Our second contribution (joint work with L. Päivärinta and M. Salo) is extending a recent result on non-existence of non-scattering energies for potentials with rectangular corners to arbitrary corners of angle smaller than 180 degrees in two dimensions, and to prove in three dimensions that the set of strictly convex circular conical corners for which non-scattering energies might exist is at most countable.

]]>In this thesis, the internal structure of flux rope CMEs and their three-dimensional evolution in the interplanetary space were investigated using the combination of white-light and extreme ultraviolet observations and in-situ measurements and modeling. The results of the analysis show that a typical flux rope CME consists of regions of physically different plasma with the flux rope occupying one of them. The methodology for studying the evolution of the individual flux rope in three-dimensional space is described. The presented technique is used to show that solar flux ropes experience significant deflections and rotations during their propagation from the Sun to the Earth's orbit that have to be taken into account for reliable space weather forecasting. These structures deflect predominantly towards the solar equatorial plane and their rotations are affected by the solar wind streams. It is discovered that 40 per cent of the flux rope evolution happens after 30 solar radii.

Flux-rope-like structures can also form in the magnetosphere during the periods of geomagnetic disturbances. They are generated in the magnetotail configurations with multiple reconnection sites and travel towards the Earth or away from it. Both types of these helical magnetic structures are addressed in this thesis as well. It is demonstrated that the properties of these structures help to get insight into the dynamics of the magnetosphere. The model of evolution of earthward-traveling flux ropes is presented, according to which they deteriorate and degrade into dipolarization fronts, another magnetic field configuration that is characteristic for geomagnetic disturbances.

This thesis contributes both to the improvement of the flux rope analysis techniques as well as conducts a comprehensive analysis of solar and magnetospheric flux ropes and their evolution. The results of the research advance our understanding of the Sun-Earth coupling in one dynamical process and can be used for improving the space weather forecasting tools.

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