Morgan, Nicolás M. (2022) Cálculo del equilibrio MHD a partir de información experimental en tokamaks avanzados / Calculation of the MHD equilibrium from experimental information on advanced. Maestría en Ingeniería, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
La tecnología para obtener energía aprovechable de la fusión de núcleos livianos se encuentra aún en desarrollo. Si bien este tipo de reacciones se han logrado en el laboratorio hace muchos años, aún no se ha logrado fabricar un reactor capaz de liberar más potencia producida por fusión que la necesaria para mantener las condiciones requeridas, en forma estacionaria o casi-estacionaria. El próximo paso en esta carrera tecnológica es la construcción de ITER (International Thermonuclear Reactor) que, usando un plasma producido por una configuración tipo tokamak, ha sido diseñado para liberar una potencia de fusión diez veces mayor que la potencia de calentamiento requerida para mantener las condiciones del plasma que forman los reactivos. Para lograr este objetivo, se requiere lograr un plasma con buena estabilidad en las condiciones que permiten una cantidad de reacciones de fusión suficientemente grande. Para lograr esto se debe tener un modelo preciso del plasma y su estructura interna y un buen sistema de control de sus perfiles, entre otros requisitos. La mayoría de este tipo de modelos requieren como insumo la configuración de campo en estado de equilibrio de fuerzas magnetohidrodinámicas (equilibrio MHD). De los numerosos métodos y códigos para resolver el equilibrio MHD que existen a día de hoy, la mayoría lo hacen partiendo de información que no se puede obtener directamente en forma experimental. Para obtener la configuración magnética en la práctica se recurren a códigos de reconstrucción del equilibrio que resuelven una aproximación linealizada del problema y ajustan parámetros para aproximar lo mejor posible una serie de observables (problema de minimización con restricciones). Aunque esta estrategia permite describir adecuadamente los campos en experimentos actuales, su adaptación al diseño de escenarios y estrategias de control en plasmas con nuevas condiciones puede volverse un factor limitante. En esta tesis se introduce un esquema numérico para obtener la configuración de campo magnético de equilibrio MHD en tokamaks, y configuraciones axisimétricas en general, a partir de información experimental. La información requerida es una estimación del perfil de presión en función del radio menor del toroide y el perfil radial de ángulo de inclinación del campo magnético en el plano ecuatorial. El perfil de presión se puede inferir a partir de la emisión de ciclotrón de los electrones del plasma, mientras que el ángulo del campo magnético se determina rutinariamente mediante una técnica denominada Motional Stark Effect (MSE). A partir de esta información, el esquema iterativo propuesto permite obtener y resolver la ecuación diferencial de Grad-Shafranov que describe el equilibrio. Para la resolución de este problema inverso, se emplea una secuencia de problemas diferenciales no lineales de segundo orden, que se aproximan mediante el método de elementos finitos. Además de introducir y validar el esquema numérico, se analiza la estructura y distribución de corrientes en los escenarios de operación previstos para ITER.
Resumen en inglés
The technology to obtain usable energy from the fusion of light nuclei is still under development. Although these types of reactions have been achieved in the laboratory for many years, it has not yet been possible to manufacture a reactor capable of releasing more power produced by fusion than is necessary to maintain the required conditions, in a stationary or quasistationary manner. The next step in this technological race is the construction of ITER (International Thermonuclear Reactor) which, using a plasma produced by a tokamak-type configuration, has been designed to release a fusion power ten times greater than the heating power required to maintain the plasma conditions that form the reactants. To achieve this goal, it is required to achieve a plasma with good stability under conditions that allow a sufficiently large number of fusion reactions. For this reason it is necessary to have an accurate model of the plasma and its internal structure and a good control system for its profiles, among other requirements. Most of this type of models require as input the configuration of the field in equilibrium state of magnetohydrodynamic forces (MHD equilibrium). Of the numerous methods and codes to solve the MHD equilibrium that exist today, most do so starting from information that cannot be directly obtained experimentally. To obtain the magnetic configuration in practice, equilibrium reconstruction codes are used that solve a linearized approximation of the problem and adjust parameters to best approximate a series of observables (constrained minimization problem). Although this strategy allows adequately describing the fields in current experiments, its adaptation to the design of scenarios and control strategies in plasmas with new conditions can become a limiting factor. In this thesis, a numerical scheme is introduced to obtain the equilibrium magnetic field configuration MHD in tokamaks, and axisymmetric configurations in general, from experimental information. The information required is an estimate of the pressure profile as a function of the minor radius of the toroid and the radial profile of the angle of inclination of the magnetic field in the equatorial plane. The pressure profile can be inferred from the cyclotron emission of plasma electrons, while the magnetic field angle is routinely determined by a technique called Motional Stark Effect (MSE). From this information, the proposed iterative scheme allows obtaining and solving the Grad-Shafranov differential equation that describes the equilibrium. To solve this inverse problem, a sequence of second-order nonlinear differential problems is used, which are approximated using the finite element method. In addition to introducing and validating the numerical scheme, the structure and distribution of currents in the operation scenarios foreseen for ITER are analyzed.
| Tipo de objeto: | Tesis (Maestría en Ingeniería) |
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| Palabras Clave: | Equilibrium; Equilibrio; Plasma; Fusión; Magnetohydrodynamics; Magnetohidrodinámica; [Tokamaks; Finite elements; Elemento finito] |
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| Materias: | Física > Fisica del plasma orientada a tokamaks |
| Divisiones: | Investigación y aplicaciones no nucleares > Física > Fusión nuclear y física de plasmas |
| Código ID: | 1128 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 03 Nov 2022 14:30 |
| Última Modificación: | 03 Nov 2022 15:04 |
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