2021GL093296
3 of 10 Figure 1. Schematic demonstration of how a flux rope may form under the (a) boundary wave instabilities mechanism, (b) external reconnection mechanism, and (c) internal reconnection mechanism. Red and blue ovals represent regions of crustal fields that point radially outward and inward, respectively. Red arrows represent the right-handed flux rope axis. Arrows represent crustal magnetic field lines (black), draped interplanetary magnetic field lines (green), flowing sheath plasma streamlines (yellow), induced current (light blue), X-lines (dark blue).

Instrumentation
We investigate Martian FRs and their impact on the global magnetosphere and ionosphere through an analysis of data provided by the MAVEN spacecraft (Jakosky et al., 2017). MAVEN's orbit precesses in both local time and longitude to provide global coverage of the Mars atmosphere and space environment with periapsis at ∼150 km and apoapsis reaching ∼6,200 km. In particular, we analyze data provided by the Magnetometer (MAG) instrument (Connerney et al., 2015) which measures vector magnetic fields at a maximum sampling rate of 32 vectors/s, the Solar Wind Electron Analyzer (SWEA) (Mitchell et al., 2016), and the SupraThermal And Thermal Ion Composition (STATIC) instrument (McFadden et al., 2015).

Methodology
Here, MAG data are analyzed in the Mars Solar Orbital (MSO) and Minimum Variance Analysis (MVA) coordinate system. The MSO coordinate system is defined so that the X-axis points from the center of Mars toward the Sun, the Z-axis points towards geographic north, and the Y-axis completes the right-handed coordinate system. Magnetic FR signatures identified in the MAG data depend heavily on the orientation of the FR, as well as the spacecraft trajectory through the structure. In order to account for this variability, we transform the magnetic field data into MVA coordinates (Sonnerup & Scheible, 1998). In the MVA coordinate system for an FR, the N-direction defines the axis along which the magnetic field varies the least (i.e., minimum variance axis), and the N component (B N ) of the magnetic field remains steady throughout the extent of an FR. Note, the mean value of the B N component of the magnetic field is smallest for spacecraft trajectories that pass closest to the center of quasi-cylindrical FRs. The M-direction (intermediate variance) points orthogonal to the N-direction and along the central axis of quasi-force free FRs (Slavin et al., 2003). B M for an FR would therefore exhibit a unimodal peak corresponding to the axial field enhancement at the center of the FR. The L-direction (maximum variance) completes the right-handed coordinate system and points in the direction of the bipolar magnetic field (B L ) signature defined by the outer helical wraps. The full amplitude of this bi-polar B L signature maximizes for spacecraft trajectories passing closest to the central axis of the FR.
We also analyze superthermal (>1 eV) electron data from the SWEA instrument onboard MAVEN to estimate the source of the electrons that populate the FR. SWEA is capable of measuring electron fluxes at a 4 s cadence. We use these fluxes compared to the local magnetic field orientation and spacecraft location to parameterize the electron distribution as demonstrated by Weber et al. (2017). This parameter is known as the pitch angle distribution (PAD) score and is defined by: (f FA −f perp )/σ, where f FA is the electron flux in the field aligned direction (the most field-aligned 10° available within pitch angles 0°-30° and 150°-180°), f perp is the electron flux in perpendicular direction (pitch angles 85°-95°), and σ is the propagated uncertainty. PAD score distinguishes among three electron distributions: (a) Field-aligned beam distribution (PAD score > 2), (b) isotropic distribution (-3 < PAD score < 2), (c) loss cone distribution (PAD score < -3). We also compare the electron energy distribution to an expected distribution for photoelectrons at Mars to parameterize the likelihood that the measured electrons are composed of primarily photoelectrons or solar wind electrons ; this is known as the shape parameter. The shape parameter distinguishes between two electron populations: (a) Photoelectrons (shape parameter <1) and (b) solar wind electrons (shape parameter > 1). Both the PAD score and shape parameter are calculated for populations that are moving towards Mars and away from Mars by measuring the local inclination of the magnetic field and comparing it with the pitch angle distribution of the electrons. Xu et al. (2019) describes how to combine these parameters to estimate up to seven types of topologies.
MAVEN has a precessing elliptical orbit where the spacecraft samples throughout the magnetosphere and into the solar wind. This ensures that there are extended periods in which the spacecraft does not sample the low-altitude dayside of Mars, where we assume most of the ionospheric FRs form. From MAVEN observations taken between January 2015 and January 2019, we selected for orbits that sampled the low altitude (<1,200 km) near-dayside (solar zenith angle (SZA) < 110°) of the planet and visually inspected the MAG data for FR signatures.

Results
Throughout the 1,900 orbits inspected, we identified 171 magnetic FRs. Of the 171 FRs identified, 156 show a sufficiently large (>2) max/intermediate eigenvalue ratio calculated from MVA. In MVA, the max/intermediate eigenvalue ratio is an indication of the accuracy of the coordinate definition. These FRs display a wide range in core field intensity (5-110 nT), and location in latitude (−75°-+75°) and longitude (1°-358°).
Of the 156 FRs selected, 140 contain sufficient electron data from SWEA to estimate magnetic topology. Below 160 km altitude, the superthermal electrons are dominated by local processes such as production and collisions which makes the topology score unreliable (Xu et al., 2019). We therefore omit FR events that were detected below 160 km, leaving us with 121 events. The FRs that comprise our database exhibit three primary magnetic topologies (draped, open-dayside, closed-dayside). This variety in magnetic topology suggests that these FRs may have been formed via different formation mechanisms.
In order to categorize the formation mechanism of each FR, we examine the MAG, SWEA, and STATIC data for each event. An FR is assigned a formation mechanism of BWI, ER, or IR based on the following observations: If FR were to form via the BWI mechanism, it would be populated primarily by solar wind electrons gyrating around magnetic field lines connected on both ends to the IMF and classified as a draped magnetic field line. Draped topology throughout an FR suggests that it had been formed via the BWI mechanism. If an FR formed via the ER mechanism, the "opening up" of crustal magnetic field lines would allow solar wind plasma to mix with the ionospheric plasma that previously populated the closed magnetic loops of the crustal anomalies. FRs formed via the ER mechanism would contain both solar wind electrons and photoelectrons and exhibit some open-dayside magnetic field topology. An FR formed via the IR mechanism would be surrounded by closed magnetic topology and contain exclusively photoelectrons because the FR does not require reconnection involving the IMF. FRs that exhibit closed-dayside magnetic topology throughout their structure are consistent with having been formed via the IR mechanism.  (Figure 2c). The shape parameter is > 1 in both the away and toward directions throughout the FR signature (Figure 2e), indicating that the FR is populated primarily by solar wind electrons rather than photoelectrons in both directions. Therefore, the topology score throughout the FR is seven (Figure 2f), indicating draped magnetic topology. Draped topology is expected if the FR were formed via the BWI mechanism illustrated in Figure 1a. Of the 121 FRs in our database, 11 (9%) are consistent with having been formed via the BWI formation mechanism. The second FR shown in Figure 3 maintains a shape parameter <1 and a topology score of one throughout the structure, indicating the presence of photoelectrons and closed-dayside magnetic topology, respectively. Closed-dayside topology is expected if the FR were formed via the IR mechanism illustrated in Figure 1c. 69 (57%) of the FRs in our database are consistent with having been formed via the IR formation mechanism. Figure 4a shows histograms of altitudes at which FRs were detected, separated by formation mechanism and grouped within the same bins. BWI FRs tend to occur at higher altitudes (median altitude = 670 km) than ER or IR FRs (median altitudes = 222 and 198 km, respectfully), which is consistent with the idea that  BWI FRs form closer to the boundary between the magnetosheath and ionospheric plasma. Furthermore, Figure 4b shows the occurrence rate of FRs measured by MAVEN in different latitude bins. BWI FRs tend to occur more frequently near the poles. This is consistent with BWI FRs forming as a result of velocity shear because we expect the gradient between magnetosheath and ionospheric plasma to be greatest near the terminators. The ER and IR FRs occur most frequently in the mid-southern latitudes where the crustal magnetic fields are strongest, which is consistent with the notion that they were formed via reconnection between an anomaly and the IMF (ER), or reconnection of the crustal anomalies themselves IR.

Discussion
We implement a model in which FRs are assumed to be force-free (     0 J B ) and stationary in order to estimate properties of the FRs including radii and core-field strength at the center of the structure. Assuming cylindrical symmetry, Lepping et al. (1996) showed that the axial and tangential magnetic field of an FR can be expressed with Bessel functions: , J αr J αr are the zeroth-and first-order Bessel functions, 0 B is the magnetic field magnitude of the FR's core, and H is the handedness of the helicity. The parameter α is a constant at 2.4048 and represents the x-intercept of the zeroth-order Bessel function. The components of this modeled field thus depend on  r , which is the radial distance from the center of the FR. We can apply this fitting technique to all 121 events in this study and implement a 2 χ test to select a radius that produces a best fit for each FR event. This best fit radius also allows us to estimate BOWERS ET AL.  the absolute core-field strength of each event. Selecting for events where  2 .02 χ , we find that 102 of the 121 FRs can be considered force-free. Of these 102 FRs, we see a variety of radius estimates (2-311 km) and core-field strength (6-110 nT).
We produce a histogram of radius and core-field strength separated by estimated FR formation mechanism (Figures 4c and 4d). FRs formed through ER, IR have median radii of 64 and50 km, respectively. FRs formed through BWI are the smallest of the three, with a median radius of 5 km. This radius is in agreement with FRs found at Venus which have an estimated radius of ∼10 km (Luhmann & Elphic, 1985), further suggesting that these FRs may have formed via a process similar to that at unmagnetized objects like Venus and Titan. A previous statistical study of FR properties throughout the dayside and nightside of the Martian ionosphere (Briggs et al., 2011) reported a median radius of 80 km (σ = 97 km) which is in agreement with the overall force-free FR radii in our study. This suggests the FRs analyzed in Briggs et al. (2011) were likely formed by a variety of mechanisms including, but not limited to, ER and IR. Using data from the STATIC instrument, we are able to estimate the local gyroradius for three main species in the Martian ionosphere: H + , O + , and O 2 + (median local gyroradii of 11, 74, and 113 km, respectively). If the radius of an FR is smaller than the gyroradius of a particle, then the particle cannot be frozen into the magnetic field of the FR, and the FR could not be a mechanism for ionospheric escape at Mars. Of the 102 FRs that are considered force-free, 77 (75%), 50(47%), and 41 (40%) have radii larger than the local gyroradius of H + , O + , and O 2 + , respectively. This suggests that only a fraction of the FRs found in our database may contribute to the escape of planetary ions. While BWI FRs are magnetically disconnected from the ionosphere and cannot play a role in ionospheric transport, there is no significant difference between the IR and ER FRs in their ability to lead to ionospheric escape via plasma entrainment and propagation downstream. The core-field strength of the BWI, ER, and IR FRs does not vary greatly depending on formation mechanism (median values of 25, 33,and 33 nT, respectively). We note that there is a possibility of misclassification of FRs. If an FR were to form via multiple X-line external reconnection between an open magnetic field line and a draped IMF field line, it would produce an FR with both ends attached to the IMF, a draped topology score, and a classification of BWI. The disparity between FR sizes of BWI and ER FRs suggests that either the misclassification of FRs is uncommon, or that FRs formed via this mechanism are quite small and do not contribute to atmospheric mass loss.

Summary
We visually inspected over 1,900 orbits in which MAVEN sampled the dayside ionosphere of Mars. We transformed the MAG data into MVA coordinates to identify 156 magnetic FRs within the Martian ionosphere. Electron data from the SWEA instrument were used to determine magnetic topology of the FRs in order to estimate their formation mechanism. Each of the three magnetic topologies (draped, open-dayside, closed-dayside) that comprise the FRs within our database are consistent with a distinct formation mechanism: (a) boundary wave instabilities (BWI) like KH similar to FRs observed at Venus, (b) external reconnection (ER) between the IMF and the crustal anomalies, and (c) internal reconnection (IR) of the crustal anomalies themselves. The BWI FRs are the least common in our data-set, making up only 9% of the FRs, while the ER and the IR formation mechanisms make up 33% and 58% of the FRs, respectively. Using a force-free model fit, we were able to estimate the radii and core-field strength of 102 FRs. The radii of FRs range from 2--360 km, and the core-field strength range from 5-110 nT. Interestingly, the properties of BWI FRs including altitude at which they are detected, latitude, and median radius differ from the ER and IR FRs. Comparisons between the local gyroradii of planetary ions and the radii of the FRs suggests that roughly a third of the ER and IR FRs are large enough to trap heavy ions like O + and O 2 + , while no BWI FRs could contribute to mass loss of planetary ions.

Data Availability Statement
In accordance with the AGU data policy, MAVEN data are publicly available through the Planetary Plasma Interactions Node of the Planetary Data System (https://pds-ppi.igpp.ucla.edu/mission/MAVEN).