34 / 2021-04-13 23:40:52

Sawtooth simulations in the Compact Toroidal Hybrid (CTH) experiment

stellarators,sawtooth,Greene's residue

Sawtooth oscillations in tokamaks and current-carrying stellarators are characterized by a slow rise in the core temperature with a subsequent fast crash, and the latter is attributed to a growing mode driven when the safety factor on the magnetic axis (q₀) drops below one. The Compact Toroidal Hybrid (CTH) experiment is a current-carrying five field period torsatron (N_fp = 5) in which a variable external rotational transform enables the study of the impact of 3D magnetic fields on MHD stability. In this work, we reconsider 3D non-linear NIMROD simulations of sawtooth oscillations in a CTH-like configuration [1]. A recent Greene’s residue [2] implementation permits a detailed description of the sawtooth cycles. Greene’s residues are defined for fixed points: the intersection of a closed magnetic field line with a 2D surface, such as a Poincaré cross-section. In view that a small Greene’s residue for the center of a magnetic island monotonically increases with its width, this quantity has been employed as a proxy for the degree of stochasticity of stellarator vacuum magnetic fields [3]. In regards to sawtooth simulations, this diagnostic facilitates the accurate tracking of both the original magnetic axis and the center of the growing magnetic island during the reconnection process that converts the latter into a new magnetic axis. Moreover, to explore the distribution of energy among the Fourier modes, we have expanded the Ho & Craddock [4] power transfer analysis to a 3D equilibrium. This diagnostic highlights the difference the n=N_fp−1 and n=N_fp+1 modes play in the saturation of the dominantly n = 1 internal kink.



[1] N. A. Roberds, L. Guazzotto, J. D. Hanson, J. L. Herfindal, E. C. Howell, D. A. Maurer, and C. R. Sovinec, Phys. Plasmas 23, 092513 (2016).

[2] J. H. Greene, J. Math. Phys. 20, 1183 (1979).

[3] J. R. Cary and J. D. Hanson, Phys. Fluids 29, 2464 (1986).

[4] Y. L. Ho and G. G. Craddock, Physics of Fluids B: Plasma Physics 3, 721 (1991).



This work was supported by the U.S. DOE Grant No. DE-FG02-03ER54692 and DE-SC0018313.