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

In this thesis, the author studies 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. Using physical parameters for a typical tokamak, the order of magnitude of various effects are estimated. A reduced system is obtained by neglecting small terms in the two-fluid thirteen moment equations. This reduced model includes small particle flows, pressure anisotropy and temperature variation in flux surfaces. The reduced model is compared with standard fluid models. To better understand the behavior of solutions in this system, the solution is formally expanded 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 and a Grad-Shafranov equation relating the poloidal flux and the toroidal current. The energy dynamics of the system are complicated and require 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 τ3mi/me, time independent solutions are in general not possible. The slow time evolution of the steady state is calculated