Polynomial Reconstruction of the Reconnection Magnetic Field Observed by Multiple Spacecraft

Denton, R. E.; Torbert, R. B.; Hasegawa, Hiroshi; Dors, I.; Genestreti, K. J.; Argall, M. R.; Gershman, D. J.; Contel, O. Le; Burch, J. L.; Russell, C. T.; Strangeway, R. J.; Giles, B. L.; Fischer, D.

doi:10.1029/2019ja027481

Cited by 50 publications

(138 citation statements)

References 43 publications

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“…This leads to neglect of other terms, as described in more detail by Denton et al. (2020). The resulting model is

B_{l} = B_{l, 0} + \frac{\partial B_{l}}{\partial n} n + \frac{\partial B_{l}}{\partial l} l + \frac{\partial B_{l}}{\partial m} m + \frac{\partial^{2} B_{l}}{\partial n^{2}} \frac{n^{2}}{2}

B_{m} = B_{m, 0} + \frac{\partial B_{m}}{\partial n} n + \frac{\partial B_{m}}{\partial l} l + \frac{\partial B_{m}}{\partial m} m + \frac{\partial^{2} B_{m}}{\partial n^{2}} \frac{n^{2}}{2} + \frac{\partial^{2} B_{m}}{\partial n \partial l} n l + \frac{\partial^{2} B_{m}}{\partial l^{2}} \frac{l^{2}}{2}

B_{n} = B_{n, 0} + \frac{\partial B_{n}}{\partial n} n + \frac{\partial B_{n}}{\partial l} l + \frac{\partial B_{n}}{\partial m} m + \frac{\partial^{2} B_{n}}{\partial l^{2}} \frac{l^{2}}{...}

…”

Section: Methodsmentioning

confidence: 99%

“…With Equation 9, there are a total of 25 equations that can be used to solve for 17 parameters for a best least squares fit. A more detailed description of the method is given by Denton et al (2020). Figure 2 shows the results of MDD and Minimum Gradient Analysis (MGA), both applied to the vector magnetic field (Shi et al, 2019).…”

Section: Reduced Quadratic Polynomial Reconstruction Modelmentioning

confidence: 99%

“…Denton et al. (2020) described a number of variations of Torbert and coworker's method and tested the validity of the magnetic field model during times in which the magnetic structure was roughly two dimensional. In this study, we will use Denton and coworker's Reduced Quadratic model that results from the assumption that λ 1 ≫ λ 2 ≫ λ 3 , where λ i are the eigenvalues of Minimum Directional Derivative (MDD) analysis that determines the eigenvectors of the gradient of the vector magnetic field (Shi et al., 2005).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two‐Dimensional Velocity of the Magnetic Structure Observed on July 11, 2017 by the Magnetospheric Multiscale Spacecraft

et al. 2021

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In magnetic reconnection, plasma flows toward the magnetic X line (a magnetic null in the reconnection plane, in which it appears as an X point) with an inflow velocity and is accelerated and ejected in an orthogonal direction with an outflow velocity because of the large curvature of the magnetic field in the vicinity of the X line (e.g., Sonnerup, 1979; Vasyliunas, 1975). To determine these velocities, one needs to determine the frame of reference in which the X line is stationary. Thus an important part of the process of understanding a magnetic reconnection event is to determine the velocity of the magnetic structure relative to the observing spacecraft. Although on large scales, plasma may be "frozen in" to the magnetic field, at least in directions perpendicular to the magnetic field, this is typically not the case on small scales close to the X line, especially in the region known as the electron diffusion region (Hesse et al., 2011, 2014). Shi et al. (2019) has reviewed methods to determine a coordinate system and magnetic structure velocity. Methods to determine the velocity include calculating the deHoffmann-Teller frame in which the electric field is approximately zero, various types of timing analysis, various reconstruction methods, and the Spatial-Temporal Difference (STD) method (Shi et al., 2006). STD has been used by Denton et al. (2016a, 2016b) and Yao et al. (2016, 2018) to determine the time-dependent velocity of a magnetic structure in the normal direction. Alm et al. (2017) used STD to calculate the time-dependent two-dimensional velocity of the spacecraft moving through a structure of ion-scale magnetopause flux ropes. Manuzzo et al. (2019)

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“…This leads to neglect of other terms, as described in more detail by Denton et al. (2020). The resulting model is

B_{l} = B_{l, 0} + \frac{\partial B_{l}}{\partial n} n + \frac{\partial B_{l}}{\partial l} l + \frac{\partial B_{l}}{\partial m} m + \frac{\partial^{2} B_{l}}{\partial n^{2}} \frac{n^{2}}{2}

B_{m} = B_{m, 0} + \frac{\partial B_{m}}{\partial n} n + \frac{\partial B_{m}}{\partial l} l + \frac{\partial B_{m}}{\partial m} m + \frac{\partial^{2} B_{m}}{\partial n^{2}} \frac{n^{2}}{2} + \frac{\partial^{2} B_{m}}{\partial n \partial l} n l + \frac{\partial^{2} B_{m}}{\partial l^{2}} \frac{l^{2}}{2}

B_{n} = B_{n, 0} + \frac{\partial B_{n}}{\partial n} n + \frac{\partial B_{n}}{\partial l} l + \frac{\partial B_{n}}{\partial m} m + \frac{\partial^{2} B_{n}}{\partial l^{2}} \frac{l^{2}}{...}

…”

Section: Methodsmentioning

confidence: 99%

Section: Reduced Quadratic Polynomial Reconstruction Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two‐Dimensional Velocity of the Magnetic Structure Observed on July 11, 2017 by the Magnetospheric Multiscale Spacecraft

et al. 2021

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show abstract

“…The polynomial reconstruction 13,44 recovers 3-D magnetic fields in and around the tetrahedron formed by the four spacecraft from instantaneous measurements by the four spacecraft of the magnetic field and particle current density. Several versions 13 In this study, we used the 3-D reduced quadratic (RQ-3D) model 13 in which less significant parts of the quadratic terms and higher-order terms are neglected. For 3-D fields, the calculation of magnetic flux inside a magnetic island (Fig.…”

Section: Polynomial Reconstructionmentioning

confidence: 99%

“…The other is a multi-spacecraft method based on polynomial (second-order Taylor) expansion of the magnetic field that can recover three-dimensional (3-D) magnetic field using instantaneous measurements by the four spacecraft of the magnetic field and particle current density, called the polynomial reconstruction 13 . (Fig.…”

mentioning

confidence: 99%

Magnetic-field annihilation and island formation in electron-scale current sheet in Earth's magnetotail

Hasegawa

Denton

Genestreti

et al. 2020

Preprint

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Establishing the mechanism of magnetic-to-particle energy conversion through magnetic reconnection in current sheets1 is the key to understanding the impact of fast release of magnetic energy in many space and astrophysical plasma systems, such as during magnetospheric substorms2,3. It is generally believed that an electron-scale diffusion region (EDR), where a magnetic-to-electron energy conversion occurs, has an X-type magnetic-field geometry4 around which the energy of anti-parallel magnetic fields injected is mostly converted to the bulk-flow energy of electrons by magnetic tension of reconnected field-lines5,6. However, it is at present unknown exactly how this energy conversion occurs in EDRs, because there has been no observational method to fully address this problem. Here we present state-of-the-art analysis of multi-spacecraft observations in Earth’s magnetotail of an electron-scale current sheet, which demonstrates that contrary to the standard model of reconnection with an X-type EDR geometry, the fast energy conversion in the detected EDR was caused mostly by magnetic-field annihilation, rather than reconnection. Furthermore, we detected a magnetic island forming in the EDR itself, implying that the EDR had an elongated shape ideal for island generation7 and magnetic-field annihilation. The experimental discovery of the annihilation-dominated EDR reveals a new form of energy conversion in the reconnection process that can occur when the EDR has evolved from the X-type to planar geometry.

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Two-dimensional velocity of the magnetic structure observed on 11 July 2017 by the Magnetospheric Multiscale spacecraft

Denton

Torbert

Genestreti

et al. 2020

Preprint

View full text Add to dashboard Cite

In magnetic reconnection, plasma flows toward the magnetic X line (a magnetic null in the reconnection plane, in which it appears as an X point) with an inflow velocity and is accelerated and ejected in an orthogonal direction with an outflow velocity because of the large curvature of the magnetic field in the vicinity of the X line (e.g., Sonnerup, 1979;Vasyliunas, 1975). To determine these velocities, one needs to determine the frame of reference in which the X line is stationary. Thus an important part of the process of understanding a magnetic reconnection event is to determine the velocity of the magnetic structure relative to the observing spacecraft. Although on large scales, plasma may be "frozen in" to the magnetic field, at least in directions perpendicular to the magnetic field, this is typically not the case on small scales close to the X line, especially in the region known as the electron diffusion region (Hesse et al., 2011(Hesse et al., , 2014. Shi et al. (2019) has reviewed methods to determine a coordinate system and magnetic structure velocity. Methods to determine the velocity include calculating the deHoffmann-Teller frame in which the electric field is approximately zero, various types of timing analysis, various reconstruction methods, and the Spatial-Temporal Difference (STD) method (Shi et al., 2006). STD has been used by Denton et al. (2016aDenton et al. ( , 2016b and Yao et al. (2016Yao et al. ( , 2018 to determine the time-dependent velocity of a magnetic structure in the normal direction. Alm et al. ( 2017) used STD to calculate the time-dependent two-dimensional velocity of the spacecraft moving through a structure of ion-scale magnetopause flux ropes. Manuzzo et al. (2019)

show abstract

Polynomial Reconstruction of the Reconnection Magnetic Field Observed by Multiple Spacecraft

Cited by 50 publications

References 43 publications

Two‐Dimensional Velocity of the Magnetic Structure Observed on July 11, 2017 by the Magnetospheric Multiscale Spacecraft

Two‐Dimensional Velocity of the Magnetic Structure Observed on July 11, 2017 by the Magnetospheric Multiscale Spacecraft

Magnetic-field annihilation and island formation in electron-scale current sheet in Earth's magnetotail

Two-dimensional velocity of the magnetic structure observed on 11 July 2017 by the Magnetospheric Multiscale spacecraft

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