The magnetic structure of the subsolar MPB current layer from MAVEN observations: Implications for the Hall electric force
G. Boscoboinik, C. Bertucci, D. Gomez, L. Morales, C. Mazelle, J. Halekas, J. Gruesbeck, D. Mitchell, B. Jakosky, E. Penou
mmanuscript submitted to
Geophysical Research Letters
The fine structure of the subsolar MPB current layerfrom MAVEN observations: Implications for theLorentz force
G. Boscoboinik , C. Bertucci , , D. Gomez , , L. Morales , , C. Mazelle , J.Halekas , J. Gruesbeck , D. Mitchell , B. Jakosky , E. Penou IAFE, UBA CONICET, Buenos Aires, Argentina INFIP, UBA CONICET, Buenos Aires, Argentina Departament of Physics, FCEyN, UBA, Buenos Aires, Argentina IRAP, UPS CNRS CNES, Toulouse, France University of Iowa, Iowa City, IA, USA GSFC, Greenbelt, MD, USA SSL, University of California, Berkeley, USA LASP, University of Colorado, Boulder, CO, USA
Key Points: • We analyse the fine structure of the current layer at the Martian Magnetic PileupBoundary (MPB) in the subsolar sector. • MPB thickness is of the order of the solar wind proton inertial length or convec-tive Larmor radius in the magnetosheath. • The work done by the Lorentz Force suggests that solar wind ions can be stoppedby magnetic pressure at the MPB.
Corresponding author: Gabriela Boscoboinik, [email protected] –1– a r X i v : . [ phy s i c s . s p ace - ph ] J un anuscript submitted to Geophysical Research Letters
Abstract
We report on the local structure of the Martian subsolar Magnetic Pileup Boundary (MPB)from minimum variance analysis of the magnetic field measured by the Mars Atmosphereand Volatile EvolutioN (MAVEN) spacecraft for six orbits. In particular, we detect a welldefined current layer within the MPBs fine structure and provide a local estimate of itscurrent density which results in a sunward Lorentz force. This force accounts for the de-flection of the solar wind ions and the acceleration of electrons which carry the interplan-etary magnetic field through the MPB into the Magnetic Pileup Region. We find thatthe thickness of the MPB current layer is of the order of both the upstream (magnetosheath)solar wind proton inertial length and convective gyroradius. This study provides a highresolution view of one of the components of the current system around Mars reportedin recent works.
Plain Language Summary
We investigate the fine structure of the current layer associated with the outer bound-ary of the Martian induced magnetosphere in the subsolar sector from selected MAVENmagnetic field and solar wind plasma observations. We measure the variance of the mag-netic field across the boundary to detect the current layer and measure the strength ofthe current that circulates there. The current density we obtain is such that its derivedLorentz force is strong enough to stop the solar wind ions at the outer boundary of Marsmagnetosphere. On the other hand, this force would push the solar wind electrons andthe interplanetary magnetic field frozen into the electron plasma into the induced mag-netosphere. We also find that the thickness of this current layer in terms of typical lengthsof the solar wind ion plasma is similar to the thickness of the terrestrial magnetopause.
Mars (1 R M = 3390 km) has either no or negligible present global magnetic field( | M | < × G · cm ) (Acu˜na et al., 1998). This makes the solar wind interact di-rectly with its ionosphere and the charged particles from its exosphere. The Martian at-mosphere is mostly composed of carbon dioxide (CO ), carbon monoxide (CO), argon(Ar) and molecular nitrogen (N ). In smaller quantities are found molecular and atomicoxygen (O and O), nitrogen monoxide (NO), atomic nitrogen (N) and helium (He). Therelative proportions of the species that populate the atmosphere vary with altitude. Inparticular, in the high atmosphere (altitudes greater than 200 km), which is the regionof interest for this work, the dominant species are atomic oxygen, molecular oxygen andhydrogen (Anderson Jr. & Hord, 1971; Anderson Jr., 1974; Mahaffy et al., 2015).The interaction of the solar wind with Mars’ atmosphere produces the so-called in-duced magnetosphere , a region where the solar wind flow and field are disturbed by thepresence of the planet. With an areocentric distance of approximately 2 R M for the bowshock (BS) and 1 . R M for the MPB (between 800 and 1000 km), the magnetosphereof Mars is one of the smallest of the solar system (Moses et al., 1988). However, it is inthis small portion of space that most of the solar wind’s energy and momentum are trans-ferred to the planetary plasma. Recent estimates of atmospheric escape on Mars (Jakoskyet al., 2015) suggest that the interaction with the solar wind has played a significant rolein the removal of water from Mars for billions of years. In this context, the study of theseelectric fields is essential to understanding the processes of energy and momentum trans-fer from the solar wind to the plasma of planetary origin that lead to atmospheric es-cape. The supermagnetosonic nature of the solar wind needs a bow shock to form aheadof the obstacle to avoid it. Downstream from the BS, the solar wind plasma is mostlysubsonic and significantly hotter. Also in this region -named magnetosheath- the mag- –2–anuscript submitted to Geophysical Research Letters netic field is highly variable due to the presence of turbulence (Ruhunusiri et al., 2017)and waves generated from electron and ion instabilities taking place both upstream andlocally. In the lower part of the magnetosheath, the solar plasma slows down further asit increasingly incorporates cold protons and heavier ions from Mars exosphere. Theseparticles, being relatively slow, heavy and numerous compared to the solar wind, decreasethe average speed of the solar wind (Szego et al., 2000) in areas where the influence ofcrustal magnetic fields is negligible (J. E. P. Connerney et al., 2001). This decelerationprecedes a change in the composition of the plasma, from solar wind ions to heavy ionsof planetary origin, at the Ion Composition Boundary (ICB), which on the dayside is al-most coincident with the MPB. (Breus et al., 1991; Sauer et al., 1994; Matsunaga et al.,2017; Halekas et al., 2018; Holmberg et al., 2019)In areas where crustal magnetic field can be ignored, the mass-loading causes thefrozen in interplanetary magnetic field to increase in the subsolar region and to drapearound the planet. On the dayside, the increase in the magnetic field strength has beenfound to be a permanent feature although single spacecraft magnetic field time series sug-gest a variety of values for this gradient. Following the nomenclature of a similar struc-ture at active comets (Neubauer, 1987) the layer where the magnetic field strength gra-dient occurs received the name Magnetic Pileup Boundary (Acu˜na et al., 1998). Pre MAVENmeasurements (Dubinin et al., 2008; Bertucci et al., 2011) have shown that the MPB islocated between the region dominated by the solar plasma -the magnetosheath- from thatgoverned by the plasma of planetary origin -the Magnetic Pileup Region (MPR), alsocalled Induced Magnetosphere-, which is characterized by a strong and organized mag-netic field of solar origin as a result of pileup and draping (Bertucci et al., 2003). Onceagain these features apply for regions where crustal fields are not important. The MPRlies above the ionospheric boundary, sometimes called ionopause, its lower limit. Belowthe ionopause, the frequency of collisions between particles increases above the typicalfrequencies of a plasma, allowing the diffusion of the magnetic field.In addition to the former, other features allow the detection of the MPB at Marsand other atmospheric bodies (Bertucci et al., 2011): a marked increase in the magni-tude of the magnetic field (by a factor of 2 or 3) followed by a decrease in the magneticfield fluctuations, a decrease in the temperature, velocity and density of the solar windions and suprathermal electrons and an increase in the total plasma density as an increasein the number of charged particles of planetary origin. These features have allowed forstatistical studies on its average location and shape (Vignes et al., 2000; Trotignon etal., 2006; Edberg et al., 2008). So far the fine structure of the MPB has been studied fromsingle spacecraft observations (Bertucci et al., 2005) or multifluid simulations of high spa-tial resolution (Harnett & Winglee, 2007). Bertucci et al. (2005) applied minimum vari-ance analysis (MVA) (Sonnerup & Scheible, 1998) to MGS magnetometer observationsnear the terminator and found that inside the MPB there is a layer of typically 100 kmwhere the magnetic field vector rotates on a plane that is nearly perpendicular to theboundary normal obtained from the MPB static fit. The surface and volume current den-sities were 6.5 × nA/m and 81 nA/m respectively, comparable to values obtainedfrom multi fluid simulations. Unfortunately, this work was limited to high solar zenithangles or SZA (i.e., larger than 30) because of the geometry of MGS pre-mapping or-bits. But also, the lack of ion measurements precluded any local estimate of relevant plasmalength scales necessary to assess the origin of the detected currents.In previous studies it has been shown that in the different regions of the Martianmagnetosphere different terms of the electric field prevail (Dubinin et al., 2011). Withthe arrival of the Mars Atmosphere and Volatile Evolution (MAVEN) mission, reliable,high resolution particle and magnetic field measurements have become available for adeeper analysis of the macroscopic current systems within Mars’ magnetosphere. Halekaset al. (2017) obtained averaged values of the current density and the derived Lorentz force –3–anuscript submitted to Geophysical Research Letters ( J × B ) around the MPB by estimating the curl of the magnetic field accumulated instatic bins with a resolution of 500 km in the x-y plane and 2000 km in z .More recently Ramstad et al. (2020) have reported on a global, coupled current sys-tem at Mars by computing J = µ ( ∇ × B ) as center-point differences for every loca-tion of two 3D magnetic field map. This map was obtained averaging the magnetic fieldobtained over 9814 orbits with a grid spacing of 0.1 R M or 0.2 R M depending on the al-titude.As we have access to high resolution data we can determine more precisely wherethe current sheet is located inside the MPB and obtain its thickness in order to under-stand where this current is originated.In the absence of collisions, local particle acceleration is produced by electric fields.Within the framework of a multifluid plasma, the equation of motion for each species s is m s n s d v s dt = q s n s ( E + v s × B ) − ∇ · P (1)where m s , q s are the individual mass and electric charge of particles of species s , n s and v s are the particle density and velocity of the fluid formed of s -particles and P is thepressure tensor. If we assume a plasma made of electrons and a single ion species, quasi-neutrality dictates that n e = n i = n and the current density is simply given by j = en ( v − v e ). If we further assume that the electron mass is negligibly small ( m e ≈ E = − v × B + 1 en ( j × B − ∇ · P e ) (2)This equation is also known as the generalized Ohm’s law.The bulk velocity of the plasma is v = v i , since momentum is fully carried by ionsin this approximation. The equation of motion for the ions, after replacing Eqn 2 intoEqn 1 and using the identity j × B = µ ( B · ∇ ) B − ∇ B µ , reduces to m i n d v dt = 1 µ ( B · ∇ ) B − ∇ B µ − ∇ · ( P e + P i ) (3)where the first term on the RHS is the magnetic tension force, the second term is themagnetic pressure force and the last term is the total thermodynamic pressure. The mag-netic pressure is directly proportional to the square of the magnetic field and inverselyproportional to the thickness of the MPB. In contrast, the term of the tension, while alsodirectly proportional to the square of the magnetic field, is inversely proportional to thecurvature radius of the magnetic field lines.In the present work we analyse MAVEN data to identify and characterize the lo-cal structure of the Martian subsolar MPB. Then we apply MVA to MAVEN magneticfield measurements to estimate the local current density flowing along the MPB and itsassociated Lorentz force in order to evaluate its importance in the plasma dynamics aroundthe boundary. In section 2 we describe the data and methods used, the results are dis-played in section 3 and are discussed in section 4. We analysed six subsolar MPB crossings between October 2015 and November 2017from MAVEN data. The magnetic field data measured by the Magnetometer (MAG) (J. Con-nerney et al., 2015) has a 32Hz sampling rate. The solar wind electron data from the So- –4–anuscript submitted to
Geophysical Research Letters lar Wind Electron Analyzer (SWEA) (Mitchell et al., 2016) measures electrons in an en-ergy range between 3 eV and 4600 eV with a 2 s resolution. The Solar Wind Ion An-alyzer (SWIA) (Halekas et al., 2015) provided the solar wind proton data in an energyrange between 25 eV and 25 keV with a 4 s resolution.
The Minimum Variance Analysis, or MVA for a single spacecraft (Sonnerup & Scheible,1998) is a technique widely used to find the normal vector for a one-dimensional discon-tinuity from magnetic field measurements obtained by the probe across the boundary(e.g. Knetter, Neubauer, Horbury, and Balogh (2004)). The main purpose of the MVAis to estimate the normal to a one-dimensional current sheet in a collisionless plasma.This is achieved by determining the eigenvectors and eigenvalues of the covariance ma-trix defined as M Bµν ≡ (cid:104) B µ B ν (cid:105)−(cid:104) B µ (cid:105)(cid:104) B ν (cid:105) in terms of the magnetic field data and thecoordinate system in which the data is presented, then find its three eigenvalues λ i andtheir corresponding eigenvectors x i . The eigenvector corresponding to the smaller eigen-value ( x and λ ), is the estimate for the direction of the normal vector to the currentsheet and λ represents the variance of the magnetic field component in that direction.In general, for any set of vectors { B ( m ) } across a transition layer, the set of M Bµν eigen-vectors provides a convenient coordinate system to analyse the data. It must be notedthat the variance matrix M Bµν is independent of the temporal order of the measured vec-tors. In the present work MVA is applied to the MAG data in the MPB in order to ob-tain an estimate of the normal vector to this boundary and therefore to the associatedcurrent sheet.Another estimate of the normal vector to the MPB can be obtained from the conicsection fit representing its average position (e.g (Vignes et al., 2000)). The functionalform of the fit is the following: r = L (cid:15) cos( θ ) (4)where r and θ are polar coordinates with origin at x , (cid:15) is the eccentricity and L is thesemi-latus rectum. From this fit it can be therefore obtained the normal vector to thesurface ˆ n .In this first study we deliberately selected crossings that show an apparently sharpincrease in the magnetic field amplitude, are located on the northern hemisphere and allhave Solar Zenith Angle (SZA) <
30. The crustal magnetic field according to the modelby Cain, Ferguson, and Mozzoni (2003) does not exceed 10% of the total field in the anal-ysed crossings. These crossings occurred in the span of more than one Martian year andhave varied solar wind conditions and heliocentric distance.
Fig. 1 shows a time series of magnetic field and plasma data from MAVEN nearthe MPB for one of the orbits analysed in this work. All vector magnitudes are repre-sented in the Mars-centered Solar Orbital (MSO) coordinate system, in which the ˆ x axispoints from Mars towards the Sun, the ˆ y axis points antiparallel to Mars’ orbital veloc-ity and ˆ z completes the right-handed coordinate system.Between 17:40 and 18:40 UTC on March 16th, 2016 MAVEN headed from the undis-turbed solar wind to Mars, crossing the bow shock a few minutes after 17:50 UTC andthe MPB near the subsolar point around 18:10 UTC. Then, MAVEN continued withinthe induced magnetosphere and ionosphere and at 18:30 UTC entered the region of themagnetic tail. –5–anuscript submitted to Geophysical Research Letters
Figure 1.
Time series of the magnetic field and plasma data from MAVEN for the March16th 2016 crossing. From top to bottom: Magnetic field magnitude, Magnetic field components,Relative variation of the magnetic field, Differential energy fluxes for solar wind electrons andSolar wind proton density. The MPB is shaded in green.
For the identification of the MPB we rely on the criteria described by Bertucci etal. (2011): a sharp increase in the magnetic field strength by a factor of 2-3, a sharp de-crease in the magnetic field fluctuations, a sharp enhancement of the magnetic field drap-ing, a decrease in the temperature of electrons and a decrease in the solar wind protondensity.In order to determine the MPB thickness, we selected four times which we called t , t , t , t so that outside the interval between t and t MAVEN would be unambigu-ously outside the MPB while in the interval between t and t MAVEN would be insidethe MPB. In this interval we observe the defining characteristics of this boundary. Thetimes thus determined were t = 18:13:00 UTC, corresponding to an altitude of 734 km –6–anuscript submitted to Geophysical Research Letters and an SZA of 23, t = 18:13:13 UTC with altitude 720 km and SZA 24, t = 18:14:06UTC with altitude 663 km and SZA 26 and t = 18:14:51 UTC with altitude 615 kmand SZA 29.In this interval we observe the drastic changes in the plasma near the MPB: themagnetic field changes direction while its magnitude goes from 20 nT to 45 nT in lessthan 2 minutes. We also observe that the relative variations of B (both parallel and per-pendicular to the mean field) cease abruptly. This decrease is due to the diminishing am-plitude of the fluctuations as well as the increase in magnetic field magnitude. The dif-ferential energy fluxes decrease in a range from one to two orders of magnitude in theMPB depending on the electron energy, which is consistent with the electron impact ion-ization described by Crider et al. (2000). The solar wind proton density decreases from6 cm − down to the instrumental noise for protons with energies above 25 eV. Once the times t , t , t and t delimiting the MPB were identified we applied MVAin the interval 18:13:37 - 18:14:06 UTC (shown shaded in Fig. 2); the data consisted of922 high resolution measurements. We chose this interval in order to have the best MVAresult within the MPB thus identified. Looking at the upper panel of the Fig. 2, wherethe magnetic field components are plotted, we can anticipate that the minimum variancedirection will be approximately parallel to the ˆ x axis. We also see that the field pointsmainly in the ˆ y and ˆ z directions, so we can anticipate that B in the MPR will be mostlytangential.The intermediate-to-minimum eigenvalue ratio for the analysed crossing is λ /λ =9 .
48, which ensures that the minimum variance vector is well defined (Knetter et al., 2004).The normal obtained with this method is x = ˆ n MVA = (0 . , − . , . x axis. The mean magnetic fieldcomponent along the normal is (cid:104) B n (cid:105) = − . ± .
08 nT and the mean magnetic fieldmagnitude is B = |(cid:104) B (cid:105)| = 34 .
79, the quotient between both being (cid:104) B n (cid:105) /B = 0 . (cid:104) B (cid:105) and the nor-mal is θ B = 93, that is, the magnetic field is almost tangential and lies mostly in the(ˆ e , ˆ e ) plane. The hodograms in Fig. 2 show the magnetic field projection on the planes(ˆ e , ˆ e ) and (ˆ e , ˆ e ) in the interval where MVA was applied (between 18:13:37 and 18:14:06UTC). The hodogram to the right (depicting the projection ˆ e , ˆ e ) has an elongated shape,consistent with a good eigenvalue ratio and the plane containing the normal being welldefined.In order to obtain the MPB thickness, we calculated the angle θ v between the av-erage spacecraft velocity (cid:104) v sc (cid:105) in the MPB and the normal; the calculation yielded θ v =117. This means that MAVEN motion was almost parallel to the MPB.Once we have the normal we can estimate the thickness of the MPB h assumingthat the boundary is one dimensional and static. We then approximate h = | ( r in − r out ) · ˆ n | , where r in is the position of the spacecraft when entering the MPB and r out is the po-sition when leaving; being that it is not uniquely defined, we actually approximate a min-imum thickness corresponding to the interval between t − t and a maximum thicknessin the interval t − t . In this way, we obtained h = 82 km and h = 174 km. Thesevalues are comparable to both the magnetosheath solar wind proton inertial length ( λ = c/ω pi = 97 . r g = mv ⊥ | q | B =68 . km ). The solar wind proton inertial length was calculated from SWIA data, as ω pi is the proton plasma frequency obtained using the mean proton density in the upstreamregion (shown shaded in Fig. 2). On the other hand, for obtaining the magnetosheath –7–anuscript submitted to Geophysical Research Letters
Figure 2.
Magnetic field components in MVA coordinates and amplitude (up). The upstreamand downstream intervals from the MPB and interval where MVA was applied are shaded. Mag-netic hodograms (N=922, λ /λ = 9.8) depicting the magnetic field projection on the planes (ˆ e ,ˆ e ) and (ˆ e , ˆ e ) in the interval where MVA was applied (down). The start point is marked with acircle and the end point with a cross. convective proton gyroradius we considered B as the average magnetic field and v ⊥ asthe velocity perpendicular to B in the upstream region.For the other MPB normal estimate, fitting the mean MPB position with an el-lipsoid given by equation 4, we used the parameters x = 0 . R M and (cid:15) = 0 . t = 18:13:49, the semi-latus rectum is L = 0 . R M . We chosethis point as it corresponds to half the interval which delimits the current sheet.The normal thus obtained is ˆ n fit = (0.856, -0.066, 0.512), a value that differs by21 from that of the normal obtained by applying MVA and by 31 from the ˆ x axis. Themean value of the magnetic field along this normal is (cid:104) B (cid:105) = − .
72 nT, which whencomparing it to B yields (cid:104) B (cid:105) /B = 0 .
05. The angle θ B between the mean magneticfield vector and this normal is θ B = 92.8. We observe again that the magnetic field isalmost tangential to the boundary. –8–anuscript submitted to Geophysical Research Letters
We obtained θ v = 101, which is consistent with the idea that the motion of thespacecraft is almost parallel to the surface of the MPB.In the same way as before, we estimated the MPB thickness h in the intervals t − t and t − t . In this case, the obtained values are smaller, which is to be expected giventhat the angle θ v is smaller, yielding h = 34 km and h = 71 km.In general, we consider the results derived from MVA to be more representative ofreality, since this method is based on the local properties of the magnetic field at the timeof the crossing. Nonetheless, results show a good agreement between the local (MVA)and the macroscopic (fit) normals and in both cases we observe that the normal pointsmostly along +ˆ x , which is consistent with a SZA close to 25.In table 1 are displayed the thickness of the MPB obtained from MVA, the solarwind convective proton inertial length and the convective Larmor radius for six subso-lar MPB crossings (SZA < λ /λ >
9) andpoints mainly along the ˆ x axis. A case for the MPB thickness being of the order of theion inertial length as well as the Larmor radius could be made for all crossings. Table 1.
In the successive columns, the following data of the six MPB crossings are displayed:date, time, minimum and maximum MPB thickness, ion inertial length, Larmor radius, volumecurrent density, Lorentz force per unit volume, work done by the Lorentz force per volume unit,kinetic energy of solar wind ions upstream from the MPB.
Date t + t h h c/ω pi r g | j v | | F | W E k (UTC) (km) (km) (km) (km) (nA/m2) (N/m3) (J/m3) (J/m3) × − × − × − ∗ × − × − × − × − × − × − × − × − × − × − × − × − × − × − × − We estimated the current density along the boundary from Amp`ere’s Law in a dis-continuity, assuming that the MPB is a planar surface of negligible thickness. If ˆ n is thesurface normal and B u , B d are the magnetic field measurements upstream -in the magnetosheath-and downstream -in the MPR- respectively, the surface current density j s will be givenby j s = 1 µ ˆ n × ( B u − B d ) (5)We calculated B u by taking the average value of B between 18:12:06 and 18:13:00UTC and B d between 18:14:51 and 18:15:45 UTC; these intervals are shaded in Fig. 2.The values thus obtained were B u = (4 . , . , − .
2) nT and B d = (18 . , . , − .
59) nT.The intervals were selected because they were outside the MPB but without large vari- ∗ This value was obtained using SWICS data as there is no SWICA data available for the selectedcrossing. –9–anuscript submitted to
Geophysical Research Letters ations in the magnetic field, in order to be representative of what happens at the bound-ary. The surface current density obtained based on the MVA normal yields j MVA s =( − . , − . , − . | j MVA s | = 23 . j fit s = (3 . , − . , − . | j fit s | = 23 . j s being constant throughoutthe MPB. In that case, a volume current density can simply be estimated as j s /h = j v ;we considered for this the minimum thickness h yielded by both the MVA and the fit.Using the MVA normal we obtained j MVA v = ( − , − , − and its mag-nitude | j MVA v | = 282 nA/m . On the other hand, using the fit normal we obtained j fitv =(48 , − , − with modulus | j fitv | = 284 nA/m .The values of j s and j v obtained with both methods are consistent not only betweenthem but with the values we obtained for different MPB crossings (shown in table 1) andthose given by Bertucci et al. (2005) for an MPB crossing with SZA = 63 from MGS datawhere they obtained | j s | = 6 . | j v | = 81 nA/m .Next, we calculate the Lorentz force per unit volume as F = j v × B . From j MVA v we obtained the force F MVA = (10 . , − . , . × − N/m and from j fit v the force F fit = (9 . , − . , . × − N/m .The work done by the Lorentz force along the MPB normal is W = F L h = 9 . × − J/m . This value is greater than the average kinetic energy of the solar wind pro-tons in the magnetosheath upstream from the MPB (shaded in Fig. 2), E k = m p v n n =1 . × − J/m , by almost two orders of magnitude; v n is the mean proton velocityin the direction of the MPB normal. Calculating the average kinetic energy of the so-lar wind protons before the shock (between 17:50 and 17:55 UTC), we find that it is E k =4 × − J/m , roughly half the work done by the Lorentz force.The Lorentz force is associated with the Hall term E H = en j × B in the gener-alized Ohm’s Law (eq. 2). The force (and therefore, the Hall electric field) points mainlyalong the +ˆ x axis, opposing the movement of the solar wind ions, which travel in − ˆ x ,and accelerating the planetary ions. The Hall electric field calculated from the valuesobtained through the MVA is E MVA H = (26 . , − . , .
85) mV/m while the field cal-culated from the values obtained from the fit is E fit H = (24 . , − . , .
52) mV/m.
In this work we report on the microscopic properties of the Lorentz force associ-ated with the current layer detected at the Martian MPB in the subsolar region fromhigh-resolution data. The current is detected from the change in the tangential compo-nent of the magnetic field at the MPB. The intensities of the surface current density forthe six analysed crossings range from 10.7 to 39.2 mA/m. This represents a factor twoincrease with respect to the values derived from MGS data by Bertucci et al. (2005) closerto the terminator (6.5 mA/m at SZA = 63). Although the sample is too small to deduceany general trend with SZA, the higher j s values in the subsolar sector would be con-sistent with a stronger pileup (Dubinin et al., 2011) and/or a narrower MPB around thesubsolar sector. The volume current density ranges from 92 nA/m to 400 nA/m , upto 20 times greater than the values obtained by Ramstad et al. (2020). Nonetheless, thisdiscrepancy is to be expected as our study is centered on the fine structure of the MPBwhereas theirs does not resolve structures smaller than 339 km. It too must be notedthat as our selection consisted in crossings with a sharp increase in the magnetic fieldit may be biased towards greater values of j . –10–anuscript submitted to Geophysical Research Letters
A recent study by Haaland et al. (2020) shows a decrease in the Earth magnetopausecurrent density with increasing SZA such that the current is two times stronger in thesubsolar point than in the terminator.Another key point is the thickness of the MPB. We find a strong variability in ourestimates (from 18 km to 450 km) which is likely a result of the MPB moving with re-spect to the planet at speeds comparable to the spacecraft velocity during the crossing(Bertucci et al., 2005). Unfortunately this effect cannot be corrected due to the natureof single spacecraft observations. Nevertheless, most cases display thicknesses that areloosely compatible with both the magnetosheath solar wind proton inertial length andwith their gyro-radius (see Table 1). If the MPB thickness is somehow determined by c/ω pi , a two-fluid MHD description should be able to theoretically capture this feature.On the other hand, if the thickness is determined by the Larmor radius, kinetic effectswould need to be considered. The fact that these two length scales are not too dissim-ilar, makes it more difficult to discriminate between these two scenarios. A similar dis-cussion takes place with the Earth magnetopause, as reported by Haaland et al. (2020)using MMS data for a large number of crossings.The magnetic pressure term in the Lorentz force is roughly inversely proportionalto the MPB thickness while the magnetic tension is inversely proportional to the cur-vature radius of the magnetic field lines. As the MPB thickness is of the order of the hun-dred kilometers, while the typical radius of curvature of the draped magnetic field in thesubsolar region is roughly 4000 km (Vignes et al., 2000), the first term will be at leastone order of magnitude greater than the second. In the induced magnetotail, however,the magnetic tension dominates (Dubinin et al., 1993).In the six subsolar passes, the Lorentz force points in a direction not far from ˆ x (i.e.sunward) and its strength varies between 2.4 × − N/m and 4.37 × − N/m . Thesevalues are one or two orders of magnitude stronger than the magnetic pressure gradi-ents obtained by Halekas et al. (2017). However, they report that their Lorentz force es-timations might be underestimated as their values were averaged over large spatial in-tervals. The work of the Lorentz force per unit volume is of the same order as the up-stream mean kinetic density per unit volume in the solar wind while being at least anorder higher than the mean kinetic density per unit volume upstream from the MPB.This strongly suggests that these ions can indeed be stopped by magnetic forces at theMPB in the subsolar sector.A net force in the sunward direction contributes to the deceleration of the solar windions near the MPB while pushing the solar wind electrons inwards into the MPR. Thiswould favor a decoupling between the solar wind protons and electrons (due to the Halleffect) as they struggle to enter the induced magnetosphere, while the solar wind elec-trons push the IMF through the MPB thus contributing to the magnetic barrier buildup(Dubinin et al., 2011). In such a scenario the IMF would be frozen in to the electron plasma,not the ion plasma; quantifying this from direct measurements is a a major challenge evenfor multi-satelites missions such as MMS (Lundin et al., 2005). In the meantime, quasi-neutrality across the MPB would be ensured by planetary ions which would be accel-erated upwards by the sunward force. Some of these planetary ions would be able evento get out of the MPR although once in the magnetosheath they could be reacceleratedeither by the electron pressure gradient (back into the MPR) or by the convective elec-tric field into the plume (Dong et al., 2015).In summary, our results are consistent with a thickness for the martian MPB ofthe order of an ion inertial length. However, we cannot rule out the possibility that theMPB thickness is determined by the convective Larmor radius of solar wind protons, since:(1) these two length scales are not too dissimilar and, (2) we are bound by the limita-tions of single spacecraft observations. –11–anuscript submitted to Geophysical Research Letters
Acknowledgments
All data used are publicly available on the NASA Planetary Data System (https://pds.nasa.gov),under Search Data, MAVEN Mission, Planetary Plasma Interactions Node. The authorswould like to thank the LIA-MAGNETO, CNRS-CONICET collaboration. G.B. is fel-low of CONICET and C.B., L.M., D.O.G. are researchers of CONICET. The authorsacknowledge financial support from the Agencia de Promocin Cientfica y Tecnolgica (Ar-gentina) through grants PICT 1707/2015 and 1103/2018.
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