Reduced modelling for dynamic inversion of magnetic field observations at planets

Die Wechselwirkung eines planetaren Magnetfeldes mit dem Sonnenwind ruft elektrische Ströme hervor, die die Magnetfeldverteilung am Planeten beeinflussen. In dieser Arbeit werden Methoden vorgestellt, mit denen der planetare Anteil des Magnetfeldes mit Raumfahrzeugdaten aus der Planetenumgebung bestimmt und die Prozesse der Interaktion analysiert werden können. So lässt sich mit der kommenden BepiColombo-Mission das intrinsisch erzeugte Magnetfeld von Merkur schätzen. Zunächst wird die Wechselwirkung über einen magnetohydrodynamischen (MHD) Simulationscode berechnet, wobei das Magnetfeld des Planeten über Parameter in das Modell eingeht. Eine Schätzung dieser Parameter erfolgt durch Minimierung der Abweichungen zwischen den Modelllösungen und Raumfahrzeugmessungen. Für die effiziente Berechnung vieler Parameter wird die Anwendung eines adjungierten Modells untersucht. Eine Bestimmung des Erdmagnetfeldes mit THEMIS-Daten aus der Magnetosheath validiert das Schätzverfahren im Rahmen statistischer und systematischer Fehler. Über eine Reihenentwicklungsmethode werden reduzierte MHD-Modelle hergeleitet, um mit einem geschätzten planetaren Magnetfeld die Wechselwirkungsprozesse zu analysieren. Die Modelle beschreiben die wichtigsten Prozesse in der Magnetosheath, wie ein Anstauen des Sonnenwindmagnetfeldes, magnetische Diffusion und Rekonnexion. Mit den Ergebnissen lässt sich der magnetische Diffusionsparameter des Plasmas schätzen. Weiterhin wird der Einfluss einer Inhomogenität in der Leitfähigkeitsverteilung auf die Bedingungen für Stoßwellen und die damit zusammenhängende Ausbreitungsgeschwindigkeit von Wellen betrachtet. Die Ergebnisse der reduzierten Modelle zeigen, dass der Simulationscode einen zu großen numerischen Diffusionsparameter benötigt, welcher die Schätzung des planetaren Magnetfeldes systematisch verfälscht. Mit einem reduzierten Modell lässt sich aus Daten nahe der Stagnationslinie eine verbesserte Schätzung durchführen. Um den statistischen Fehler zu minimieren, kann mit den reduzierten Modellen eine zeitaufwendige simultane Schätzung von planetaren Magnetfeld- und Sonnenwindparametern durchgeführt werden, wenn sich zwei Raumfahrzeuge innerhalb der Wechselwirkungsregion befinden. Weiterhin lässt sich durch eine Projektionsabbildung die Gültigkeit der reduzierten Modelle von der Stagnationslinie auf das Gebiet der MHD-Simulation erweitern.The interaction of a planetary magnetic field with the solar wind causes electrical currents which modify the magnetic field distribution around the planet. In this thesis, models are developed with respect to the upcoming BepiColombo mission which can be used to precisely estimate the planetary magnetic field of Mercury from the time-dependent measurements. First, the interaction is calculated using a magnetohydrodynamic simulation which depends on the parameters of the planetary magnetic field. These parameters are estimated by minimizing the misfit of the model and the spacecraft observations in the interaction region using a gradient based minimization algorithm. To perform this time-consuming procedure for a large number of planetary magnetic field parameters, an adjoint model of the interaction is derived and investigated. The estimation procedure is applied to THEMIS data of the magnetosheath to estimate the earth's magnetic field. Therefore, reduced models are derived to understand and improve the model of the interaction. These models are based on a series expansion procedure and describe the most important processes of the interaction such as the magnetic pile-up of the solar wind magnetic field in front of the magnetopause, magnetic diffusion, and reconnection. Furthermore, analytical approximations of the solutions are derived. Among others, the results are used to estimate the parameter of the magnetic diffusion at the subsolar point of the magnetopause. Additionally, it is shown that a nonuniform electrical conductivity can cause shocks and modify the speed of wave propagation in the plasma. The results of the reduced models indicate that a large numerical diffusion parameter required by the simulation produces errors which lead to a systematic error in the estimation of the planetary magnetic field. Using a reduced model, the interaction close to the stagnation streamline can be calculated quickly without magnetic diffusion and the systematic error. This model can also be used to perform the time-consuming estimation of solar wind and planetary magnetic field parameters simultaneously, if two spacecraft are in the interaction region. A transformation is introduced to extend the results of the reduced model to the domain of the magnetohydrodynamic simulation

The THEMIS Mission (http://themis.ssl.berkeley.edu/data/themis/)

The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment

Estimation of a planetary magnetic field using a reduced magnetohydrodynamic model

Knowledge of planetary magnetic fields provides deep insights into the structure and dynamics of planets. Due to the interaction of a planet with the solar wind plasma, a rather complex magnetic environment is generated. The situation at planet Mercury is an example of the complexities occurring as this planet’s field is rather weak and the magnetosphere rather small. New methods are presented to separate interior and exterior magnetic field contributions which are based on a dynamic inversion approach using a reduced magnetohydrodynamic (MHD) model and time-varying spacecraft observations. The methods select different data such as bow shock location information or magnetosheath magnetic field data. Our investigations are carried out in preparation for the upcoming dual-spacecraft BepiColombo mission set out to precisely estimate Mercury’s intrinsic magnetic field. To validate our new approaches, we use THEMIS magnetosheath observations to estimate the known terrestrial dipole moment. The terrestrial magnetosheath provides observations from a strongly disturbed magnetic environment, comparable to the situation at Mercury. Statistical and systematic errors are considered and their dependence on the selected data sets are examined. Including time-dependent upstream solar wind variations rather than averaged conditions significantly reduces the statistical error of the estimation. Taking the entire magnetosheath data along the spacecraft’s trajectory instead of only the bow shock location into account further improves accuracy of the estimated dipole moment

Estimating a planetary magnetic field with time-dependent global MHD simulations using an adjoint approach

The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment

Der Konflikt in Afghanistan : Historischer und gesellschaftlicher Hintergrund, Evolution und Lageentwicklung – ein Positionspapier

This study is part of a larger project, the aim of which is to elucidate “mental health nurses” attitudes towards their patients'. In this study, nurses' and patients' attitudes are described from the perspective of both parties using a qualitative approach. The informants were selected from a rehabilitation unit for young adults, below 40, suffering from psychosis at a psychiatric clinic that provides acute psychiatric care. The informant group consisted of three dyads: three patients with various diagnoses and three nurses with primary responsibility for the patients' daily care. The aim of this particular study was to extend our preliminary understanding of nurses' attitudes towards psychiatric patients in the context of psychiatric in-patient care, by elucidating the patient's “inner” picture of her/his past, present and future and the nurse's picture of the same patient's past, present and future. Data were collected and analysed using a phenomenological-hermeneutic approach and the narrative picturing technique. For each picture and group, 15 related sub-themes emerged, on the basis of which six themes were formulated. The findings show that the nurses overrate their own importance when it comes to the patient's well-being on the ward. All the nurses emphasize confirmation and safety as the basis of their nursing care, while in the patient's picture the nurses represent a replication of childhood demands, which probably means that nursing care risks becoming a continuation of the patient's childhood estrangement

Statistical survey of day-side magnetospheric current flow using Cluster observations: magnetopause

We present a statistical survey of current structures observed by the Cluster spacecraft at high-latitude day-side magnetopause encounters in the close vicinity of the polar cusps. Making use of the curlometer technique and the fluxgate magnetometer data, we calculate the 3-D current densities and investigate the magnetopause current direction, location, and magnitude during varying solar wind conditions. We find that the orientation of the day-side current structures is in accordance with existing magnetopause current models. Based on the ambient plasma properties, we distinguish five different transition regions at the magnetopause surface and observe distinctive current properties for each region. Additionally, we find that the location of currents varies with respect to the onset of the changes in the plasma environment during magnetopause crossings