Invariant tori (flux surfaces) reside in the ordered regions of phase space of a dynamical system and represent the well-confined region of a magnetic confinement fusion (MCF) device, which may be threatened in non-axisymmetric cases such as tokamaks under resonant magnetic perturbation and stellarators. In MCF devices, the structure of nested closed flux surfaces governs radial transport and thus plays a critical role in confinement performance. Using the method of variation as a mathematical foundation (the vector field itself as a spatial function is considered as an argument of the geometry of these tori), this paper derives the formulae that describewhich can calculate the deformation in tens of seconds for stellarator configuration optimisation by Julia programming language without delicate hardware acceleration and almost instantly for tokamaks.
This paper examines how the well-confined regions (flux surfaces) in magnetic confinement fusion (MCF) devices can be affected by non-axisymmetric perturbations. It provides a mathematical framework to calculate the deformation of these flux surfaces, which is crucial for optimizing stellarator configurations and understanding tokamak performance.