COTSIM-based Numerical Solver for the Steady State Condition in Tokamak Plasmas

Determining the steady-state condition of a tokamak plasma given fixed total plasma current, line-average density, heating and current-drive powers, and plasma shape is usually of high interest at the moment of developing a plasma scenario. A numerical solver has been developed in this work to provide such steady-state condition. The considered model, which is embedded in the Control Oriented Transport SIMulator (COTSIM), combines the Magnetic Diffusion Equation (MDE) with either semi-empirical scaling laws or transport equations for the electron density and temperature profiles. Imposing steady-state conditions to this model results in a Two-Point Boundary Value (TPBV) problem. The TPBV problem is solved by combining the finite-difference discretization technique with the Newton-Raphson method. Not only the plasma shape (which can always be regulated by external coils) but the whole magnetohydrodynamic (MHD) equilibrium are assumed fixed while solving the TPBV. The nonlinear dependence between MHD equilibrium and plasma state could be taken into account by combining an equilibrium solver with the proposed TPBV problem solver in a Piccard-iteration fashion. This approach would guarantee a steady-state plasma condition consistent with the MHD equilibrium. The proposed numerical method is illustrated by several representative cases.