Why is it hard to generate 3D MHD equilibria with smooth nested flux-surfaces ?

This talk was given at the 4th Asian-Pacific Conference on Plasma Physics on October 28 2020. I am sharing it here because it provides a rapid introduction to the business of MHD equilibria calculation. Abstract Renewed interest in stellarator design has sparked questions on the existence and accessibility of three-dimensional magneto-hydrodynamics (MHD) equilibria with “good” nested flux-surfaces. Several numerical tools exist to obtain three-dimensional MHD equilibria. These methods aspire to

Elasticae and Stellarators

Motivation Stellarators are weird-looking fusion devices. The reason is that ions and electrons are better confined when the magnetic field is “twisting” around the centre-line of the device called the magnetic axis. In tokamaks, the vacuum field generated by the evenly-positioned toroidal field coils is somewhat “flat”, as shown on the figure below. In order to generate twisting, a strong toroidal plasma current (in red in the figure below) is

A billion trillion “clashes” make a plasma

A systematic treatment of microscopic collisions to extend fluid models of plasmas At the microscopic level, binary collisions between charged particles conserve two fundamental quantities, namely momentum and energy. This conservation must be present in fluid models in order to describe the macroscopic evolution of plasmas correctly. A systematic treatment of collisional effects is presented to derive fluid models beyond the usual assumption of “thermal equilibrium”. Such extended models will