The fine print of the magneto-hydrostatics problem

The conjecture by Grad, namely that equilibrium solutions to the magneto-hydrodynamics equations featuring nested toroidal pressure surfaces (and non-recurrent field-lines) can only exist in the presence of symmetry by isometry, is a splinter in the design and optimization of magnetic confinement fusion devices. That the well-posedness of magneto-hydrostatics (MHS) remains unchecked leaves the possibility for unattainable or untameable solutions. The numerical results from various tools are nevertheless remarkably convincing in accuracy and fidelity, and stellarators displaying outstanding confinement properties have been built, and hopefully continue to be improved. To agree on the “fine print” of the MHS problem, namely the explicit and implicit assumptions made to guarantee the desired properties of solutions, David Pfefferlé will review the relationship between magneto-hydrostatics (MHS) states, the existence of symmetries and the availability of straight field-line coordinates. Pfefferlé will delve into peculiar/pathological examples that may occur when detail in assumptions is omitted. In the process, Pfefferlé will highlight a range of robust techniques to analyze magnetic fields.