Axisymmetric Tokamak Equilibria computed with a Predefined Safety Factor Profile as CHEASE input

The CHEASE code, which has been developed at the Swiss Plasma Center, generates an accurate reconstruction of toroidal magnetohydrodynamics equilibria by numerically solving the Grad-Shafranov equation. Having demonstrated its ability to achieve good convergence while remaining fast and very flexible, this code is now extensively used at different research facilities. From two input profiles, usually the pressure and the current density as well as specified boundary conditions, the code provides a complete equilibrium description which is essential for the study of tokamak plasmas. This project focuses on computing axisymmetric equilibria within ideal magnetohydrodynamics (MHD) by imposing a specific shape for the safety factor $q$. The Grad-Shafranov equation requires two free functions to be specified: one for the current density and one for the pressure (p=nT). Until now, the options in CHEASE allowed to give the pressure profile or its derivative on one hand and either $TT'$, $I^*$, $I_{\parallel}$, or $J_{\parallel}$ on the other hand. The safety factor profile was therefore a result of the computation of the equilibrium. However, this profile and its radial derivative are essential for stability and transport issues into the tokamak. The goal of the present project is thus to modify the code so as to be able to provide a safety factor profile as a CHEASE input. However, equilibria generated with the safety factor profile as input can easily lead to surface currents if strong variation of the derivative $\frac{dq}{d\rho}$ appears in the solution. It is therefore necessary to develop a method to avoid these problems, especially at the edge of the plasma. A further aim of this work is hence to demonstrate that there is no continuity problem within solutions computed with a q-profile as input. There are two ways of achieving this: one is to impose the current profile within one iteration to obtain the desired safety factor profile and the other is to impose the $TT'$ profile in the same way. The two solutions are explored in this project with the purpose to determine which one is most appropriate. Finally, the extended version of CHEASE developed in this master project is used to study the influence of safety factor profiles on the stability of tearing modes by solving the energy principle equation within the cylindrical approximation which depends directly on $q$, $q'$ and $q''$