Analysis of sawtooth simulations in the Compact Toroidal Hybrid (CTH) experiment

Sawtooth oscillations in tokamaks and current-carrying stellarators display a gradual temperature rise in the core followed by a fast crash. In the Kadomtsev model [1], the crash is due to a linear mode that is triggered as the on-axis safety factor drops below unity. The Compact Toroidal Hybrid (CTH) device is a current-carrying five field period torsatron in which a variable external rotational transform enables the study of the influence of 3D magnetic fields on MHD stability. Here, we analyze 3D non-linear NIMROD sawtooth simulations for a CTH-like scenario [2]. A new fixed points finder implementation in NIMROD enhances the description of sawtooth cycles. Fixed points result from the intersection of a closed magnetic field line with a Poincare cross-section; they constitute the skeleton of the magnetic field structure. The implementation allows for the determination of Greene's residues [3], which can serve to estimate an island width and have also been used to measure the degree of stochasticity of stellarator vacuum magnetic fields [4]. In this work, the determination of order-1 fixed points, Greene's residues, and local values for the rotational transform lead to a description of sawtooth oscillations in CTH consistent with the Kadomtsev model. Finally, to explore the distribution of energy among the Fourier modes and the quasilinear and non-linear interactions during sawtooth cycles, we have expanded the Ho and Craddock [5] power transfer analysis to a 3D equilibrium.

[1] B. B. Kadomtsev, Soviet J. Plasma Phys. 1, 389 (1975).

[2] 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).

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

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

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