Stability of a high-beta, large-aspect-ratio, toroidally rotating tokamak plasma by the Spectral-Web-Method

Macroscopic flows are present during routine tokamak operation and have been the subject of plenty of theoretical work. In particular, stability magnetohydrodynamic studies can be carried out through the Lagrangian description for the plasma displacement proposed by Frieman and Rotenberg [1]. In this work, we build upon an analytic solution [2] of the Grad-Shafranov-Bernoulli system for plasma equilibrium with a linearly increasing toroidal flow profile, in the high-beta, large-aspect-ratio limit for circular and elliptical configurations. By simplifying the eigenvalue problem into a second order, non-linear, ordinary differential equation for the radial displacement first, we then employ the Spectral-Web formalism [3] to conduct a stability analysis of external modes developed in the presence of ideal and resistive walls. The results generalize the rigid body toroidal rotation scenario considered in Betti’s work [4] and are benchmarked against it.

[1] E. Frieman and M. Rotenberg. Rev. Mod. Phys., 32, 898 (1960)
[2] O. E. López and L. Guazzotto, Phys. Plasmas, 24, 032501 (2017)
[3] J. P. Goedbloed. Phys. Plasmas, 16, 122110 (2009)
[4] R. Betti. Phys. Plasmas, 5, 3615 (1998)