Minimum Variance Analysis Research Articles

How Accurately Can We Measure the Reconnection Rate E M for the MMS Diffusion Region Event of 11 July 2017?

We investigate the accuracy with which the reconnection electric field E M can be determined from in situ plasma data. We study the magnetotail electron diffusion region observed by National Aeronautics and Space Administration's Magnetospheric Multiscale (MMS) on 11 July 2017 at 22:34 UT and focus on the very large errors in E M that result from errors in an L M N boundary normal coordinate system. We determine several L M N coordinates for this MMS event using several different methods. We use these M axes to estimate E M. We find some consensus that the reconnection rate was roughly E M = 3.2 ± 0.6 mV/m, which corresponds to a normalized reconnection rate of 0.18 ± 0.035. Minimum variance analysis of the electron velocity (MVA‐v e), MVA of E, minimization of Faraday residue, and an adjusted version of the maximum directional derivative of the magnetic field (MDD‐B) technique all produce reasonably similar coordinate axes. We use virtual MMS data from a particle‐in‐cell simulation of this event to estimate the errors in the coordinate axes and reconnection rate associated with MVA‐v e and MDD‐B. The L and M directions are most reliably determined by MVA‐v e when the spacecraft observes a clear electron jet reversal. When the magnetic field data have errors as small as 0.5% of the background field strength, the M direction obtained by MDD‐B technique may be off by as much as 35°. The normal direction is most accurately obtained by MDD‐B. Overall, we find that these techniques were able to identify E M from the virtual data within error bars ≥20%.

The Identification of a Planar Magnetic Structure within the ICME Shock Sheath and Its influence on Galactic Cosmic-Ray Flux

Abstract A Forbush decrease is a sudden decrease in cosmic-ray intensity caused by transient interplanetary disturbances. The substructure of an interplanetary counterpart of a coronal mass ejection (ICME) such as a shock sheath and/or a magnetic cloud independently contributes to cosmic-ray decrease, which is evident as a two-step decrease. Our earlier work has shown multistep decrease and recovery within the ICME-driven shock-sheath region. Further, we have suggested that the presence of a small-scale flux rope within the shock-sheath region causes a steady/gradual recovery in cosmic-ray intensity. Here, we demonstrate the presence of a planar magnetic structure (PMS) and small-scale flux rope within a single shock sheath of an ICME. The plot of the elevation (θ) versus azimuthal (ϕ) angle of the interplanetary magnetic field (IMF) is used for the identification of the PMS. The planarity, efficiency, and a plane-normal vector are estimated by employing a minimum variance analysis (MVA) technique, which confirmed the presence of the PMS. In addition, a 2D-hodogram method in conjunction with the MVA technique is utilized to identify the flux-rope structure and turbulent conditions in the corresponding ICME region. The observation in the visible suggests that the PMS region within the ICME shock sheath caused the decrease in the cosmic-ray flux observed at Earth. It has also been observed that the sharp variations in the IMF (i.e., turbulence) cause a decrease, whereas the flux-rope structure is responsible for the recovery of the CR flux. Further studies are needed to investigate their origins and to confirm their effects on space weather.

Oblique Ion‐Scale Magnetotail Flux Ropes Generated by Secondary Tearing Modes

AbstractWe examine Magnetospheric Multiscale observations of three ion‐scale magnetic flux ropes (diameter ~6–9 ion inertial lengths) in the Earth's magnetotail reconnection diffusion region with a small guide field. During the event, the electron reconnection exhaust reversed direction together with the reversal of normal magnetic field component. After that, the three ion‐scale flux ropes were observed near the ion diffusion region, in which flat‐top distributions were found at the field‐aligned electrons (<2 keV). The axis orientation and motion velocity of the flux ropes are determined by minimum variance analysis of the electric field component along the flux rope axis, using single‐spacecraft measurements. Results show that the three flux rope axes form 13°, 55°, and 55° to the guide field direction and are mostly tilted toward the direction of the reconnecting field. These results are also validated by multiple‐spacecraft analysis methods. It is found that the tilted angles agree reasonably well with the predicted angles for secondary tearing modes, suggesting that these ion‐scale flux ropes are likely generated by secondary tearing instabilities as those recently found in the three‐dimensional kinetic simulations of turbulent magnetic reconnection.

A Statistical Study of Ionospheric Boundary Wave Formation at Venus

AbstractPrevious missions to Venus have revealed that encounters with plasma irregularities of atmospheric origin outside the atmosphere are not uncommon. A number of mechanisms have been proposed to discuss their origins as well as their roles in the atmospheric evolution of Venus. One such mechanism involves an ionopause with a wavelike appearance. By utilizing the magnetic field and plasma data from Venus Express, we present the first observational statistical analysis of the ionospheric boundary wave phenomena at Venus using data from 2006 to 2014. Results from the minimum variance analysis of all the photoelectron dropout events in the ionosphere reveal that the ionopause of Venus does not always appear to be smooth but often exhibits a wavelike appearance. In the northern polar region of Venus, the normal directions of the rippled ionospheric boundary crossings lie mainly in the terminator plane with the largest component predominantly along the dawn‐dusk (YVSO) direction. The average estimated wavelength of the boundary wave is 212 ± 12 km, and the average estimated velocity difference across the ionopause is 104 ± 6 km/s. The results suggest that the rippled boundary is a result of Kelvin‐Helmholtz instability. Analysis reveals a correlation between the normal directions and the locations of the boundary wave with respect to Venus. This indicates that the draping of magnetic field lines may play a role in enhancing the plasma flow along the dawn‐dusk direction, which could subsequently set up a velocity shear that favors the excitation of ionospheric boundary wave by the Kelvin‐Helmholtz instability along the dawn‐dusk direction.

Statistical Study of the Properties of Magnetosheath Lion Roars.

Lion roars are narrowband whistler wave emissions that have been observed in several environments, such as planetary magnetosheaths, the Earth’s magnetosphere, the solar wind, downstream of interplanetary shocks, and the cusp region. We present measurements of more than 30,000 such emissions observed by the Magnetospheric Multiscale spacecraft with high-cadence (8,192 samples/s) search coil magnetometer data. A semiautomatic algorithm was used to identify the emissions, and an adaptive interval algorithm in conjunction with minimum variance analysis was used to determine their wave vector. The properties of the waves are determined in both the spacecraft and plasma rest frame. The mean wave normal angle, with respect to the background magnetic field (B0), plasma bulk flow velocity (Vb), and the coplanarity plane (Vb × B0) are 23°, 56°, and 0°, respectively. The average peak frequencies were ~31% of the electron gyrofrequency (ωce) observed in the spacecraft frame and ~18% of ωce in the plasma rest frame. In the spacecraft frame, ~99% of the emissions had a frequency < ωce, while 98% had a peak frequency < 0.72 ωce in the plasma rest frame. None of the waves had frequencies lower than the lower hybrid frequency, ω. From the probability density function of the electron plasma βe, the ratio between the electron thermal and magnetic pressure, ~99.6% of the waves were observed with βe < 4 with a large narrow peak at 0.07 and two smaller, but wider, peaks at 1.26 and 2.28, while the average value was ~1.25.

A tail like no other

Context. The Rosetta Plasma Consortium (RPC) magnetometer (MAG) data during the tail excursion in March–April 2016 are used to investigate the magnetic structure of and activity in the tail region of the weakly outgassing comet 67P/Churyumov–Gerasimenko (67P). Aims. The goal of this study is to compare the large scale (near) tail structure with that of earlier missions to strong outgassing comets, and the small scale turbulent energy cascade (un)related to the singing comet phenomenon. Methods. The usual methods of space plasma physics are used to analyse the magnetometer data, such as minimum variance analysis, spectral analysis, and power law fitting. Also the cone angle and clock angle of the magnetic field are calculated to interpret the data. Results. It is found that comet 67P does not have a classical draped magnetic field and no bi-lobal tail structure at this late stage of the mission when the comet is already at 2.7 AU distance from the Sun. The main magnetic field direction seems to be more across the tail direction, which may implicate an asymmetric pick-up cloud. During periods of singing comet activity the propagation direction of the waves is at large angles with respect to the magnetic field and to the radial direction towards the comet. Turbulent cascade of magnetic energy from large to small scales is different in the presence of singing as without it.

Analyzing the Magnetopause Internal Structure: New Possibilities Offered by MMS Tested in a Case Study

AbstractWe explore the structure of the magnetopause using a crossing observed by the Magnetospheric Multiscale (MMS) spacecraft on 16 October 2015. Several methods (minimum variance analysis, BV method, and constant velocity analysis) are first applied to compute the normal to the magnetopause considered as a whole. The different results obtained are not identical, and we show that the whole boundary is not stationary and not planar, so that basic assumptions of these methods are not well satisfied. We then analyze more finely the internal structure for investigating the departures from planarity. Using the basic mathematical definition of what is a one‐dimensional physical problem, we introduce a new single spacecraft method, called LNA (local normal analysis) for determining the varying normal, and we compare the results so obtained with those coming from the multispacecraft minimum directional derivative (MDD) tool developed by Shi et al. (2005). This last method gives the dimensionality of the magnetic variations from multipoint measurements and also allows estimating the direction of the local normal when the variations are locally 1‐D. This study shows that the magnetopause does include approximate one‐dimensional substructures but also two‐ and three‐dimensional structures. It also shows that the dimensionality of the magnetic variations can differ from the variations of other fields so that, at some places, the magnetic field can have a 1‐D structure although all the plasma variations do not verify the properties of a global one‐dimensional problem. A generalization of the MDD tool is proposed.

The Plasma Sheet as Natural Symmetry Plane for Dipolarization Fronts in the Earth's Magnetotail

AbstractIn this work, observations of multispacecraft mission Time History of Events and Macroscale Interactions during Substorms are used for statistical investigation of dipolarization fronts in the near‐Earth plasma sheet of the magnetotail. Using very stringent criteria, 460 events are detected in almost 10 years of mission data. Minimum variance analysis is used to determine the normal directions of the phase fronts, providing evidence for the existence of a natural symmetry of these phenomena, given by the neutral sheet of the magnetotail. This finding enables the definition of a local coordinate system based on the Tsyganenko model, reflecting the intrinsic orientation of the neutral sheet and, therefore, the dipolarization fronts. In this way, the comparison of events with very different background conditions is improved. Through this study, the statistical results of Liu, Angelopoulos, Runov, et al. (2013) are both confirmed and extended. In a case study, the knowledge of this plane of symmetry helps to explain the concave curvature of dipolarization fronts in the XZ plane through phase propagation speeds of magnetoacoustic waves. A second case study is presented to determine the central current system of a passing dipolarization front through a constellation of three spacecraft. With this information, a statistical analysis of spacecraft observations above and below the neutral sheet is used to provide further evidence for the neutral sheet as the symmetry plane and the central current system. Furthermore, it is shown that the signatures of dipolarization fronts are under certain conditions closely related to that of flux ropes, indicating a possible relationship between these two transient phenomena.

Characterization of the Complex Ejecta Measured In Situ on 19 – 22 March 2001 by Six Different Methods

This article proposes some traditional and newly developed methods to evaluate the properties of the magnetic cloud (MC) observed on 19 – 22 March 2001. We used physical and mathematical approaches to analyze the time series of solar wind plasma and interplanetary magnetic field data. Two methods that are commonly used to derive the MC properties, the minimum variance analysis and the Grad–Shafranov reconstruction, were applied to derive the properties of the MCs by fitting in situ measurements in the corresponding time intervals, as discussed in previous studies. Other methods developed by us (a travel time analysis of the interplanetary coronal mass ejection, spatio-temporal entropy, nonlinear fluctuation analysis, and wavelet analysis) are used as auxiliary tools to help identify whether the event consists of one or possibly two MCs. Our results suggest that the 19 – 22 March 2001 event was composed by two MCs. Our results agree with those of other researchers who used various fitting methods and identified the solar origin of this event as two CMEs.

Comparison of CME and ICME Structures Derived from Remote-Sensing and In Situ Observations

We present results from the comparison of the near-Sun and in situ analysis of two Earth-directed coronal mass ejections (CMEs) with different 3D orientations and solar source region characteristics. The CME on 14 July 2000, the so-called Bastille Day storm, a well-studied event, was observed from a single-point perspective by the Large Angle and Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO). It caused a major geomagnetic storm with a peak Kp of 9. The CME originated from a magnetic bipolar photospheric source region with the polarity inversion line being oriented rather parallel to the heliographic equator. In contrast, the CME on 29 September 2013, which caused a geomagnetic storm with a peak Kp intensity of 8-, originated from a magnetic quadrupolar photospheric source region with the polarity inversion line between the two bipoles almost vertically oriented with respect to the heliographic equator. The results of a graduated cylindrical shell (GCS) analysis of the CMEs near the Sun are compared with the minimum variance analysis (MVA) of the magnetic field structure of the interplanetary CME (ICME) measured in situ near Earth’s orbit. The results are in good agreement for the September 2013 CME and ICME, whereas the July 2000 ICME appears substantially inclined near Earth’s orbit. The discrepancy can likely be explained taking into account kinks in the CME’s near-Sun structure of the CME that expands into the interplanetary medium.

On the origins of magnetic flux ropes in near‐Mars magnetotail current sheets

AbstractWe analyze Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of magnetic flux ropes embedded in Martian magnetotail current sheets, in order to evaluate the role of magnetotail reconnection in their generations. We conduct a minimum variance analysis to infer the generation processes of magnetotail flux ropes from the geometrical configuration of the individual flux rope axial orientation with respect to the overall current sheet. Of 23 flux ropes detected in current sheets in the near‐Mars (∼1–3 Martian radii downstream) magnetotail, only 3 (possibly 4) can be explained by the magnetotail reconnection scenario, while the vast majority of the events (19 events) are more consistent with flux ropes that are originally generated in the dayside ionosphere and subsequently transported into the nightside magnetotail. The mixed origins of the detected flux ropes imply complex nature of generation and transport of Martian magnetotail flux ropes.

Flux ropes in the Hermean magnetotail: Distribution, properties, and formation

AbstractAn automated method was applied to identify magnetotail flux rope encounters in MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) magnetometer data. The method identified significant deflections of the north‐south component of the magnetic field coincident with enhancements in the total field or dawn‐dusk component. Two hundred forty‐eight flux ropes are identified that possess well‐defined minimum variance analysis (MVA) coordinate systems, with clear rotations of the field. Approximately 30% can be well approximated by the cylindrically symmetric, linearly force‐free model. Flux ropes are most common moving planetward, in the postmidnight sector. Observations are intermittent, with the majority (61%) of plasma sheet passages yielding no flux ropes; however, the peak rate of flux ropes during a reconnection episode is ∼5 min−1. Overall, the peak postmidnight rate is ∼0.25 min−1. Only 25% of flux ropes are observed in isolation. The radius of flux ropes is comparable to the ion inertial length within Mercury's magnetotail plasma sheet. No clear statistical separation is observed between tailward and planetward moving flux ropes, suggesting the near‐Mercury neutral line (NMNL) is highly variable. Flux ropes are more likely to be observed if the preceding lobe field is enhanced over background levels. A very weak correlation is observed between the flux rope core field and the preceding lobe field orientation; a stronger relationship is found with the orientation of the field within the plasma sheet. The core field strength measured is ∼6 times stronger than the local dawn‐dusk plasma sheet magnetic field.

A New DMSP Magnetometer & Auroral Boundary Dataset and Estimates of Field Aligned Currents in Dynamic Auroral Boundary Coordinates.

We have developed a method for reprocessing the multi-decadal, multi-spacecraft Defense Meteorological Satellite Program Magnetometer (DMSP SSM) dataset and have applied it to fifteen spacecraft-years of data (DMSP Flight 16-18, 2010-2014). This Level-2 dataset improves on other available SSM datasets with recalculated spacecraft locations and magnetic perturbations, artifact signal removal, representations of the observations in geomagnetic coordinates, and in-situ auroral boundaries. Spacecraft locations have been recalculated using ground-tracking information. Magnetic perturbations (measured field minus modeled main-field) are recomputed. The updated locations ensure the appropriate model field is used. We characterize and remove a slow-varying signal in the magnetic field measurements. This signal is a combination of ring current and measurement artifacts. A final artifact remains after processing: step-discontinuities in the baseline caused by activation/deactivation of spacecraft electronics. Using coincident data from the DMSP precipitating electrons and ions instrument (SSJ4/5), we detect the in-situ auroral boundaries with an improvement to the Redmon et al. [2010] algorithm. We embed the location of the aurora and an accompanying figure of merit in the Level-2 SSM data product. Finally, we demonstrate the potential of this new dataset by estimating field-aligned current (FAC) density using the Minimum Variance Analysis (MVA) technique. The FAC estimates are then expressed in dynamic auroral boundary coordinates using the SSJ-derived boundaries, demonstrating a dawn-dusk asymmetry in average FAC location relative to the equatorward edge of the aurora. The new SSM dataset is now available in several public repositories.

MMS observations of oblique small‐scale magnetopause flux ropes near the ion diffusion region during weak guide‐field reconnection

AbstractWe report Magnetospheric Multiscale observations of a series of five small‐scale magnetic flux ropes (FR1–5) embedded in the southward reconnection outflow during a magnetopause reconnection event with a small guide field (~2.2 nT). These small‐scale flux ropes (diameter ~3–11 ion inertial lengths) are found inside or near the ion diffusion region on the magnetosheath side of the magnetopause boundary layer. A consistent result for determining the axis orientation of the flux ropes is achieved using two different methods, namely, minimum variance analysis of the axial electric field and constrained minimum variance analysis of the magnetic field. Our results show that the axes of these flux ropes (FR1–4) form a large angle (53°−66°) to the guide‐field orientation and are tilted toward the direction of the reconnecting field. These observations provide evidence for the presence of oblique ion‐scale flux ropes near the ion diffusion region during reconnection with a weak guide field. Our findings are similar to those obtained from a 3‐D kinetic simulation of turbulent reconnection.

Review article: Wave analysis methods for space plasma experiment

Abstract. A review of analysis methods is given on quasi-monochromatic waves, turbulent fluctuations, and wave–wave and wave–particle interactions for single-spacecraft data in situ in near-Earth space and interplanetary space, in particular using magnetic field and electric field data. Energy spectra for different components of the fluctuating fields, minimum variance analysis, propagation and polarization properties of electromagnetic waves, wave distribution function, helicity quantities, higher-order statistics, and detection methods for wave–particle interactions are explained.

Quasiperiodic field‐aligned current dynamics associated with auroral undulations during a substorm recovery

AbstractA substorm recovery event in the early morning sector is explored by means of ground and spacecraft data. The ground data are provided by stations of the MIRACLE network, in northern Scandinavia and Svalbard, while spacecraft data are observed by the Cluster satellites, toward the end of the recovery phase. Additional information is provided by the Fast Auroral SnapshoT (FAST) satellite, conjugate to Cluster 3 (C3). A prominent signature in the Cluster data is the low‐frequency oscillations of the perturbation magnetic field, in the Pc5 range, interpreted in terms of a motion of quasi‐stationary mesoscale field‐aligned currents (FACs). Ground magnetic pulsations in the Ps6 range suggest that the Cluster observations are the high‐altitude counterpart of the drifting auroral undulations, whose features thus can be explored closely. While multiscale minimum variance analysis provides information on the planarity, orientation, and scale of the FAC structures, the conjugate data from FAST and from the ground stations can be used to resolve also the azimuthal motion. A noteworthy feature of this event, revealed by the Cluster observations, is the apparent relaxation of the twisted magnetic flux tubes, from a sequence of 2‐D current filaments to an undulated current sheet, on a timescale of about 10 min. This timescale appears to be consistent with the drift mirror instability in the inner magnetosphere, mapping to the equatorward side of the oval, or the Kelvin‐Helmholtz instability related to bursty bulk flows farther downtail, mapping to the poleward side of the oval. However, more work is needed and a better event statistics, to confirm these tentative mechanisms as sources of Ω‐like auroral undulations during late substorm recovery.

Automated force‐free flux rope identification

AbstractWe describe a method developed to automatically identify quasi force‐free magnetotail flux ropes from in situ spacecraft magnetometer data. The method locates significant (greater than 1σ) deflections of the north‐south component of the magnetic field coincident with enhancements in other field components. The magnetic field data around the deflections are then processed using Minimum Variance Analysis (MVA) to narrow the selection down to those that exhibit the characteristics of flux ropes. The subset of candidates that fulfills the requirements are then compared to a cylindrical, linear (constant‐α) force‐free model. Those that can be well approximated as force free are then accepted. The model fit also provides a measure of the physical parameters that describe the flux rope (i.e., core field and radius). This process allows for the creation of a repeatable, consistent catalog of flux ropes. Automation allows a greater volume of data to be covered, saving time and allowing the exploration of potential selection biases. The technique is applied to MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) magnetometer data in the Hermean magnetotail and successfully locates flux ropes, some of which match previously known encounters. Assumptions of the method and potential future applications are discussed.

MESSENGER observations of cusp plasma filaments at Mercury

AbstractThe MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft while in orbit about Mercury observed highly localized, ~3‐s‐long reductions in the dayside magnetospheric magnetic field, with amplitudes up to 90% of the ambient intensity. These magnetic field depressions are termed cusp filaments because they were observed from just poleward of the magnetospheric cusp to midlatitudes, i.e., ~55° to 85°N. We analyzed 345 high‐ and low‐altitude cusp filaments identified from MESSENGER magnetic field data to determine their physical properties. Minimum variance analysis indicates that most filaments resemble cylindrical flux tubes within which the magnetic field intensity decreases toward its central axis. If the filaments move over the spacecraft at an estimated magnetospheric convection speed of ~35 km/s, then they have a typical diameter of ~105 km or ~7 gyroradii for 1 keV H+ ions in a 300 nT magnetic field. During these events, MESSENGER's Fast Imaging Plasma Spectrometer observed H+ ions with magnetosheath‐like energies. MESSENGER observations during the spacecraft's final low‐altitude campaign revealed that these cusp filaments likely extend down to Mercury's surface. We calculated an occurrence‐rate‐normalized integrated particle precipitation rate onto the surface from all filaments of (2.70 ± 0.09) × 1025 s−1. This precipitation rate is comparable to published estimates of the total precipitation rate in the larger‐scale cusp. Overall, the MESSENGER observations analyzed here suggest that cusp filaments are the magnetospheric extensions of the flux transfer events that form at the magnetopause as a result of localized magnetic reconnection.

New method for determining central axial orientation of flux rope embedded within current sheet using multipoint measurements

A new method for determining the central axial orientation of a two-dimensional coherent magnetic flux rope (MFR) via multipoint analysis of the magnetic-field structure is developed. The method is devised under the following geometrical assumptions: (1) on its cross section, the structure is left-right symmetric; (2) the projected structure velocity is vertical to the line of symmetry. The two conditions can be naturally satisfied for cylindrical MFRs and are expected to be satisfied for MFRs that are flattened within current sheets. The model test demonstrates that, for determining the axial orientation of such structures, the new method is more efficient and reliable than traditional techniques such as minimum-variance analysis of the magnetic field, Grad-Shafranov (GS) reconstruction, and the more recent method based on the cylindrically symmetric assumption. A total of five flux transfer events observed by Cluster are studied using the proposed approach, and the application results indicate that the observed structures, regardless of their actual physical properties, fit the assumed geometrical model well. For these events, the inferred axial orientations are all in excellent agreement with those obtained using the multi-GS reconstruction technique.

Two-point observations of low-frequency waves at 67P/Churyumov-Gerasimenko during the descent of PHILAE: comparison of RPCMAG and ROMAP

Abstract. The European Space Agency's spacecraft ROSETTA has reached its final destination, comet 67P/Churyumov-Gerasimenko. Whilst orbiting in the close vicinity of the nucleus the ROSETTA magnetometers detected a new type of low-frequency wave possibly generated by a cross-field current instability due to freshly ionized cometary water group particles. During separation, descent and landing of the lander PHILAE on comet 67P/Churyumov-Gerasimenko, we used the unique opportunity to perform combined measurements with the magnetometers onboard ROSETTA (RPCMAG) and its lander PHILAE (ROMAP). New details about the spatial distribution of wave properties along the connection line of the ROSETTA orbiter and the lander PHILAE are revealed. An estimation of the observed amplitude, phase and wavelength distribution will be presented as well as the measured dispersion relation, characterizing the new type of low-frequency waves. The propagation direction and polarization features will be discussed using the results of a minimum variance analysis. Thoughts about the size of the wave source will complete our study.