Quadratic Magnetic Gradients from 7-SC and 9-SC Constellations

Abstract. To reveal the dynamics of magnetised plasma, it is essential to know the geometrical structure of the magnetic field, which is closely related to its linear and quadratic gradients. Estimation of the linear magnetic gradient requires at least four magnetic measurements, whereas calculation of the quadratic gradients of the magnetic field generally requires at least ten. This study is therefore aimed at yielding linear and quadratic gradients of the magnetic field based on magnetic measurements from nine-spacecraft HelioSwarm or seven-spacecraft Plasma Observatory constellations. Time-series magnetic measurements and transfer relationships between different reference frames were used to yield the apparent velocity of the magnetic structure as well as the components of the quadratic magnetic gradient along the direction of motion, while simultaneously elucidating the linear gradient and remaining components of the quadratic magnetic gradient using the least-squares method. Calculation via several iterations was applied to achieve satisfactory accuracy. The tests for the situations of magnetic flux ropes and dipole magnetic field have verifies the validity and accuracy of this approach. The results suggest that using time-series magnetic measurements from constellations comprising at least seven spacecraft and nonplanar configurations can yield linear and quadratic gradients of the magnetic field.