* The Properties of Resistive Mhd Modes and Unstable Spectra in Advanced Tokamak Regimes

M. Coste-Sarguet; J. P. Graves

Advanced tokamak regimes, featuring extended regions of low magnetic shear, are promising candidates for future fusion reactors but are also more prone to specific kinds of MHD instabilities. The proximity to a rational surface in a very low shear region weakens field line bending stabilisation and amplifies the effects of toroidal coupling between modes, leading to the emergence of long-wavelength resistive infernal modes. These modes can grow collectively as a discrete spectrum, leading to a cascade of different perturbations for single mode numbers (m, n), with subdominant modes showing increasingly oscillatory radial structures. These spectra of fast-growing modes are significant for developing stable scenarios in future reactors, and for the understanding of global reconnection events like sawteeth, motivating a deeper investigation into their fundamental physics. Deriving new analytic solutions, including a generalisation of the ideal interchange dispersion relation to non monotonic q profiles, and extending a modular linear resistive MHD solver, we investigate how resistivity, compressibility, toroidal effects, and shaping influence stability, especially in reversed shear q profiles. It is also shown that common assumptions in numerical calculations prevent the observation of the full variety of modes present in these advanced scenarios.

DOI : 10.1088/1361-6587/ae23fc

* Fundamental properties of ideal and resistive infernal modes in tokamaks

M. M. Y. Coste-Sarguet; J. P. Graves

Infernal modes are unstable in regions of weak magnetic shear and significant pressure gradients. These modes comprise a broad class of instabilities, encompassing interchange modes and kink modes, with both short and long length scales. Toroidal effects and fully electromagnetic fields are of crucial importance for their description. The role of resistive diffusion and compressibility are also critical. In order to investigate this awkward problem while still enabling fundamental physics interpretation, a new resistive MHD eigensolver has been developed. An outcome of this study is the identification of an unstable spectrum of resistive infernal modes in regions of the plasma with weak average curvature, and in regions where the average curvature is destabilising. These fast growing modes may be collectively important for our understanding of global reconnection events, stochastic magnetic fields states, and neighbouring supercritical bifurcations.

DOI : 10.1088/1361-6587/ad5ff2

* Pressure driven long wavelength MHD instabilities in an axisymmetric toroidal resistive plasma

J. P. Graves; M. Coste-Sarguet; C. Wahlberg

A general set of equations that govern global resistive interchange, resistive internal kink and resistive infernal modes in a toroidal axisymmetric equilibrium are systematically derived in detail. Tractable equations are developed such that resistive effects on the fundamental rational surface can be treated together with resistive effects on the rational surfaces of the sidebands. Resistivity introduces coupling of pressure driven toroidal instabilities with ion acoustic waves, while compression introduces flute-like flows and damping of instabilities, enhanced by toroidal effects. It is shown under which equilibrium conditions global interchange, internal kink modes or infernal modes occur. The m = 1 internal kink is derived for the first time from higher order infernal mode equations, and new resistive infernal modes resonant at the q = 1 surface are reduced analytically. Of particular interest are the competing effects of resistive corrections on the rational surfaces of the fundamental harmonic and on the sidebands, which in this paper is investigated for standard profiles developed for the m = 1 internal kink problem.

DOI : 10.1088/1361-6587/ac3496

* Core MHD instabilities and their spectra in advanced tokamak regimes: ideal and resistive physics

M. M. Y. Coste-Sarguet

Advanced tokamak regimes, featuring extended regions of low magnetic shear, are promising candidates for future fusion reactors (record breaking DT pulses at JET in hybrid mode) but are also more prone to specific MHD instabilities. The proximity to a rational surface in a very low shear region weakens field line bending stabilisation and amplifies the effects of toroidal coupling between modes, leading to the emergence of long-wavelength ideal or resistive infernal modes. These modes can grow collectively as a discrete spectrum, leading to a cascade of different perturbations for single mode numbers (m, n). Subdominant modes with lower growth rates have distinct radial structures, oscillating more (they can be characterized by Bessel functions). These spectra of fast-growing modes are significant for developing stable scenarios for future reactors, and for the understanding of global reconnection events like sawteeth, motivating a deeper investigation into their fundamental physics. Considering resistive diffusion, compressibility, toroidal effects, and shaping, we explore in this thesis the critical regions and parameters which influence the linear stability of advanced tokamak regimes. To do so, we start from an analytic model, which provides a unified and global description of pressure and current driven internal instabilities, in an inverse aspect ratio expansion. The first part of the thesis details the main steps of this derivation and presents an extension to include some flux surface shaping effects. We then develop a new resistive modular MHD eigensolver based on this analytical description. This tool is introduced and verified across various ideal and resistive configurations in the early part of the thesis. The main results are then divided into ideal and resistive chapters, with the ideal part featuring mainly analytical derivations, which are checked against the solver, in order to verify newly established theoretical stability criteria. The impact of using reduced MHD models is assessed for various types of instabilities. For non-resonant monotonic $q$ profiles, we derive an analytic dispersion relation with higher-order corrections in $q-q_s$, providing a more accurate description of a non-resonant kink mode spectrum with $q_s=1$. In the presence of resonance, for $q_s<1$, the modular solver allows us to identify a novel resistive spectrum of infernal modes, with quite high linear growth rate values even for the subdominant modes. We also extend the dispersion relation to include flux surface shaping, and we find that shaping significantly influences the mode spectrum behaviour. Using the modular solver, we discover that even for $q_s=1$, a spectrum of unstable infernal modes can emerge, due to the combined effect of resistivity and negative triangularity. Finally, we also study non-monotonic $q$ profiles. Using the solver, we examine different strengths of shear reversal and study the transition between double tearing and resistive infernal behaviour as the pressure increases. On the analytical side, we extend the interchange dispersion relation to these non-monotonic $q$ profiles, yielding a compact expression to assess stability in shaped equilibria with reversed shear.