Field Gradient Analysis Based on a Geometrical Approach

Using multi‐point observations from a spacecraft constellation, the spatial gradients of measured physical quantities can be calculated, and thus other derived parameters for the plasma (e.g., current density, topology of magnetic field lines, and wave vectors) can also be calculated. In this resear...

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Bibliographic Details
Published in:Journal of geophysical research. Space physics Vol. 128; no. 6
Main Authors: Shen, C., Dunlop, M.
Format: Journal Article
Language:English
Published: Washington Blackwell Publishing Ltd 01.06.2023
Subjects:
curl
divergence
Error analysis
Estimators
integral theorem
Interpolation
linear gradient of physical quantity
Magnetic fields
Mathematical analysis
Spacecraft
spacecraft constellation measurement
Tetrahedra
Theorems
Topology
truncation error
ISSN:2169-9380, 2169-9402
Online Access:Get full text
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Summary:Using multi‐point observations from a spacecraft constellation, the spatial gradients of measured physical quantities can be calculated, and thus other derived parameters for the plasma (e.g., current density, topology of magnetic field lines, and wave vectors) can also be calculated. In this research, a geometrical method based on integral theorems has been applied to deduce estimators of the linear gradients of various fields based on constellation measurements. Integral forms are best suited to the particular case of four‐point measurements and indeed using this geometrical approach, it is very easy to derive the field gradients for observations made by a planar constellation (e.g., as defined by three spacecraft). It is verified here that the method based on integral theorems and the method based on spatial interpolation are equivalent for deriving formulas for the gradients. An error analysis found that the accuracy of the estimators is very high and enters at the second order of the tetrahedron size. This makes the estimates, derived from the integral approach rather stable. Key Points Obtain the estimators of field gradients for 4‐spacecraft constellation observations by using integral theorems at second‐order accuracy Verify that the gradient calculation method based on integral theorems and the method based on spatial interpolation are equivalent Easily derive the estimators of the field gradients for planar constellations with the integral theorems
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ISSN:2169-9380
2169-9402
DOI:10.1029/2023JA031313