Astrofysische Instabiliteit in Flux Ropes en Accretieschijven

Instability. This word often has a negative connotation, signifying exponential growth spiraling out of control. But instability also drives change and is behind many fascinating phenomena in astrophysics. This PhD thesis explores two quite different astrophysical instabilities. The first part of the thesis focuses on the thermal instability in the Sun's atmosphere (corona) -- driving the formation of cool clouds. We investigate how the interplay between heating and cooling in the corona leads to the formation of prominences, large, dense clouds suspended by the magnetic field structure, e.g. a twisted flux rope. We perform non-linear 2.5D simulations (2D simulations with the full three-component vectors) to determine the effect of assuming various heating models for the solar corona. Quantifying the different outcomes in terms of prominence characteristics is important since a definitive coronal heating model does not exist. We furthermore introduce a method to take the 3D shape of flux ropes into consideration in 2D simulations, for which we traced the flux rope during runtime. In the second and largest part of the thesis, we study generalisations of the magneto-rotational instability in accretion disks -- driving angular momentum transport. Accretion disks, rotating disks of plasma around objects like black holes or young stars, lose mass to the central object quite fast. The most likely explanation is that disks are turbulent, and that stresses induced by turbulent eddies generate some effective viscosity that slows down some parts of the fluid and speeds up other parts. The likely source of turbulence covered in this thesis are linear instabilities thriving on magnetic fields convected in differentially rotating flows. We use numerical and analytical methods to study the spectra of linear operators that determine the reaction of plasmas in the fluid approximation to small perturbations. The focus is in particular on a recently described non-axisymmetric instability in global disk models with surprising properties, and its implications for instability in various disk equilibria, from weakly to strongly magnetised field topologies. After exploring these modes using visualisations, we provide some pointers to how to bridge the gap between these new modes and the currently accepted view on accretion disk instability.