Spatial gradients from irregular, multiple‐point spacecraft configurations

Shen, Chao; Rong, Zhaojin; Dunlop, M. W.; Ma, Y. H.; Li, X.; Zeng, Gang; Yan, Guoguo; Wan, Weixing; Liu, Z. X.; Carr, C.; Rème, H.

doi:10.1029/2012ja018075

Cited by 37 publications

(81 citation statements)

References 36 publications

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“…As pointed by Vogt et al [], with three point magnetic measurements, the current density can be obtained as if the direction of the current is known. As shown in Figure a, the current density j n deduced from THEMIS three‐point analysis has an angle α from j φ (also see Shen et al [] for example). Therefore, j φ can be calculated by | j φ | = | j n |/cos α , where cos α = ê n ⋅ ê φ ( ê n is the unit vectors along the normal to the spacecraft plane).…”

Section: Methodsmentioning

confidence: 97%

“…The approach for calculating the current density with three spacecraft measurements follows Shen et al []. For three THEMIS measurements of magnetic field B α at the positions r α ( α = 1, 2, 3), the magnetic field and position at the mesocenter are

B_{normalc normali} = \frac{1}{3} true {true\sum}_{α = 1}^{3} B_{α i}

and

r_{normalc normali} = \frac{1}{3} true {true\sum}_{α = 1}^{3} r_{α i}

( i = 1, 2, 3), respectively.…”

Section: Methodsmentioning

confidence: 99%

“…It is convenient to make the calculations in the coordinates of the eigenvectors of the volume tensor. The gradient of the magnetic field projected onto the eigenvectors can be calculated by the following formula [ Shen et al , ]

\nabla_{l} B_{i} = \frac{1}{3 w_{l}} true \underset{α}{true\sum} B_{α i} r_{α l}, l, i = 1, 2, 3,

…”

Section: Methodsmentioning

confidence: 99%

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Storm time current distribution in the inner equatorial magnetosphere: THEMIS observations

et al. 2016

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For the first time, the current density distribution in the inner equatorial magnetosphere ranging from 4 to 12 RE (RE is the Earth radius, 6371 km) has been obtained by using Time History of Events and Macroscale Interactions during Substorms (THEMIS) (P3, P4, and P5) three point magnetic measurements. This study mainly focuses on the storm events when the constellation of the three THEMIS spacecraft has relatively small separation distance. Two cases with different storm activities are first displayed to illustrate the effectiveness of the method. The inner magnetospheric equatorial current distribution ranging from 4 to 12 RE is shown through statistical analysis. The features of current density are separately analyzed for the storm main phase and the recovery phase. The statistical study reveals that with increasing radial distance the predominant ring current density reverses from Eastward (below r = 4.8 RE, where r is the geocentric radial distance) to Westward, but that the distribution behaves differently for the two phases of activity. During the main phase, both the westward and eastward current are enhanced by added signal and are more dynamic so that both radial profile and magnetic local time (MLT) structure is obscured. During the recovery phase, the radial profile of the westward current is smooth and peaks, then falls, between r = 5–7.5 RE showing some MLT dependence in this region. Beyond r = 7.5 RE, the current is lower and nearly constant and shows little MLT variation. The results also suggest that the change from eastward to westward current depends on the storm phase and hence storm activity.

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Section: Methodsmentioning

confidence: 97%

B_{normalc normali} = \frac{1}{3} true {true\sum}_{α = 1}^{3} B_{α i}

and

r_{normalc normali} = \frac{1}{3} true {true\sum}_{α = 1}^{3} r_{α i}

( i = 1, 2, 3), respectively.…”

Section: Methodsmentioning

confidence: 99%

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Storm time current distribution in the inner equatorial magnetosphere: THEMIS observations

et al. 2016

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“…In 2007 two of four Cluster spacecraft were very close to each other (in comparison with distances to another pair of spacecraft). Thus, the Cluster tetrahedron was close to triangle with the corresponding problems of estimations of magnetic field gradients (Dunlop et al, 2002;Shen et al, 2012). In 2008 and 2009 we observe only few cases of flapping CSs (maybe due to evolution of spacecraft orbit).…”

Section: Data Set and Analysis Techniquesmentioning

confidence: 98%

Current sheet flapping in the near-Earth magnetotail: peculiarities of propagation and parallel currents

et al. 2016

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Abstract. We consider series of tilted current sheet crossings, corresponding to flapping waves in the near-Earth magnetotail. We analyse Cluster observations from 2005 to 2009, when spacecraft visited the magnetotail neutral plane near X ∈ [−17, −8], Y ∈ [−16, −2] R E (in the GSM system). Large separation of spacecraft allows us to estimate both local and global properties of flapping current sheets. We find significant variation in flapping wave direction of propagation between the middle tail and flanks. Th series of tilted current sheets represent the system of periodic, almost parallel currents with typical thickness of current filaments about L = 0.4 R E . The earthward gradients of B z magnetic field are reduced within this current system in comparison with the gradients in the quiet near-Earth magnetotail. The wavelength (i.e. a distance between two crossings of current sheets with the same orientations) of the flapping waves is larger than 2π L for most of observations. The velocity of flapping wave propagation is about ion bulk velocity and is significantly lower than the velocity of ion drift relative to electrons. We discuss possible drivers of flapping and estimate the amplitude of the total parallel current generated by flapping waves.

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“…In addition, we described the shape of the structures in the elongation‐planarity diagram introduced by Harvey [] for tetrahedron geometric factors of Cluster constellation. These geometric factors are essential in studying spatial gradients, calculated with the use of the volumetric tensor [ Shen et al , ]. Elongation E and planarity P are defined as

E = 1 - b / a,

P = 1 - c / b,

where a, b , and c and a > b > c are the volumetric tensor eigenvalues that in our analysis have been substituted by the structure sizes along three eigenvectors of the covariance matrix of equation .…”

Section: Analysis Of Spacecraft Measurementsmentioning

confidence: 99%

Determination of the shape and orientation of nonlinear magnetic structures measured by Cluster spacecraft in the vicinity of the bow shock

et al. 2016

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We present a new method of determination of the size and the orientation of nonlinear electromagnetic structures observed in space plasmas. The method is based on the analysis of covariance matrix of gradients of fields estimated from multipoint spacecraft measurements. It does not make use of Taylor hypothesis and gives fully three‐dimensional estimates without assuming any symmetries of the structures. The method has been tested first on synthetic data and then applied to four‐point Cluster spacecraft measurements to determine geometrical properties of nonlinear electromagnetic structures observed in the vicinity of the bow shock. These structures comprise ULF waves that steepen to form shocklets (short large‐amplitude magnetic structures) in the foreshock region and large‐amplitude mirror mode structures observed in the magnetosheath downstream of the bow shock. In the case of foreshock ULF waves we find the three‐axis structure sizes of 1000, 3000, and 7000 km oriented to the ambient field at angles of 75, 30, and 60°, respectively. For the mirror modes our results give sizes of 150, 300, and 700 km oriented at angles close to the perpendicular direction for the shortest and middle scales and parallel orientation for the longest scale. The estimated geometry and properties of analyzed nonlinear structures follow, in general, those obtained previously.

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Spatial gradients from irregular, multiple‐point spacecraft configurations

Cited by 37 publications

References 36 publications

Storm time current distribution in the inner equatorial magnetosphere: THEMIS observations

Storm time current distribution in the inner equatorial magnetosphere: THEMIS observations

Current sheet flapping in the near-Earth magnetotail: peculiarities of propagation and parallel currents

Determination of the shape and orientation of nonlinear magnetic structures measured by Cluster spacecraft in the vicinity of the bow shock

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