Abstract: In laboratory plasmas, instabilities play a prominent role in predicting and explaining the governing dynamics. But also on much larger scales throughout the Universe, plasma instabilities crucially shape and drive many fascinating phenomena. This talk will introduce two important MHD instabilities in astrophysical plasmas, going from the Sun to black hole accretion disks, and recent progress in their understanding. We first focus on the thermal instability in the solar corona, which is responsible for the formation of cool prominences that are suspended like clouds in the solar atmosphere. These are worthwhile to study since they can erupt and be launched towards Earth, but understanding their formation relies heavily on the unsolved coronal heating problem. We then cover generalisations of the magneto-rotational instability, which drives the turbulent dynamo in accretion disks of all sizes. Mathematical techniques from fusion research have proven invaluable to study disk stability, but current research on non-axisymmetric instabilities is stirring up the dust on what was thought to be a long-solved problem.
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