Toroidal geometry effects on the performance of resonant helical fields in Tokamaks

Author(s)

Elton Cesar da Silva

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2001-03-01

Examining board members

Ibere Luiz Caldas; Maria Celia Ramos de Andrade; Felipe Barbedo Rizzato; Alvaro Vannucci; Othon Cabo Winter

• Advisor: Ibere Luiz Caldas

Abstract

In this work, we have considered the effects of an external resonant magnetic field on the plasma confined in a tokamak. This resonant field can be produced by helical windings or by a chaotic magnetic limiter. The main purpose of this resonant magnetic field is to create a region of chaotic field lines at the edge of the plasma that can improve the confinement of the plasma. The equilibrium tokamak field was obtained by solving the GRAD-SHAFRANOV equation in an intrinsically toroidal coordinate system (the toroidal polar coordinates). We have obtained the magnetic field which has been generated by helical windings through an explicit solution of the LAPCACE equation in the same coordinate system. From this magnetic field, taken in its lowest order, we have analytically obtained a sympletic stroboscopic map for a set of chaotic magnetic limiters. We have calculated this sympletic stroboscopic map by using a Hamiltonian formulation and by supposing the action of the chaotic magnetic limiters as a sequence of delta-function pulses. With this sympletic stroboscopic map we have characterized some resonant magnetic islands and the onset of global chaos through their overlap. We have used this sympletic stroboscopic map in order to study the transport of the field lines at the edge of the plasma. The loss of chaotic field lines that reach the inner wall of the tokamak follows a POISSON distribution. We have also calculated the average number of toroidal turns for a chaotic field line to reach the inner wall of the tokamak. (AU)