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 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.