Frontiers in Physics | Space Physics section | New and Recent Articles
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RSS Feed for Space Physics section in the Frontiers in Physics journal | New and Recent Articlesen-usFrontiers Feed Generator,version:12021-03-07T19:25:42.7420354+00:0060https://www.frontiersin.org/articles/10.3389/fphy.2020.610625
https://www.frontiersin.org/articles/10.3389/fphy.2020.610625
Olbertian Partition Function in Scalar Field Theory2020-12-08T00:00:00ZR. A. TreumannWolfgang BaumjohannThe Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau–Ginzburg action, respectively, Hamiltonian. In order to make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau–Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, that is, once the field equations are written down such that the interactions can be formulated.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.604857
https://www.frontiersin.org/articles/10.3389/fphy.2020.604857
The Effect of Solar-Wind Turbulence on Magnetospheric Activity2020-11-25T00:00:00ZR. D’AmicisD. TelloniR. BrunoThe solar wind is a highly turbulent medium exhibiting scalings of the fluctuations ranging over several decades of scales from the correlation length down to proton and electron gyroradii, thus suggesting a self-similar nature for these fluctuations. During its journey, the solar wind encounters the region of space surrounding Earth dominated by the geomagnetic field which is called magnetosphere. The latter is exposed to the continuous buffeting of the solar wind which determines its characteristic comet-like shape. The solar wind and the magnetosphere interact continously, thus constituting a coupled system, since perturbations in the interplanetary medium cause geomagnetic disturbances. However, strong variations in the geomagnetic field occur even in absence of large solar perturbations. In this case, a major role is attributed to solar wind turbulence as a driver of geomagnetic activity especially at high latitudes. In this review, we report about the state-of-art related to this topic. Since the solar wind and the magnetosphere are both high Reynolds number plasmas, both follow a scale-invariant dynamics and are in a state far from equilibrium. Moreover, the geomagnetic response, although closely related to the changes of the interplanetary magnetic field condition, is also strongly affected by the intrinsic dynamics of the magnetosphere generated by geomagnetic field variations caused by the internal conditions.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.584063
https://www.frontiersin.org/articles/10.3389/fphy.2020.584063
Higher-Order Statistics in Compressive Solar Wind Plasma Turbulence: High-Resolution Density Observations From the Magnetospheric MultiScale Mission2020-10-30T00:00:00ZOwen Wyn RobertsJessica ThwaitesLuca Sorriso-ValvoRumi NakamuraZoltán VörösTurbulent density fluctuations are investigated in the solar wind at sub-ion scales using calibrated spacecraft potential. The measurement technique using the spacecraft potential allows for a much higher time resolution and sensitivity when compared to direct measurements using plasma instruments. Using this novel method, density fluctuations can be measured with unprecedentedly high time resolutions for in situ measurements of solar wind plasma at 1 a.u. By investigating 1 h of high-time resolution data, the scale dependant kurtosis is calculated by varying the time lag τ to calculate increments between observations. The scale-dependent kurtosis is found to increase towards ion scales but then plateaus and remains fairly constant through the sub-ion range in a similar fashion to magnetic field measurements. The sub-ion range is also found to exhibit self-similar monofractal behavior contrasting sharply with the multi-fractal behavior at large scales. The scale-dependent kurtosis is also calculated using increments between two different spacecraft. When the time lags are converted using the ion bulk velocity to a comparable spatial lag, a discrepancy is observed between the two measurement techniques. Several different possibilities are discussed including a breakdown of Taylor’s hypothesis, high-frequency plasma waves, or intrinsic differences between sampling directions.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.586082
https://www.frontiersin.org/articles/10.3389/fphy.2020.586082
Topside Reconnection2020-10-06T00:00:00ZR. A. TreumannW. BaumjohannIt is proposed that reconnection would be a main mechanism governing the plasma processes on auroral time scales in the topside ionosphere/high-latitude magnetosphere transition. It occurs in the downward current region between two narrow parallel closely spaced though separated downward current sheets. The field-aligned currents are carried by upward cold upper-ionospheric electrons closing the upward current in an adjacent region. This local process does primarily not affect the ambient field but generates an anomalous diffusivity.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00386
https://www.frontiersin.org/articles/10.3389/fphy.2020.00386
Auroral Kilometric Radiation and Electron Pairing2020-09-23T00:00:00ZRudolf A. TreumannWolfgang BaumjohannWe suggest that pairing of bouncing medium-energy electrons in the auroral upward current region close to the mirror points may play a role in driving the electron cyclotron maser instability to generate an escaping narrow band fine structure in the auroral kilometric radiation. We treat this mechanism in the gyrotron approximation, for simplicity using the extreme case of a weakly relativistic Dirac distribution instead the more realistic anisotropic Jüttner distribution. Promising estimates of bandwidth, frequency drift and spatial location are given.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00317
https://www.frontiersin.org/articles/10.3389/fphy.2020.00317
Electron-Only Reconnection in Plasma Turbulence2020-09-04T00:00:00ZFrancesco CalifanoSilvio Sergio CerriMatteo FaganelloDimitri LavederManuela SistiMatthew W. KunzHybrid-Vlasov–Maxwell simulations of magnetized plasma turbulence including non-linear electron-inertia effects in a generalized Ohm's law are presented. When fluctuation energy is injected on scales sufficiently close to ion-kinetic scales, the ions efficiently become de-magnetized and electron-scale current sheets largely dominate the distribution of the emerging current structures, in contrast to the usual picture, where a full hierarchy of structure sizes is generally observed. These current sheets are shown to be the sites of electron-only reconnection (e-rec), in which the usual electron exhausts are unaccompanied by ion outflows and which are in qualitative agreement with those recently observed by MMS in the Earth's turbulent magnetosheath, downstream of the bow shock. Some features of the e-rec phenomenology are shown to be consistent with an electron magnetohydrodynamic description. Simulations suggest that this regime of collisionless reconnection may be found in turbulent systems where plasma processes, such as micro-instabilities and/or shocks, overpower the more customary turbulent cascade by directly injecting energy close to the ion-kinetic scales.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00348
https://www.frontiersin.org/articles/10.3389/fphy.2020.00348
Short-Term Lightning Response to Ground Level Enhancements2020-09-04T00:00:00ZQiong WuHui LiChi WangCosmic rays (CRs) are considered the primary energetic particle source of atmospheric ionization on Earth. Under the modulation of severe solar eruption events, CR variations are further speculated to impact the Earth's lightning activities. Previous researches show that CR intensity and lightning incidence are positively correlated on the time scale of several days to decades. However, to our knowledge, the global lightning response to short-term CR variation has not been studied in the literature. Ground level enhancements (GLEs) provide the opportunity to study such a possible link. As a small fraction of solar energetic particle events that could reach the energy level of several GeVs, GLEs can thus generate atmospheric cascades that could be recorded by ground-based neutron monitors. Furthermore, as GLEs generally take place within several 10 min to an hour, the lightning variations caused by potential meteorological factors could be maximally diminished in such a short time. During the operational period of the World Wide Lightning Location Network (Aug 2004 to now), three typical GLEs with the intensity >15% are analyzed from the International GLE Database, namely #69 (Jan 20, 2005), #70 (Dec 13, 2006), and #71 (May 17, 2012). For each GLE event, the global lightning incidence presents a positive response to GLE (i.e., a significant enhancement within 20 min right after the GLE onset). Meanwhile, the relative amplitude of lightning response seems to be in direct proportion to GLE intensity (i.e., the more intensive the GLE is, the more obvious the increase in the lightning incidence is), which is further verified to be statistically significant by Monte Carlo test. By comparing lightning responses in different latitudinal zones, we find that more intensive lightning responses to GLEs seem to be at higher latitudes.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00221
https://www.frontiersin.org/articles/10.3389/fphy.2020.00221
Lorentzian Entropies and Olbert's κ - Distribution2020-07-21T00:00:00ZRudolf A. TreumannWolfgang BaumjohannThis note derives the various forms of entropy of a systems subject to Olbert distributions (generalized Lorentzian probability distributions known as κ-distributions), which are frequently observed, particularly in high-temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high-energy truncation. We find the representation of the mean energy as a function of probability, and we provide the implicit form of Olbert (Lorentzian) entropy as well as its high-temperature limit. The relation to phase space density of states is obtained. We then find the entropy as a function of probability, an expression that is fundamental to statistical mechanics and, here, to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations that add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might do so at temperatures that are sufficiently far from zero.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00249
https://www.frontiersin.org/articles/10.3389/fphy.2020.00249
The Capon Method for Mercury's Magnetic Field Analysis2020-07-14T00:00:00ZSimon ToepferYasuhito NaritaDaniel HeynerUwe MotschmannCharacterization of Mercury's internal and external magnetic field is one of the primary goals of the magnetometer experiment on board the BepiColombo MPO (Mercury Planetary Orbiter) spacecraft. A novel data analysis tool is developed to determine the Gauss coefficients in the multipole expansion using Capon's minimum variance projection method. The construction of the estimator is presented along with a test against the numerical simulation data of Mercury's magnetosphere and a comparison with the least square fitting method shows, that Capon's estimator is in better agreement with the coefficients, implemented in the simulation, than the least square fit estimator.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00227
https://www.frontiersin.org/articles/10.3389/fphy.2020.00227
The Dust-to-Gas Ratio, Size Distribution, and Dust Fall-Back Fraction of Comet 67P/Churyumov-Gerasimenko: Inferences From Linking the Optical and Dynamical Properties of the Inner Comae2020-06-24T00:00:00ZRaphael MarschallJohannes MarkkanenSelina-Barbara GerigOlga Pinzón-RodríguezNicolas ThomasJong-Shinn WuIn this work, we present results that simultaneously constrain the dust size distribution, dust-to-gas ratio, fraction of dust re-deposition, and total mass production rates for comet 67P/Churyumov-Gerasimenko. We use a 3D Direct Simulation Monte Carlo (DSMC) gas dynamics code to simulate the inner gas coma of the comet for the duration of the Rosetta mission. The gas model is constrained by ROSINA/COPS data. Further, we simulate for different epochs the inner dust coma using a 3D dust dynamics code including gas drag and the nucleus' gravity. Using advanced dust scattering properties these results are used to produce synthetic images that can be compared to the OSIRIS data set. These simulations allow us to constrain the properties of the dust coma and the total gas and dust production rates. We determined a total volatile mass loss of (6.1 ± 1.5) · 10^{9} kg during the 2015 apparition. Further, we found that power-laws with q=3.7-0.078+0.57 are consistent with the data. This results in a total of 5.1-4.9+6.0·109 kg of dust being ejected from the nucleus surface, of which 4.4-4.2+4.9·109 kg escape to space and 6.8-6.8+11·108 kg (or an equivalent of 14-14+22 cm over the smooth regions) is re-deposited on the surface. This leads to a dust-to-gas ratio of 0.73-0.70+1.3 for the escaping material and 0.84-0.81+1.6 for the ejected material. We have further found that the smallest dust size must be strictly smaller than ~30μm and nominally even smaller than ~12μm.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00156
https://www.frontiersin.org/articles/10.3389/fphy.2020.00156
On the Nature and Origin of Bipolar Electrostatic Structures in the Earth's Bow Shock2020-06-12T00:00:00ZIvan Y. VaskoRachel WangForrest S. MozerStuart D. BaleAnton V. ArtemyevWe present a statistical analysis of large-amplitude bipolar electrostatic structures measured by Magnetospheric Multiscale spacecraft in the Earth's bow shock. The analysis is based on 371 large-amplitude bipolar structures collected in nine supercritical quasi-perpendicular Earth's bow shock crossings. We find that 361 of the bipolar structures have negative electrostatic potentials, and only 10 structures (< 3%) have positive potentials. The bipolar structures with negative potentials are interpreted in terms of ion phase space holes produced by ion streaming instabilities, particularly the two-stream instability between incoming and reflected ions. We obtain an upper estimate for the amplitudes of the ion phase space holes that is in agreement with the measurements. The bipolar structures with positive potentials could be electron phase space holes produced by electron two-stream instabilities. We argue that the negligible number of electron phase space holes among large-amplitude bipolar structures is due to the electron hole transverse instability, the criterion for which is highly restrictive at ω_{pe}/ω_{ce} ≫ 1, a parameter range typical of collisionless shocks in the heliosphere and various astrophysical environments. Our analysis indicates that the original mechanism of electron surfing acceleration involving electron phase space holes is not likely to be efficient in realistic collisionless shocks.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00166
https://www.frontiersin.org/articles/10.3389/fphy.2020.00166
Transport Ratios of the Kinetic Alfvén Mode in Space Plasmas2020-05-29T00:00:00ZYasuhito NaritaOwen Wyn RobertsZoltán VörösMasahiro HoshinoFluctuation properties of the kinetic Alfvén mode, such as polarization of the wave electric and magnetic field around the mean magnetic field, parallel fluctuation to the mean field, ratios of the electric to magnetic field, and density fluctuations are analytically estimated by constructing the dielectric tensor of plasma based on the linear Vlasov theory. The dielectric tensor contains various fluid-picture processes in the lowest order, including polarization drift, Hall current, and diamagnetic current. Major discoveries from the dielectric tensor method in the kinetic Alfvén mode study are (1) identification of the mechanism of the field rotation sense reversal as a result of competition between the Hall and diamagnetic currents, (2) behavior of the parallel magnetic field fluctuation (in the compressive sense). The analytic expression of transport ratios serves as a diagnostic tool to study and identify the kinetic Alfvén mode in space plasma observations in the inner heliospheric domain.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00089
https://www.frontiersin.org/articles/10.3389/fphy.2020.00089
AME: A Cross-Scale Constellation of CubeSats to Explore Magnetic Reconnection in the Solar–Terrestrial Relation2020-04-15T00:00:00ZLei DaiChi WangZhiming CaiWalter GonzalezMichael HessePhilippe EscoubetTai PhanVytenis VasyliunasQuanming LuLei LiLinggao KongMalcolm DunlopRumi NakamuraJianshen HeHuishan FuMeng ZhouShiyong HuangRongsheng WangYuri KhotyaintsevDaniel GrahamAlessandro RetinoLev ZelenyiElena E. GrigorenkoAndrei RunovVassilis AngelopoulosLarry KepkoKyoung-Joo HwangYongcun ZhangA major subset of solar–terrestrial relations, responsible, in particular, for the driver of space weather phenomena, is the interaction between the Earth's magnetosphere and the solar wind. As one of the most important modes of the solar–wind–magnetosphere interaction, magnetic reconnection regulates the energy transport and energy release in the solar–terrestrial relation. In situ measurements in the near-Earth space are crucial for understanding magnetic reconnection. Past and existing spacecraft constellation missions mainly focus on the measurement of reconnection on plasma kinetic-scales. Resolving the macro-scale and cross-scale aspects of magnetic reconnection is necessary for accurate assessment and predictions of its role in the context of space weather. Here, we propose the AME (self-Adaptive Magnetic reconnection Explorer) mission consisting of a cross-scale constellation of 12+ CubeSats and one mother satellite. Each CubeSat is equipped with instruments to measure magnetic fields and thermal plasma particles. With multiple CubeSats, the AME constellation is intended to make simultaneous measurements at multiple scales, capable of exploring cross-scale plasma processes ranging from kinetic scale to macro scale.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00045
https://www.frontiersin.org/articles/10.3389/fphy.2020.00045
Space Weather Related to Solar Eruptions With the ASO-S Mission2020-03-11T00:00:00ZLi FengWeiqun GanSiqing LiuHuaning WangHui LiLong XuWeiguo ZongXiaoxing ZhangYaguang ZhuHaiyan WuAnqin ChenYanmei CuiXinghua DaiJuan GuoHan HeXin HuangLei LuQiao SongJingjing WangQiuzhen ZhongLing ChenZhanle DuXingliang GuoYu HuangHu LiYing LiSenlin XiongShenggao YangBeili YingThe Advanced Space-based Solar Observatory (ASO-S) is a mission aiming at exploring solar flares, coronal mass ejections (CMEs), solar magnetic field and their relationships. To fulfill its major scientific objectives, ASO-S has three elaborately-designed payloads onboard: the Full-disk vector MagnetoGraph (FMG), the Lyman-alpha Solar Telescope (LST), and the Hard X-ray Imager (HXI) dedicated to observe vector magnetic fields, CMEs, and flares, respectively. Beside the scientific objectives, we have an operational objective to observe solar eruptions and magnetic field for making related space weather forecasts. More specifically, we have set a priority for the downlink of CME data observed by LST, and will distribute those data to different space weather prediction centers in China within 2 h once the Science Operation and Data Center (SODC) of ASO-S receive the data. After data downlink and archiving, different automatic detection, tracking, and cataloging procedures are planned to run for the most critical solar eruptive features. On the other hand, based on the distributed and downloaded data, different space weather prediction centers are to activate their forecast systems for the ASO-S observed solar eruption events. Our particular interests are currently focused on nowcast of different eruption events, prediction of CME arrivals, forecast of solar flares and the onset of solar eruptions. We are also working on further forecast potentials using the ASO-S data to make contributions to other possible important issues of space weather.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00184
https://www.frontiersin.org/articles/10.3389/fphy.2019.00184
Anisotropy of the Spectral Index in Ion Scale Compressible Turbulence: MMS Observations in the Magnetosheath2019-11-20T00:00:00ZOwen Wyn RobertsYasuhito NaritaRumi NakamuraZoltán VörösDaniel GershmanTurbulence in the Earth's magnetosheath at ion kinetic scales is investigated with the Magnetospheric MultiScale (MMS) spacecraft. The multi-point measurements allow the three dimensional power spectra in wave-vector space to be determined. Previously the three dimensional structure of fluctuations in the magnetic field and density (using spacecraft potential as a proxy) were possible with Cluster. However, using the excellent time resolution data set provided from both the Fluxgate Magnetometer (FGM) and the Fast Plasma Investigation (FPI) on MMS the spectra can be determined for a number of different parameters such as ion velocity, and ion temperatures parallel and perpendicular to the mean magnetic field directions. The spectra for different fluctuations show similar features to one another such as a strong power anisotropy with respect to the mean magnetic field direction, such that the energy decays faster in the direction parallel to the mean magnetic field than the perpendicular direction. A weak non-gyrotropy is also seen in the direction of the bulk velocity similar to what has been seen in magnetic field fluctuations with Cluster at ion kinetic scales in the solar wind. Velocity fluctuations are shown to be the most anisotropic. The density and temperature fluctuations exhibit similar anisotropies but are much weaker in comparison.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00151
https://www.frontiersin.org/articles/10.3389/fphy.2019.00151
Coalescence of Magnetic Flux Ropes Within Interplanetary Coronal Mass Ejections: Multi-cases Studies2019-10-04T00:00:00ZYan ZhaoHengqiang FengQiang LiuGuoqing ZhaoCoronal mass ejections (CMEs) are intense solar explosive eruptions and have significant impact on geomagnetic activities. It is important to understand how CMEs evolve as they propagate in the solar-terrestrial space. In this paper, we studied the coalescence of magnetic flux ropes embedded in five interplanetary coronal mass ejections (ICMEs) observed by both ACE and Wind spacecraft. The analyses show that coalescence of magnetic flux ropes could persist for hours and operate in scale of hundreds of earth radii. The two merging flux ropes could be very different in the axial orientation and the plasma density and temperature, which should complicate the progress of coalescence and have impact on the merged structures. The study indicates that coalescence of magnetic flux ropes should be an important factor in changing the magnetic topology of ICMEs.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00108
https://www.frontiersin.org/articles/10.3389/fphy.2019.00108
Sign Singularity of the Local Energy Transfer in Space Plasma Turbulence2019-08-20T00:00:00ZLuca Sorriso-ValvoGaetano De VitaFederico FraternaleAlexandre GurchumeliaSilvia PerriGiuseppina NigroFilomena CatapanoAlessandro RetinòChristopher H. K. ChenEmiliya YordanovaOreste PezziKhatuna ChargaziaOleg KharshiladzeDiana KvaratskheliaChristian L. VásconezRaffaele MarinoOlivier Le ContelBarbara GilesThomas E. MooreRoy B. TorbertJames L. BurchIn weakly collisional space plasmas, the turbulent cascade provides most of the energy that is dissipated at small scales by various kinetic processes. Understanding the characteristics of such dissipative mechanisms requires the accurate knowledge of the fluctuations that make energy available for conversion at small scales, as different dissipation processes are triggered by fluctuations of a different nature. The scaling properties of different energy channels are estimated here using a proxy of the local energy transfer, based on the third-order moment scaling law for magnetohydrodynamic turbulence. In particular, the sign-singularity analysis was used to explore the scaling properties of the alternating positive-negative energy fluxes, thus providing information on the structure and topology of such fluxes for each of the different type of fluctuations. The results show the highly complex geometrical nature of the flux, and that the local contributions associated with energy and cross-helicity non-linear transfer have similar scaling properties. Consequently, the fractal properties of current and vorticity structures are similar to those of the Alfvénic fluctuations.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00114
https://www.frontiersin.org/articles/10.3389/fphy.2019.00114
Kinematic Collisionless Relaxation of Ions in Supercritical Shocks2019-08-14T00:00:00ZMichael GedalinWe show that kinematic collisionless relaxation in the macroscopic electric and magnetic fields plays the main role in the formation of the downstream ion distributions in a super-critical shock with ion reflection present. It is done by comparison of a theoretically predicted magnetic profile with the magnetic profile of a shocks observed by MMS mission. It is shown that pressure balance remains the main constraint for the shock stability.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00063
https://www.frontiersin.org/articles/10.3389/fphy.2019.00063
A First Assessment of a Regression-Based Interpretation of Langmuir Probe Measurements2019-05-03T00:00:00ZJonathan ChalaturnykRichard MarchandA new approach is presented for interpreting low level Langmuir probe measurements in terms of physical plasma parameters such as density or temperature. Instead of relying on analytic expressions as in most analyses, the method uses regressions combined with a suitably prepared solution library consisting of precomputed probe characteristics for selected plasma parameters. In machine learning language, this amounts to generating a training data set, constructing and training a model, and validating it over a domain of physical parameters of interest. This study aims at establishing the feasibility and limits of the method by using synthetic data sets that can be generated quickly from analytic approximations. The ultimate goal is to use this approach with model training on data sets constructed with detailed kinetic simulations capable of accounting for more physical processes, and more realistic geometry, than are possible with analytic models.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00008
https://www.frontiersin.org/articles/10.3389/fphy.2019.00008
A Note on Capon's Minimum Variance Projection for Multi-Spacecraft Data Analysis2019-02-01T00:00:00ZYasuhito NaritaCapon's minimum variance projection for the multi-point measurements is revisited using the method of likelihood function to derive the minimum variance projection and a simplified error estimate analytically. Theoretical construction of the minimum variance projection assumes a Gaussian form of the likelihood function and also regards the data covariance as a proxy of the noise covariance. The minimum variance projection is extended to the problem of two-spacecraft mode decomposition in the Mercury magnetosphere in which the magnetic field is a superposition of the constant field from the current sheet and the dipolar field from the planet. The extension of the Capon estimator (the data-variance projection) can identify the signal amplitudes of the different fields with a sufficient accuracy when the statistical averaging is properly done. The Capon estimator serves as a powerful analysis tool when the spatial resolution is limited to only a few points.]]>