3D Nonlinear MHD modelling studies: Plasma Flow and Realistic Magnetic Boundary Impact on Magnetic self-organisation in Fusion Plasmas

The reversed-field pinch (RFP) is a toroidal device for the magnetic confinement of a fusion plasma, similar to the tokamak but with a relatively stronger induced plasma current. RFP plasmas are subject to various relaxation processes, the most macroscopic of which, the kink and the tearing modes, are suitably described in a fluid-dynamics framework called magneto-hydrodynamics (MHD). In the past two decades a new enhanced-confinement scenario has been experimentally demonstrated for the RFP. This is known as “Quasi Single Helicity” (QSH) state and consists in the intermittent dominance of a single Fourier mode over the rest of the magnetic spectrum, generating a significant part of the magnetic field through a self-organised electrostatic dynamo effect. QSH states can be stimulated by resonant edge magnetic perturbations or they can emerge as a spontaneous self-organisation when the plasma current exceeds 1 MA. Advanced numerical modelling has traditionally played a key role in the study of this process, and indeed the spontaneous helical states in the RFP were found to form in nonlinear MHD simulations even before their experimental observation. However, some features of the experimentally observed spontaneous and systematic emergence of QSH states with a certain preferential toroidal periodicity still lack of a fully self-consistent quantitative predictability. Past studies performed with the 3D nonlinear MHD simulations code SpeCyl suggest that a key role is played by the interplay between the plasma and its magnetic boundary. For this reason the past decade marked a consistent endeavour towards the implementation of more realistic boundary conditions (BCs) in SpeCyl. First qualitative experimental-like QSH states could be reproduced by implementing a fixed magnetic perturbation at plasma boundary, on the top of the traditional formulation, featuring an ideal wall in direct contact with the plasma. At the beginning of my PhD, an effort to model the boundary as a thin resistive shell had already started and was awaiting to be completed and carefully validated. The main goal of my PhD research was the formulation, implementation in SpeCyl, and verification of a realistic set of BCs, representing a resistive shell in contact with the plasma, and surrounded by a vacuum region and an ideal wall placed at finite tuneable distance, along with a realistic description of the edge flow. This is very a general set-up, of interest for various magnetic configurations, that allows to reproduce a full range of experimental conditions, from the previous ideal-wall limit to a free plasma-vacuum interface. My work was articulated in several steps: 1) in-depth study of the linear theory of current-driven MHD instabilities, along with the implementation of a linear-stability numeric tool to provide a reliable benchmark for SpeCyl; 2) careful analysis of the SpeCyl code and of its existing BCs (the ideal-wall and the resistive-shell formulations) and characterisation against the linear MHD theory. This made possible to reveal critical inconsistencies in the thin-shell BCs, motivating a major reframe in the modelling of the velocity boundary; 3) formulation and implementation of the new BCs (thin-shell, surrounding vacuum and outer ideal wall, realistic 3D edge flow). This required the implementation of an original deconvolution technique, to deal with the 3D velocity BCs in the spectral code SpeCyl; 4) nonlinear verification of the new BCs module against the independent 3D nonlinear MHD code Pixie3D, and verification benchmark against the linear MHD theory of external kink instabilities. The excellent results obtained in both verification studies clearly demonstrate the correctness of the implementation of the new SpeCyl’s BCs and motivate future validation studies against real experimental data from the RFX-mod device and its next upgrade RFX-mod2.