# Browsing by Subject "Tearing modes"

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Item Microtearing modes in the tokamak pedestal(2022-06-24) Larakers, Joseph Leland; Hazeltine, R. D. (Richard D.); Mahajan, Swadesh; Fitzpatrick, Richard; Morrison, PhilipShow more An economical thermonuclear reactor has the potential to serve as an on-demand, clean, and abundant energy source. The main difficulty is confining the fusion fuel to the large pressures required for the fuel to react. The energy produced from fusion reactions must be collected and confined such that it activates further reactions. Magnetic confinement is a promising strategy. Magnetic confinement devices, such as tokamaks, have steadily improved by identifying and suppressing different mechanisms of heat transport and instability. This dissertation focuses on a single mechanism known as the microtearing mode (MTM). The microtearing mode is an electromagnetic excitation that is localized about rational magnetic surfaces and is driven unstable by electron temperature gradients. The mode tears magnetic surfaces and modifies their structure. The resulting topology relaxes the radial temperature gradient via fast parallel motion. The MTM has recently gained attention as a potentially important instability in the pedestal region of H-mode tokamaks. It is theorized to be responsible for the anomalous electron heat transport and discrete bands of magnetic fluctuations observed experimentally. Here, we revisit the conventional microtearing theory and extend it to study features pertinent to the pedestal region. In doing so, we identify a new crucial parameter for MTM linear stability. This extended theory matches with the experimental observations of magnetic fluctuations and provides an explanation of their discrete nature. With an understanding of the linear dispersion characteristics, we proceed to study the nonlinear evolution of the mode. The dispersion suggests a strong mode-mode resonance between MTM harmonics. A weak turbulence model has been developed to study the nonlinear consequences of these resonances.Show more Item Tearing mode dynamics in tokamak plasmas(2016-05) Vergos, Nikolaos; Fitzpatrick, Richard, 1963-; Hazeltine, Richard; Breizman, Boris; Waelbroeck, Francois; Hallock, GaryShow more One of the most problematic instabilities in tokamak plasmas is tearing modes; they are driven by current and pressure gradients, and involve a reconfiguration of the magnetic and velocity fields localized into a narrow region located at a resonant magnetic surface. While the equilibrium magnetic field lines are located on concentric nested toroidal flux surfaces, the instability creates magnetic islands in which field lines connect flux tubes together, allowing for a high radial heat transport, and, thus, resulting in a loss of confinement, and, potentially, disruptions. In order for the magnetic field lines to break and reconnect, we need to take into account the resistivity of the plasma and solve the resistive magnetohydrodynamics (MHD) equations. The analytical solution consists of a boundary layer analysis (asymptotic matching) and takes advantage of the small radial width of the region where the perturbations vary significantly. Indeed, ideal magnetohydrodynamics can be used everywhere except in that narrow region where the full resistive problem must be solved. This dissertation addresses two related problems in the study of resistive tearing modes, and their interactions with externally induced resonant magnetic perturbations (error-fields). First, an in-depth investigation of the bifurcated states of a rotating, quasi-cylindrical, tokamak plasma in the presence of a resonant error-field is performed, within the context of constant-ψ resistive MHD theory. The response of the rotating plasma is studied in both the linear, and the nonlinear regime. In general, there is a "forbidden band" of tearing mode rotation frequencies that separates a branch of high-frequency solutions from a branch of low-frequency solutions. When a high-frequency solution crosses the upper boundary of the forbidden band there is a bifurcation to a low-frequency solution, and vice versa. Second, the analysis is extended to include the study of braking and locking of tearing mode rotation by the interaction of the mode with an error-field. It is found that this interaction can brake the plasma rotation, suppress magnetic island evolution and drive locked modes.Show more