Ideal MHD stability of internal kinks in circular and shaped tokamaks

Abstract

Stability limits for the internal kink mode are calculated for tokamaks with different current profiles and plasma cross-sections using ideal magnetohydrodynamics (MHD). The maximum stable poloidal beta at the q = 1 surface (0,) is sensitive to the current profile, but for circular cross-sections it is typically between 0.1 and 0.2. Large aspect ratio theory gives similar predictions when the appropriate boundary conditions are applied at the plasma-vacuum surface. It is found that the internal kink is significantly destabilized by ellipticity. For JET geometry, the ideal MHD limit in 0, is typically between 0.03 and 0.1, and arbitrarily low limits can result if the shear is reduced at the q = 1 surface. A large aspect ratio expansion of the Mercier criterion retaining the effects of ellipticity and triangularity is used to illustrate the destabilizing influence of ellipticity.

Physics Analysis of the FIRE Experiment

“…[6] for the various terms but have modified the coefficients by comparing them with the more exact results obtained by PEST and NOVA-K. We find that the Porcelli expression for ˆf ast W δ needs to be multiplied by √2 to get agreement with NOVA-K for this geometry. The PEST calculations shows the importance of calculating the ˆm hd W δ with the correct wall boundary condition, consistent with [8]. When the sawtooth is predicted to be triggered, we modify the transport coefficients in two ways.…”

Compressible magnetohydrodynamic sawtooth crash

“…10 Compressional effects also appear in the linear ideal 20 and resistive 29 internal kinks, as confirmed by many numerical solutions. [49][50][51][52] They become increasingly important nonlinearly.…”

XTOR-2F: A fully implicit Newton–Krylov solver applied to nonlinear 3D extended MHD in tokamaks

“…For this purpose, we use as initial conditions an equilibrium provided by the CHEASE code [25,26] which is unstable towards such an instability (the low shear q-profile in Ref. [27,28]). The internal kink mode is a good test case because it shifts quickly the plasma core away from the discretization mesh center, which is rather demanding numerically.…”