Nonlinear Staturation of Ballooning Modes in Stellarators*

Stellarators are claimed to be able to sustain higher pressure gradients than linear MHD stability predictions. It is therefore of interest to investigate the nonlinear MHD stability constraints by studying the nonlinear dynamical state of ideal MHD ballooning modes, which is believed to be characterized by isolated flux tubes[1]. 

In this work, previous results by Ham, et. al.[2] on the stability and saturation of such flux tubes in tokamaks were extended to stellarators. Tools based on the DESC[3] equilibrium solver were developed to calculate the saturated state of the perturbed flux tubes in general stellarator equilibrium configurations. Benchmarks against saturated states in tokamaks and linear dynamics in both tokamaks and stellarators have been performed. Saturated states of such flux tubes have been found in stellarators (particularly in NCSX equilibrium) on flux surfaces where it's ballooning unstable or close to ballooning unstable. For those linearly stable flux tubes, it is possible for them to be metastable, i.e. having a nonlinear equilibrium state with lower energy. Qualitative difference of the saturated states compared with those in tokamaks has been observed. Further studies of these meta-stable flux tubes will be performed to relate to the nonlinear MHD stability of stellarators.

[1] S. C. Cowley, et. al., Proc. R. Soc. A, 20140913 (2015)

[2] C. J. Ham, et. al., Plasma Phys. Control. Fusion, 075017 (2018)

[3] D. W. Dudt, E. Kolemen, Physics of Plasmas 27, 102513 (2020)