Date of Award

Spring 2016

Document Type



Mathematics, Engineering & Computer Science


We have studied a tokamak’s fusing medium, plasma, through a computational study of the magnetohydrodynamic equations. Throughout this study we have analyzed many plasma characteristics, like magnetic tension and compression, diffusion, advection, and viscosity. This study has shown that we can correct for naturally occurring magnetic compression and tension by implementing strong initial magnetic fields both inside and outside the reactor. We determined the magnitudes and shapes of these magnetic fields through research and mathematical modeling. The magnitudes of these fields were optimized using a numeric shooting method to increase magnetic confinement time. The best magnetic confinement regime found by our numerical methods occurs when we apply a poloidal field of the same order of magnitude as the driving toroidal field, and when a constant external vertical magnetic field, of the same order of magnitude as the the toroidal field, is implemented. By implementing an initial poloidal ring field around our toroidal Gaussian field we have found that the system evolves such that the internal peak magnetic field increases by 20% before decaying. Through the use of a constant external vertical magnetic field we have increased the plasma’s confinement time by 400%.