The magnetosheath is a transition layer surrounding the planetary magnetosphere. We develop an algorithm to compute the plasma flow velocity and magnetic field for a more general shape of magnetosheath using the concept of potential field and suitable coordinate transformation. Application to the empirical Earth magnetosheath region is shown in the paper. The developed algorithm is useful when interpreting the spacecraft data or simulation of the planetary magnetosheath region.

The upper detection limit in reciprocal space, the spatial Nyquist limit, is derived for arbitrary spatial dimensions for the wave telescope analysis technique. This is important as future space plasma missions will incorporate larger numbers of spacecraft (>4). Our findings are a key element in planning the spatial distribution of future multi-point spacecraft missions. The wave telescope is a multi-dimensional power spectrum estimator; hence, this can be applied to other fields of research.

Magnetopause is a shielding boundary of planetary magnetic field. Many mathematical models have been proposed to describe or to reproduce the magnetopause location, but they are restricted to the real-number functions. In this work, we analytically develop a magnetopause model in the complex-number domain, which is advantageous in deforming the magnetopause shape in a conformal (angle-preserving) way, and is suited to compare different models or map one model onto another.

Revealing the nature of Mercury’s internal magnetic field is one of the primary goals of the BepiColombo mission. Besides the parametrization of the magnetic field contributions, the application of a robust inversion method is of major importance. The present work provides an overview of the most commonly used inversion methods and shows that Capon’s method as well as the Tikhonov regularization enable a high-precision determination of Mercury’s internal magnetic field up to the fifth degree.

The Capon method serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. Besides the analysis of waves, the method can be used in a generalized way to compare actual measurements with theoretical models, such as Mercury's magnetic field analysis. In view to the BepiColombo mission this work establishes a mathematical basis for the application of Capon's method to analyze Mercury's internal magnetic field in a robust and manageable way.