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Publication# Exploration of the parameter space for the excitation and saturation of Edge Harmonic Oscillations

Abstract

This thesis presents advancements in the understanding of the plasma conditions leading to the excitation and saturation of the Edge Harmonic Oscillations (EHOs) observed during QH-mode operation in tokamak plasmas. Such operations represent a safer alternative with respect to H-mode due to the absence of Edge Localised Modes (ELMs) while retaining high energy confinement and pedestal height. In this work, EHOs have been assumed to be the nonlinear evolution of linearly unstable external infernal (exfernal) modes. It is consistently found that exfernal modes can be excited and nonlinearly saturated in wide regions of the parameter space. Such regions have been identified through the use of various analytical and numerical tools developed within the ideal MHD model, including linear analytical modelling, linear stability software, and nonlinear equilibrium and initial value simulations. An expanded set of large aspect ratio equations describing the linear stability of exfernal modes is derived analytically, including higher order terms in the expansion of the safety factor around the rational surface, which allows for the effects of finite edge magnetic shear. Numerical solution of the equations provides the linearly unstable exfernal mode parameter space with respect to pedestal pressure gradient, pedestal width, edge safety factor and edge magnetic shear. Nonlinearly saturated exfernal modes calculated with the 3D VMEC free boundary code are found in regions of the parameter space where the exfernal modes are linearly unstable to the 2D VMEC neighbour state. The obtained critical value of the edge magnetic shear in the VMEC simulations is also recovered by the linear stability analysis. The parameter space is found to be reduced by the presence of a plasma separatrix due to a partial stabilisation of the external kink current-driven branch of the exfernal mode. An analytical estimation of the critical magnetic shear for the excitation of exfernal modes in diverted plasmas is also presented. Finally, it is shown that the parameter space for the saturation of external modes can be expanded through the application of non-axisymmetric Magnetic Perturbations (MPs). This is done analytically using a linear time-invariant perturbation of the 2D equilibrium assuming an external helical magnetic perturbation, and also in the VMEC code by the inclusion of non-axisymmetric coils in the calculation of the vacuum field. The approaches were applied to saturated external kink and exfernal modes. For the external kink case, quantitative agreement is found in the saturated amplitude obtained with the linear model and with the VMEC code for cases where the external kink is stable in the absence of MPs. For the case of saturated exfernal modes, only qualitative agreement is found, possibly due to the approximations taken in the calculation of the analytical model. Nevertheless, a significant expansion of the parameter space of saturated exfernal modes is obtained via the introduction of symmetry breaking coils, resulting in an appealing route for future reactor operations.

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Ontological neighbourhood

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Plasma stability

The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. In many cases, a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics (MHD).

Tokamak

A tokamak (ˈtoʊkəmæk; токамáк) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power. , it was the leading candidate for a practical fusion reactor. Tokamaks were initially conceptualized in the 1950s by Soviet physicists Igor Tamm and Andrei Sakharov, inspired by a letter by Oleg Lavrentiev. The first working tokamak was attributed to the work of Natan Yavlinsky on the T-1 in 1958.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

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