Investigation of changes induced in the MHD spectrum by the presence of magnetic islands/stochastic regions with the SIESTA 3D MHD equilibrium code

SIESTA [1] is a well known 3D MHD equilibrium solver that is capable of finding ideal MHD equilibrium solutions without assuming the existence of nested toroidal magnetic surfaces everywhere in the plasma volume. As a result, SIESTA solutions that exhibit both magnetic islands and stochastic regions are possible. In addition, SIESTA uses Eulerian coordinates in which the pressure and magnetic field response to arbitrary plasma displacement can be easily calculated. SIESTA also estimates the local Hessian of the problem (i..e, the derivative of the force with respect to the local displacement) at each step of its nonlinear iteration towards equilibrium since it is often used as preconditioner for the linear problem that must be solve at each step. Once the equiilibrium is reached, the Hessian is available and the study of its eigenvalues/eigenvectors allows to explore and quantify the ideal MHD stability properties of the reached solution. In this work we will use this capability to characterise the changes that are induced in the MHD ideal spectrum, with respect to that of neighbouring solutions that assume nested tori everywhere, by the presence of islands/stochastic regions, their size and location, for both tokamak and stellarator configurations. [1] Hishman SP, Sanchez R and Cook, CR. Physics of Plasmas 18, 062504 (2011).