MHD equilibrium in Tokamaks with reversed current density

• Autor(a) principal: Taborda, David Ciro
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-11032013-131439/
• topic: Corrente reversa; Dynamical systems; Equilibrio MHD; MHD equilibrium; Reversed current; sistemas dinâmicos; Tokamaks; Tokamaks

In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis.