11:40 AM - 11:55 AM
[PEM09-11] Development of a novel method for extracting the geometrical properties of the magnetic vector fields towards the era of multi-point satellite observations
Keywords:formation flight of satellites, Multi-point observation of magnetic field, magnetic gradient tensor
We propose a new method for analyzing the evolution of a geomagnetic fields that enables us to extract the geometrical properties of the magnetic vector fields towards the era of multi-point satellite observations
In general, geometrical properties of magnetic fields (B-fields) can be represented by divergence and/or convergence of magnetic flux tube, gradient of magnetic flux density, curvature, and twist of magnetic field lines. Such geometries can be reconstructed from a dyadic tensor of B-field gradients that represents various spatial gradients of magnetic field components in a three-dimensional space. Furthermore, change of B-field can be characterized by a change of magnetic flux-density and a change of direction of B-field.
When a satellite cruse in space with finite velocity in the rest frame, the time-hysteresis of measured magnetic fields by this satellite includes contribution from a Euler differentiation of B-field at the satellite position in the rest frame and the change of B-field when the satellite moves across an inhomogeneous B-field region. In general, it is impossible to separate these two contributions from single satellite observation. To successfully measure the spatial gradients of B-field, we need an appropriate formation fright composed of multiple satellites. A formation flight composed of 4-satellites have already realized in the Cluster and the MMS missions and is a minimum configuration that enable to deduce a spatial gradient of B-field in the 3D system.
In this paper, we provide a methodology that derive the dyadic tensor of B-field in the triangular cone formed by 4-satellites, of which components describe averaged characteristic of spatial gradients of B-field. By using this methodology, we can extract the Euler differentiation of B-field at the centroid position of formation flight. This technique can be easily applied to formation flights of more than four satellites.
We also derive a novel expression of B-field development equation under any Ohm’s law, which explicitly describes what type of plasma motion causes B-field development in the parallel and perpendicular direction to B-field. The former part corresponds to the development of magnetic flux density and the latter part corresponds to the changing ratio of B-field direction. By comparing extracted Euler differentiation of B-field from observational data and results deduced from new formulation, we can identify cause and results of B-field development under an arbitrary Ohm’s law. Application to the MHD’s Ohm’s law will be discussed in the presentation.
In general, geometrical properties of magnetic fields (B-fields) can be represented by divergence and/or convergence of magnetic flux tube, gradient of magnetic flux density, curvature, and twist of magnetic field lines. Such geometries can be reconstructed from a dyadic tensor of B-field gradients that represents various spatial gradients of magnetic field components in a three-dimensional space. Furthermore, change of B-field can be characterized by a change of magnetic flux-density and a change of direction of B-field.
When a satellite cruse in space with finite velocity in the rest frame, the time-hysteresis of measured magnetic fields by this satellite includes contribution from a Euler differentiation of B-field at the satellite position in the rest frame and the change of B-field when the satellite moves across an inhomogeneous B-field region. In general, it is impossible to separate these two contributions from single satellite observation. To successfully measure the spatial gradients of B-field, we need an appropriate formation fright composed of multiple satellites. A formation flight composed of 4-satellites have already realized in the Cluster and the MMS missions and is a minimum configuration that enable to deduce a spatial gradient of B-field in the 3D system.
In this paper, we provide a methodology that derive the dyadic tensor of B-field in the triangular cone formed by 4-satellites, of which components describe averaged characteristic of spatial gradients of B-field. By using this methodology, we can extract the Euler differentiation of B-field at the centroid position of formation flight. This technique can be easily applied to formation flights of more than four satellites.
We also derive a novel expression of B-field development equation under any Ohm’s law, which explicitly describes what type of plasma motion causes B-field development in the parallel and perpendicular direction to B-field. The former part corresponds to the development of magnetic flux density and the latter part corresponds to the changing ratio of B-field direction. By comparing extracted Euler differentiation of B-field from observational data and results deduced from new formulation, we can identify cause and results of B-field development under an arbitrary Ohm’s law. Application to the MHD’s Ohm’s law will be discussed in the presentation.