The effect of parallel magnetic field fluctuations on pressure driven MHD instabilities in toroidal plasmas

Analytic derivation and numerical calculation of pressure driven MHD instabilities in toroidal plasmas is notoriously difficult. Instability is determined by apparently weak effects in the toroidal metric tensor. There are now new generations of gyro-kinetic codes that are being deployed to model MHD instabilities. Some of these codes are, or have been, only partially electromagnetic. It is usually assumed that the perturbed vector potential is parallel to the equilibrium field (so that the perturbed parallel magnetic field is nearly zero), although in some codes an imposed effective adiabatic parallel magnetic field is adopted. Similar such reduced models are also assumed in some non-linear MHD codes deployed for the study of edge localised modes. These codes also sometimes approximate the equilibrium toroidal magnetic field, by neglecting the magnetic well associated with fine pressure. The present contribution, offered in detail in Ref. [1], investigates the impact of code-relevant models for the parallel magnetic field and the equilibrium magnetic field on pressure driven instabilities in axisymmetric toroidal equilibria.