Fusion Science and Technology / Volume 75 / Number 2 / February 2019 / Pages 137-147
Technical Paper / dx.doi.org/10.1080/15361055.2018.1554391
The Deal Two Equilibrium (DTEQ) code solves the Grad-Shafranov (GS) equation for magnetohydrodynamics equilibrium in the axisymmetric toroidal geometry using the deal.II finite element library. In this paper, we introduce DTEQ that can solve the GS equation both linearly and nonlinearly. The linear solution obtained from this code is verified by comparing with a known analytic solution of the linear GS equation. For the nonlinear solution, DTEQ requires two input profiles, p(ψ) and F(ψ), to be specified as a function of the normalized minor radius ρ. The pressure profile p(ψ) is specified based on Thomson scattering, charge exchange spectroscopy data, and an energetic particle pressure model. The toroidal field profile F(ψ) is obtained from our model that makes the diamagnetic current play a significant role when the poloidal beta βp is greater than one. With these two input profiles, the nonlinear GS equation can be solved using Picard iteration within the plasma boundary from EFIT. Using this newly developed code, we obtain several meaningful results that show its validity. The calculated poloidal current density is very large in the transport barrier due to the diamagnetic current, and the characteristics of the Pfirsch-Schlüter current appear in the toroidal current density. In addition, the results obtained from this code agree well with those from EFIT, and the calculated safety factor values in the center are well correlated with the sawtooth activity in the discharge.