U. Motschmann’s research while affiliated with Technische Universität Braunschweig and other places

Constructing the dielectric tensor of a beam-component plasma necessarily introduces various kinds of singularities. Here, we present a rational singularity-removal method for constructing the dielectric tensor and solving for the dispersion relation in a cold plasma with beam components. We retain the finite electron mass. The method makes extensive use of the polynomial expression of the dielectric tensor. The wave equation is arranged into a rational expression by removing the singularities and the unphysical modes prior to finding the roots of the equation. The singularity removal method has the advantages that the seed frequency is no longer needed and that all the physically relevant modes are obtained. The method is successfully tested against the right-hand beam instability, in which both single and triple solutions may appear, depending on the beam velocity. The method is also applied to the oblique beam instability, which incorporates the full 3-by-3 dispersion matrix. Our algorithm is computationally inexpensive and can be used as a dispersion solver as well as an instability analysis tool for various setups of beams and instability scenarios.

Mercury shock-upstream region is plasma physically of great interest, as the solar wind plasma may encounter two ion beams, forming a double-beam plasma system. Properties of the double-beam instability are studied semianalytically using the magnetoionic theory (cold plasma waves including beams), such as the unstable mode, the resonance wavenumbers, and the growth rates, for various beam configurations. The cold plasma wave theory supports the idea that both the foreshock ions and the pickup ions can potentially drive the right-hand beam instability, and moreover, the instability may run simultaneously for the two beam species. Further nonlinear wave evolution scenarios are discussed, such as independent parametric instabilities and driven wave–wave couplings causing low-frequency and high-frequency splits of the waves. The double-beam instability is testable against numerical simulations of the plasma waves as well as magnetic field observations by the MESSENGER spacecraft and the upcoming BepiColombo spacecraft.

Context . We use a global 3D hybrid plasma model to investigate the interaction between Mercury’s magnetosphere and the solar wind for the second BepiColombo swingby, evaluate magnetospheric regions, and study the typical energy profile of protons. Aims . The objective of this study is to gain a better understanding of solar wind entry and analyze simulated plasma data along a trajectory using BepiColombo swingby 2 conditions, with the goal of enhancing our comprehension of measurement data and potentially providing forecasts for future swingbys. Methods . To model Mercury’s plasma environment, we used the hybrid code AIKEF and developed a method to extract the particle (ion) data in order to compute the proton energy spectrum along the trajectory of BepiColombo during its second Mercury swingby on June 23, 2022. We evaluate magnetopause and bow shock stand-off distances under average upstream solar wind conditions with the Interplanetary Magnetic Field (IMF) condition derived from the BepiColombo magnetic field measurements during the second Mercury swingby. Results . We found that the magnetosheath on the quasi-perpendicular (dusk) side of the bow shock is thicker than that on the quasi-parallel (dawn) side, where a foreshock is formed. Multiple plasma populations can be extracted from our modeled energy spectra that assist in identifying magnetospheric regions. We observed protons of solar wind origin entering Mercury’s magnetosphere. Their energies range from a few electron volts in the magnetosphere up to 10 keV in the magnetosheath.

Since its launch in 2000, the Cluster fleet visited a vast domain of the circum‐terrestrial environment, from the upstream solar wind and the distant tail, down to the plasmasphere, scanning in detail all magnetospheric regions during over two solar cycles. This led to an unprecedentedly rich data collection of multi‐point measurements which will be used for years to come to decipher the mechanisms of Solar‐Terrestrial interactions. The large volume of data gathered by Cluster requires special strategies to make efficient use of it. To address this issue we constructed a browsable database containing parameters of the detected Ultra low frequency waves and of the spacecraft formation geometry. The primary data used to derive the parameters are the magnetic field, the electric field and the electron density. The data is resampled to a cadence of 1 s and processed using a sliding analysis window of 2,048 s with a step of 256 s over 24 hr intervals. This results in time‐frequency arrays for each parameter covering the 0.5 mHz to 0.5 Hz frequency range. The database is accessible at http://plasma.spacescience.ro/cluster.html. In total there are 47 wave parameters in the database, among them being the ellipticity, the degree of polarization, the (unsigned) wave vector direction, and the Poynting vector. Plots for the planarity, elongation, and degeneration of the Cluster tetrahedron are also available. At the moment, the database covers measurements made between 01 January 2001 and 31 December 2020 with more data being added in time. Here we present this database, discuss the methods used to derive the parameters and give practical examples.

Unambiguous determination of wavevectors (wavelengths and propagation directions) is one of the major challenges of space plasma observations, since conventional wave analysis methods for the single spacecraft data are limited to the time series data analysis and the wave properties are determined as a function of the frequencies in the spacecraft frame. The wave telescope technique overcomes the problem of wavevector determination by making extensive use of the multi‐spacecraft interferometric data. The wave telescope techniques do not assume any wave mode or plasma mode, and is suited to testing for the wave and turbulence theories against the multi‐spacecraft data. This article presents an updated report on the wave telescope technique on the basis of adaptive filtering (Capon's minimum variance projection), the construction of an estimator for the multi‐point magnetic field data, the performance and limits in the wavevector analysis (aliasing and low‐wavenumber behavior), the applications to the Cluster fluxgate magnetometer data (dispersion relations, phase velocity diagrams, propagation pattern, energy spectra, helicities, and higher‐order statistics), and possible extensions of the technique.

Poloidal–toroidal magnetic field decomposition is a useful application of the Mie representation and the decomposition method enables us to determine the current density observationally and unambiguously in the local region of magnetic field measurement. The application and the limits of the decomposition method are tested against the Mercury magnetic field simulation in view of BepiColombo’s arrival at Mercury in 2025. The simulated magnetic field data are evaluated along the planned Mercury Planetary Orbiter (MPO) trajectories and the current system that is crossed by the spacecraft is extracted from the magnetic field measurements. Afterwards, the resulting currents are classified in terms of the established current system in the vicinity of Mercury. Graphical Abstract

The parameterization of the magnetospheric field contribution, generated by currents flowing in the magnetosphere is of major importance for the analysis of Mercury’s internal magnetic field. Using a combination of the Gauss and the Mie representation (toroidal–poloidal decomposition) for the parameterization of the magnetic field enables the analysis of magnetic field data measured in current carrying regions in the vicinity of Mercury. In view of the BepiColombo mission, the magnetic field resulting from the plasma interaction of Mercury with the solar wind is simulated with a hybrid simulation code and the internal Gauss coefficients for the dipole, quadrupole and octupole field are reconstructed from the data, evaluated along the prospective trajectories of the Mercury Planetary Orbiter (MPO) using Capon’s method. Especially, it turns out that a high-precision determination of Mercury’s octupole field is expectable from the future analysis of the magnetic field data measured by the magnetometer on board MPO. Furthermore, magnetic field data of the MESSENGER mission are analyzed and the reconstructed internal Gauss coefficients are in reasonable agreement with the results from more conventional methods such as the least-square fit.

The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.

The magnetometer instrument MPO-MAG on-board the Mercury Planetary Orbiter (MPO) of the BepiColombo mission en-route to Mercury is introduced, with its instrument design, its calibration and scientific targets. The instrument is comprised of two tri-axial fluxgate magnetometers mounted on a 2.9 m boom and are 0.8 m apart. They monitor the magnetic field with up to 128 Hz in a $\pm 2048$ ± 2048 nT range. The MPO will be injected into an initial $480 \times 1500$ 480 × 1500 km polar orbit (2.3 h orbital period). At Mercury, we will map the planetary magnetic field and determine the dynamo generated field and constrain the secular variation. In this paper, we also discuss the effect of the instrument calibration on the ability to improve the knowledge on the internal field. Furthermore, the study of induced magnetic fields and field-aligned currents will help to constrain the interior structure in concert with other geophysical instruments. The orbit is also well-suited to study dynamical phenomena at the Hermean magnetopause and magnetospheric cusps. Together with its sister instrument Mio-MGF on-board the second satellite of the BepiColombo mission, the magnetometers at Mercury will study the reaction of the highly dynamic magnetosphere to changes in the solar wind. In the extreme case, the solar wind might even collapse the entire dayside magnetosphere. During cruise, MPO-MAG will contribute to studies of solar wind turbulence and transient phenomena.

The fluxgate magnetometer MGF on board the Mio spacecraft of the BepiColombo mission is introduced with its science targets, instrument design, calibration report, and scientific expectations. The MGF instrument consists of two tri-axial fluxgate magnetometers. Both sensors are mounted on a 4.8-m long mast to measure the magnetic field around Mercury at distances from near surface (initial peri-center altitude is 590 km) to 6 planetary radii (11640 km). The two sensors of MGF are operated in a fully redundant way, each with its own electronics, data processing and power supply units. The MGF instrument samples the magnetic field at a rate of up to 128 Hz to reveal rapidly-evolving magnetospheric dynamics, among them magnetic reconnection causing substorm-like disturbances, field-aligned currents, and ultra-low-frequency waves. The high time resolution of MGF is also helpful to study solar wind processes (through measurements of the interplanetary magnetic field) in the inner heliosphere. The MGF instrument firmly corroborates measurements of its companion, the MPO magnetometer, by performing multi-point observations to determine the planetary internal field at higher multi-pole orders and to separate temporal fluctuations from spatial variations.