COTSIM-based Numerical Solver for the Steady State Condition in Tokamak Plasmas
E. Nuzzi, Z. Wang, S.-T. Paruchuri, H. Wang, T. Rafiq, E. Schuster
Division of Plasma Physics (DPP) Annual Meeting of the American Physical Society (APS)
Pittsburgh, PA, USA (Remote), November 8-12, 2021
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 s
caling 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.
*Supported by the US DOE DE-SC0010661 and DE-SC0021385.