Tokamak equilibria and transport based on Grad's thirteen moment description

In this thesis, I study collisional transport of a hot magnetically confined plasma in a tokamak. The weakly collisional plasma is modeled by Grad's two-fluid thirteen moment equations. This model provides a better treatment of the stresses and the heat fluxes than do collisional fluid models such as Braginski's. Using physical parameters for a typical tokamak, I estimate the orders of magnitude of various effects. I obtain a reduced system by neglecting small terms in the two-fluid thirteen moment equations. This reduced model includes small particle flows, pressure anisotropy and temperature variation within flux surfaces. The reduced model is compared with standard fluid models. To understand better the behavior of solutions of this system, I expand the solution in a formal series in powers of the small parameter (me/mi)1/4. Flux coordinates are used to solve the equations in a general axisymmetric geometry. In lowest order, the equilibrium solution consists of a number of arbitrary flux functions together with a Grad-Shafranov equation relating the poloidal flux and the toroidal current. The energy dynamics of the system is complicated and requires determining the solution to high order. As corrections to the lowest order solution are calculated, the equilibrium is extended to successively longer time scales until on the time scale τemi/me, time independent solutions are in general not possible. I calculate the time evolution of the lowest order solution on the time scale τmi/me, a time scale consistent with experiment