Fascinating aspects of magneto-hydrostatics

The talk outlines some fascinating aspects of magnetic confinement in fusion devices and the challenges involved in understanding and controlling the behaviour of magnetic fields. The layout of magnetic field-lines in a fusion device determines the confinement of particles. Qualitatively, the less chaotic the field-lines, the less heat and particles fusion devices will lose. Fusion research typically assumes that magnetic fields conform to nested toroidal flux-
surfaces. A conjecture by Grad in the 1960s suggested that nested surfaces could only exist if the system demonstrated symmetry under rotations about the z-axis (axisymmetry). That the well-posedness of magneto-hydrostatics (MHS) remains unchecked leaves the possibility for unattainable or untameable solutions. Numerical simulations are nevertheless remarkably convincing in accuracy and fidelity, and fusion devices (stellarators) displaying outstanding confinement properties have been built, and hopefully continue to be improved.
This presentation will delve into the mathematical intricacies of magnetic fields, the strange properties of solutions to the force-balance equation, the deep relationship between symmetries and nested flux-surfaces, and the main obstacles to proving/invalidating Grad’s conjecture.