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Characteristics and structure of magnetotail flux rope recovered from Grad-Shafranov method
Abstract
On 21 February 2009, THEMIS-C satellite observed the classical signal of magnetic flux rope at magnetotail of X=-15.7RE. We take the method of Grad-Shafranov reconstruction to investigate the characteristics and structure of magnetotail flux rope. The results give the characteristic physics parameters such as the invariant axis direction, the cross scale length, the magnetic flux in flux rope, etc. With no constraint from model on shape of the flux rope, we reconstruct the distribution of magnetic field and electric current density in the cross section of magnetic flux rope at magnetotail. Our results show that the magnetic field in the central region of magnetic flux rope can be described as being force-free, while with the increase of radial distance, the fields display no force-free feature in the region where the magnetic fields deviate from the axial symmetric distribution.
Three earthward flowing magnetic flux ropes observed in the duskside plasma sheet at geocentric solar magnetospheric coordinate X ∼−55 Re by P1 and P2 of acceleration, reconnection, turbulence and electrodynamics of moon’s interaction with the sun mission during 13:00–15:00 UT on July 3, 2012, were studied. The morphologies of the flux ropes were studied in detail based on Grad-Shfranov reconstruction method and electronic pitch angle distribution data. It is found that (1) the flux rope cross-sectional dimensions are 1.0 Re× 0.78 Re, 1.3 Re×0.78 Re, and 2.5 Re × 1.25 Re, respectively. The magnetic field lines were asymmetric about the center with field line compression on both sides of the current sheet at the leading region; (2) the electron energy flux data presented asymmetry with larger electron flux and lower temperature in the precursor region. The flux ropes were blocked by the resistance of compressed particle density in the front central plasma sheet and the enhanced magnetic field on its sides; and (3) it is found that the flux rope has a layered structure. From inside out, event 1 can be divided into three regions, namely electronic depletion core region, closed field line region, and the caudal area possible with fields connected with the ionosphere. It suggests that the flux ropes cannot merge with the tail magnetic field lines near the lunar orbit. Especially, the flux rope asymmetrical shape reflects the different reconnection processes that caused it on both sides of the magnetic structure. The events shown in this paper support the multiple X-line magnetic reconnection model for flux ropes with in situ observations.
[1] Examination of Geotail measurements in the near-tail (X > −30 RE) has revealed the presence of small flux ropes in the plasma sheet. A total of 73 flux rope events were identified in the Geotail magnetic field measurements between November 1998 and April 1999. This corresponds to an estimated occurrence frequency of ∼1 flux rope per 5 hours of central plasma sheet observing time. All of the flux ropes were embedded within high-speed plasma sheet flows with 35 directed Earthward, 〈Vx〉 = 431 km/s, and 38 moving tailward, 〈Vx〉 = −451 km/s. We refer to these two populations as “BBF-type” and “plasmoid-type” flux ropes. The flux ropes were usually several tens of seconds in duration, and the two types were readily distinguished by the sense of their quasisinusoidal ΔBz perturbations, i.e., ∓ for the “BBF” events and ± for the “plasmoid” events. Most typically, a flux rope was observed to closely follow the onset of a high-speed flow within ∼1–2 min. Application of the Lepping-Burlaga constant-α flux rope model (i.e., J = αB) to these events showed that approximately 60% of each class could be acceptably described as cylindrical, force-free flux ropes. The modeling results yielded mean flux rope diameters and core field intensities of 1.4 RE and 20 nT and 4.4 RE and 14 nT for the BBF and plasmoid-type events, respectively. The inclinations of the flux ropes were small relative to the GSM X–Y plane, but a wide range of azimuthal orientations were determined within that plane. The frequent presence of these flux ropes in the plasma sheet is interpreted as strong evidence for multiple reconnection X-lines (MRX) in the near-tail. Hence, our results suggest that reconnection in the near-tail may closely resemble that at the dayside magnetopause where MRX reconnection has been hypothesized to be responsible for the generation of flux transfer events.
Data from Cluster are used to study the structure of a flux transfer
event (FTE), seen near the northern cusp. We employ Grad-Shafranov
reconstruction, using measured fields from all four spacecraft to
produce a map of the FTE cross section. The FTE consists of a flux rope
of approximate size 1RE and irregular shape, embedded in the
magnetopause. Its axis $\hat{\bf{z} is tangential to the magnetopause.
Since no reconnection signatures are seen, the map provides a fossil
record of the prior reconnection process that created the flux rope: the
strong core field indicates that it was generated by component merging.
An average reconnection electric field >=0.18 mV/m must have occurred
in the burst of reconnection that created the FTE. The total axial
($\hat{\bf{z}) current and magnetic flux in the FTE were -0.66 MAmp and
+2.07 MWeber, respectively.
An analysis technique, termed MRA (magnetic rotation analysis), has been designed to probe three-dimensional magnetic field topology. It is based on estimating the gradient tensor of four-point measurements of the magnetic field which have been taken by the Cluster mission. The method first constructs the symmetrical magnetic rotation tensor and in general terms deduces the rotation rate of magnetic field along one arbitrary direction. In particular, the maximum, medium, and minimum magnetic rotation rates along corresponding characteristic directions of a magnetic structure can be obtained. The value of the curvature of a magnetic field line, for example, is given by the magnetic rotation rate along the magnetic unit vector and its corresponding radius of curvature is readily obtained. MRA has been applied here to analyze the geometrical structure of two distinct magnetospheric structures, i.e., the tail current sheet and the tail flux rope. The normal of the current sheet is the direction at which the magnetic field has the largest rotation rate. The half thickness of the one-dimensional neutral sheet can also be determined from the reciprocal of the maximum magnetic rotation rate. The advantage of the MRA method is that not only it can determine the orientation but also the internal geometrical configuration and spatial scale of the magnetic structures. A key feature of the MRA method is that it provides the detailed picture of the magnetic rotation point by point through any crossing of the current sheet. As a result, the thickness of the neutral sheet (NS) can be explicitly demonstrated to vary with time, as indicated in one case study, where the NS becomes thicker after the onset of a substorm. MRA has also been applied here to analyze the detailed features of magnetic field variations inside of a flux rope. The principal axis of the flux rope is the direction at which the magnetic field rotates at the least rate. The magnetic scale of the flux rope can also be determined (about 1RE in the case chosen). It is also found that there are both frontside-backside and dawn-dusk asymmetries for the flux rope under study.
An earthward moving plasmoid has been observed on 28 October 2002 by the Cluster spacecraft with simultaneous auroral viewing by the IMAGE satellite. This offers the opportunity to ascertain the optical and the evolutional signatures in the ionosphere of the earthward moving plasmoid. The ionospheric signatures observed in this paper are not substorm-related. Both the ground-based measurements and IMAGE satellite auroral observations show the ionospheric signatures moving to lower latitudes, when the earthward moving plasmoid is observed by the Cluster spacecraft. The intensity of the current in the center of the plasmoid is found to be weaker than that in the adjacent region. Also, the directions of the current in the central part of the plasmoid, different from the background cross-tail current, are more field-aligned. Those facts are consistent with the tail current closes through the substorm-like current wedge, since the cross-tail current is blocked by the plasmoid. On the other hand, the current in the earthward plasmoid may close through the interhemisphere. In this paper we demonstrate that the magnetic structures, plasmoids and flux ropes, will transport flux and energy from the distant tail to the Earth.
Cluster spacecraft were outbound in the northern hemisphere over the pole and entered the cusp. A cusp-like region was observed consecutively three times from 1620 to 1830 UT by all four Cluster Spacecraft although the solar wind dynamic pressure was small and stable. All three cusp encounters were characterized by turbulent magnetic fields, high density plasma and stagnant plasma flow. The cusp region identifications were further confirmed by the clock angle criterion. All three cusps were found to be associated with clear signatures of energetic ions, high He/H and O/H ratios obtained by the RAPID instrument. The observed triple cusps may be either explained as a funnel-shaped cusp trifurcated or swiveled into a complicated geometry in space or as a cusp which shifted back and forth three times in a two hour interval. Observational evidence shows that the observed triple cusps were a temporal sequence rather than a spatial effect. We suggest further that the solar wind azimuthal flow was the controlling factor of the cusp position and was stronger factor than the IMF B Y /B Z components. The importance of the solar wind azimuthal and north/south flow as a dynamic driver of the cusp, and even the whole magnetosphere has been more or less neglected or underestimated.
The THEMIS plasma instrument is designed to measure the ion and electron distribution functions over the energy range from
a few eV up to 30 keV for electrons and 25 keV for ions. The instrument consists of a pair of “top hat” electrostatic analyzers
with common 180°×6° fields-of-view that sweep out 4π steradians each 3 s spin period. Particles are detected by microchannel plate detectors and binned into six distributions
whose energy, angle, and time resolution depend upon instrument mode. On-board moments are calculated, and processing includes
corrections for spacecraft potential. This paper focuses on the ground and in-flight calibrations of the 10 sensors on five
spacecraft. Cross-calibrations were facilitated by having all the plasma measurements available with the same resolution and
format, along with spacecraft potential and magnetic field measurements in the same data set. Lessons learned from this effort
should be useful for future multi-satellite missions.
The THEMIS Fluxgate Magnetometer (FGM) measures the background magnetic field and its low frequency fluctuations (up to 64
Hz) in the near-Earth space. The FGM is capable of detecting variations of the magnetic field with amplitudes of 0.01 nT,
and it is particularly designed to study abrupt reconfigurations of the Earth’s magnetosphere during the substorm onset phase.
The FGM uses an updated technology developed in Germany that digitizes the sensor signals directly and replaces the analog
hardware by software. Use of the digital fluxgate technology results in lower mass of the instrument and improved robustness.
The present paper gives a description of the FGM experimental design and the data products, the extended calibration tests
made before spacecraft launch, and first results of its magnetic field measurements during the first half year in space. It
is also shown that the FGM on board the five THEMIS spacecraft well meets and even exceeds the required conditions of the
stability and the resolution for the magnetometer.
A recently developed technique for reconstructing approximately two-dimensional (?/?z˜0), time-stationary magnetic field structures in space is applied to two magnetopause traversals on the dawnside flank by the four Cluster spacecraft, when the spacecraft separation was about 2000km. The method consists of solving the Grad-Shafranov equation for magnetohydrostatic structures, using plasma and magnetic field data measured along a single spacecraft trajectory as spatial initial values. We assess the usefulness of this single-spacecraft-based technique by comparing the magnetic field maps produced from one spacecraft with the field vectors that other spacecraft actually observed. For an optimally selected invariant (z)-axis, the correlation between the field components predicted from the reconstructed map and the corresponding measured components reaches more than 0.97. This result indicates that the reconstruction technique predicts conditions at the other spacecraft locations quite well.
The optimal invariant axis is relatively close to the intermediate variance direction, computed from minimum variance analysis of the measured magnetic field, and is generally well determined with respect to rotations about the maximum variance direction but less well with respect to rotations about the minimum variance direction. In one of the events, field maps recovered individually for two of the spacecraft, which crossed the magnetopause with an interval of a few tens of seconds, show substantial differences in configuration. By comparing these field maps, time evolution of the magnetopause structures, such as the formation of magnetic islands, motion of the structures, and thickening of the magnetopause current layer, is discussed.
Key words. Magnetospheric physics (Magnetopause, cusp, and boundary layers) – Space plasma physics (Experimental and mathematical techniques, Magnetic reconnection)
This article describes observations of a bursty bulk flow (BBF) in the outer central plasma sheet. The observations are made with the Cluster satellites, located approximately 19 R<sub>E</sub> downtail, close to the midnight sector in the Southern Hemisphere. 40–60 s after Cluster first detected the BBF, there was a large bipolar perturbation in the magnetic field. A Grad-Shafranov reconstruction has revealed that this is created by a field-aligned current at the flank of the BBF. Further analysis of the plasma moments has shown that the BBF has the properties of a depleted flux tube. Depleted flux tubes are an important theoretical model for how plasma and magnetic flux can be transported Earthward in the magnetotail as part of the Dungey cycle. The field aligned current is directed Earthward and is located at the dawn side of the BBF. Thus, it is consistent with the magnetic shear at the flank of an Earthward moving BBF. The total current has been estimated to be about 0.1 MA.
A mathematical treatment of the coupled motion of hydrodynamic flow and electromagnetic fields is given. Two simplifying assumptions are introduced: first, the conductivity of the medium is infinite, and second, the motion is described by a plane shock wave. Various orientations of the plane of the shock and the magnetic field are discussed separately, and the extreme relativistic and unrelativistic behavior is examined. Special consideration is given to the behavior of weak shocks, that is, of sound waves. It is interesting to note that the waves degenerate into common sound waves and into common electromagnetic waves in the extreme cases of very weak and very strong magnetic fields.
We present two models of an array of flux ropes embedded in a Harris neutral sheet. The first solution satisfies the two-dimensional Vlasov-Maxwell equilibrium and is electromagnetically force free. Such a solution is pertinent to a plasma in which beta, the ratio of the thermal pressure to the magnetic pressure, is small. Several features of the model are in excellent agreement with observations of flux ropes in the magnetotail of the Earth. The maximum magnitude of the core field can be larger than the magnitude of the lobe field, BL; the scale length of the individual flux ropes equals the scale length of the current reversal region in the Harris neutral sheet; and the maximum value of the north-south component is less than BL. Magnetotail flux ropes are thought to be isolated structures. Our solution, although periodic in the down-tail direction, is interesting as it provides a consistent description not only of the flux ropes but also of the fields in which they are embedded, a feature that is lacking in other models. We use data from the December 1990 Galileo flyby of Earth and find that the unit cells of the periodic solution are unsatisfactory for the beta~1 conditions of the tail plasma sheet. We then develop a closely related solution valid in the high beta regime that incorporates particle pressure self-consistently and find that the unit cells of this solution provide an excellent fit to the Galileo flux rope observations.
By using the self-consistent stability theory it is shown that during the growth phase of a magnetospheric substorm the stability of the tail configuration decreases. Taking two-dimensionality into account explicitly, we show that the free energy built up during the growth phase can be released when the plasma sheet has become sufficiently thin and/or the normal magnetic field component has been sufficiently reduced. Then the ion-tearing mode will abruptly set in and lead to changes in the magnetic field topology. It is speculated that there is a tendency for a macroscopic neutral line to form fairly close to the earth. Lack of equilibrium will lead to energy dissipation and enhanced precipitation. Spacecraft observations [e.g., Hones et al., 1971; McPherron, 1973; McPherron et al., 1973b] together with ground-based measurements [e.g., Akasofu, 1968] and theoretical considerations [Axford, 1969; Coroniti and Kennel, 1972] have led to considerable progress in the understanding of magnetospheric substorms. It seems possible to order the observations by distinguishing between three phases: a growth phase, an expansion phase initiated by an abrupt 'breakup,' and a recovery phase [e.g., Hones et al., 1970; McPherron, 1970; Aubry, 1972; Coroniti and Kennel, 1972; Hones, 1973; Nishida and Nagayama, 1973]. Although the precise meaning of these phases cannot be regarded as fully understood, in this paper we adopt this picture as a framework for presenting our arguments. Accordingly, we assume that during the growth phase, energy is continuously transferred from the solar wind to the geomagnetic tail, where it is stored. Coroniti and Kennel [1972, 1973] developed a theoretical concept for that process based on field line erosion at the front side, as was suggested by Dungey [ 1961 ]. The cause for the energy transfer is believed to be the presence of a southward component of the interplanetary magnetic field. That picture seems to be consistent with observations made during several individual substorms [McPherron et al., 1973a]. The breakup process, which abruptly initiates the energy release during the expansion phase, however, is not yet clearly identified. Attempts concentrating on the current pattern connecting the magnetosphere with the ionosphere suffer from the lack of a plasma dynamical mechanism that is able to release plasma energy from the near-earth part of the plasma sheet. We emphasize the importance of such a mechanism because its presence seems to be a necessary condition for the sudden onset of the expansion phase if that is directly related to a rapid removal of plasma energy from plasma sheet field lines. This paper aims at identifying the breakup mechanism in the framework of a relatively simple plasma dynamical model [Schindler, 1972; Cole and Schindler, 1972]. The main restrictions are that we neglect any y dependence (-x, y, z are solarmagnetospheric coordinates), together with the y component of the magnetic field, and that we start out from equilibriums for which the pressure tensor is assumed to be isotropic in the Vx, v, plane of velocity space. For most purposes, the two-dimensionality assumption seems reasonable as long as L,
A new technique for recovering magnetic field maps that describe two-dimensional, coherent field structures observed in space is documented, bench-marked, and then applied to four magnetopause crossings by the spacecraft AMPTE/IRM (Active Magnetospheric Particle Tracer Explorers/Ion Release Module) in which the basic observed signatures were those associated with a tangential discontinuity. The calculations required for the recovery consist of the numerical solution of the Grad-Shafranov equation, using as initial values magnetic field and plasma data collected by a single spacecraft along a straight-line trajectory, produced when structures are convected past it. The integration proceeds in small spatial steps in both directions away from the trajectory. The integration domain, which is rectangular, is limited in the transverse direction by the appearance of numerically generated singularities. Nevertheless, the method offers a substantial field of view of the region surrounding the trajectory, within which the accuracy is a few percent. For the magnetopause events examined, it is found that the simple tangential-discontinuity structure is modified by embedded strings of magnetic islands, separated by X-type nulls in the transverse field. These configurations are interpreted as being the result of the tearing mode after it has reached its saturated state. Two or more islands contained within larger islands are observed, indicating that, during the active phase of the tearing mode, the reconnection rate was not the same at all X points. The possibility exists that one dominant X point produces a pair of narrow channels of open flux, connecting the magnetosphere to the magnetosheath. Even without such open flux, the presence of the islands should allow flow of plasma along magnetic field lines, from the outermost (magnetosheath) to the innermost (magnetosphere) parts of the magnetopause current layer, thus facilitating the overall plasma transport across the layer.
We develop a new approach for determining the orientation of the axis (z) of finite-beta magnetic flux ropes from single-spacecraft data. It consists of an optimization procedure based on two-dimensional magnetohydrostatic theory. From the requirement that the transverse pressure, Pt = p + Bz2/2mu0, be a function of the calculated magnetic potential, A, alone, an optimal z axis is found. Benchmark studies using analytical flux rope solutions show the feasibility of this axis-determination approach. Two magnetic cloud events, on 18 October 1995 and 9 January 1997, observed by the Wind spacecraft at 1 AU, are examined. The time series of plasma and magnetic field data, collected when the magnetic structures move past the spacecraft, are utilized as spatial initial values for numerical integration of the nonlinear, plane Grad-Shafranov equation. The recovered magnetic cloud structures show helical magnetic field configurations, representative of magnetic flux ropes, with invariance along their axes. Their cross sections consist of nested irregular loops of transverse field lines rather than the concentric circles of an axially symmetric model. In addition to their axis orientations, we obtain other quantitative features of the two magnetic clouds from their recovered cross sections, including their sizes (diameters ~ 0.2 AU), their impact parameters (|y0|
The behavior of magnetohydrodynamic phenomena associated with disruptions of ohmically heated density limit discharges (qa = 3.9) in the TEXTOR tokamak has been investigated in detail. A minor disruption is demonstrated to be only due to an m = 2 mode instability, possibly due to the magnetic reconnection of an m = 2 island. When the m = 2 mode oscillations cease, the internal m = 1 kink mode instability is drastically enhanced at once, twisting the plasma core considerably. If the twisting is too strong, the twisted plasma core is inevitably displaced to the outside and brings cold plasma to the central region, leading to the energy quench at a major disruption.
We analyze Double Star TC-1 magnetic field data from July to September in 2004 and find that plasmoids exist in the very near-Earth
magnetotail. It is the first time that TC-1 observes the plasmoids in the magnetotail at X > −13 RE. According to the difference of the magnetic field structure in plasmoids, we choose two typical cases for our study: the
magnetic flux rope on August 6 with the open magnetic field and the magnetic loop on September 14 with the closed magnetic
field. Both of the cases are associated with the high speed earthward flow and the magnetic loop is related to a strong substorm.
The ions can escape from the magnetic flux rope along its open field line, but the case of the closed magnetic loop can trap
the ions. The earthward flowing plasmoids observed by TC-1 indicate that the multiple X-line magnetic reconnection occurs
beyond the distance of X=−10 RE from the earth.
The Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission is the fifth NASA Medium-class Explorer
(MIDEX), launched on February 17, 2007 to determine the trigger and large-scale evolution of substorms. The mission employs
five identical micro-satellites (hereafter termed “probes”) which line up along the Earth’s magnetotail to track the motion
of particles, plasma and waves from one point to another and for the first time resolve space–time ambiguities in key regions
of the magnetosphere on a global scale. The probes are equipped with comprehensive in-situ particles and fields instruments
that measure the thermal and super-thermal ions and electrons, and electromagnetic fields from DC to beyond the electron cyclotron
frequency in the regions of interest. The primary goal of THEMIS, which drove the mission design, is to elucidate which magnetotail
process is responsible for substorm onset at the region where substorm auroras map (∼10 RE): (i) a local disruption of the plasma sheet current (current disruption) or (ii) the interaction of the current sheet with
the rapid influx of plasma emanating from reconnection at ∼25 RE. However, the probes also traverse the radiation belts and the dayside magnetosphere, allowing THEMIS to address additional
baseline objectives, namely: how the radiation belts are energized on time scales of 2–4 hours during the recovery phase of
storms, and how the pristine solar wind’s interaction with upstream beams, waves and the bow shock affects Sun–Earth coupling.
THEMIS’s open data policy, platform-independent dataset, open-source analysis software, automated plotting and dissemination
of data within hours of receipt, dedicated ground-based observatory network and strong links to ancillary space-based and
ground-based programs. promote a grass-roots integration of relevant NASA, NSF and international assets in the context of
an international Heliophysics Observatory over the next decade. The mission has demonstrated spacecraft and mission design
strategies ideal for Constellation-class missions and its science is complementary to Cluster and MMS. THEMIS, the first NASA
micro-satellite constellation, is a technological pathfinder for future Sun-Earth Connections missions and a stepping stone
towards understanding Space Weather.