Self-consistent solutions of the plasma transport equations in an axisymmetric toroidal system

A numerical method is presented for solving a recently derived (S. P. Hirshman and S. C. Jardin, Phys. Fluids 22(1979), 731) reduced set of equations describing two-dimensional transport in tokamak plasmas. The formulation exploits the different diffusion time scales by dividing each time advancement step into two parts. In the first part, the one-dimensional surface averaged partial differential equations are advanced implicitly. In the second part, the two-dimensional generalized differential equation for the toroidal flux surface velocity is inverted directly. Accurate efficient solutions are obtained with only explicit terms coupling these two steps. Solutions are presented illustrating the validity and the accuracy of this method.