Method for Approximating Field-Line Curves Using Ionospheric Observations of Energy-Variable Electron Beams Launched From Satellites

Using electron beam accelerators attached to satellites in Earth orbit, it may be possible to measure arc length and curvature of field-lines in the inner magnetosphere if the accelerator is designed with the capability to vary the beam energy. In combination with additional information, these measurements would be very useful in modeling the magnetic field of the inner magnetosphere. For this purpose, a three step data assimilation modeling approach is discussed. The first step in the procedure would be to use prior information to obtain an initial forecast of the inner magnetosphere. Then, a family of curves would be defined that satisfies the observed geometric attributes measured by the experiments, and the prior forecast would then be used to optimize the curve with respect to the allowed degrees of freedom. Finally, this approximation of the field-line would be used to improve the initial forecast of the inner magnetosphere, resulting in a description of the system that is optimally consistent with both the prior information and the measured curvature and arc length. This article details the method by which a family of possible approximations of the field-line may be defined via a numerical procedure, which is central to the three step approach. This method serves effectively as a pre-conditioner for parameter estimation problems using field-line curvature and arc length measurements in combination with other measurements.