Development of Resistive MHD Code in Cylindrical Geometry and its Applications on EXTRAP T2R

Abstract: A resistive magnetohydrodynamic (MHD) code is presented in detail for a cylindrical plasma column surrounded by a perfect conducting wall. The objective is to develop a full eigenvalue problem solver with resistive wall type boundary conditions that can be integrated into the feedback control algorithms of the EXTRAP T2R reversed field pinch (RFP). For the straight tokamak model, linear analysis is carried out around a flowless background equilibrium followed by the normal mode expansion. The numerical method here applied relies on the weak formulation of the Galerkin method. Its implementation gives rise to a general eigenvalue problem which concerns the discretization of non-self adjoint matrix operator. Hence, we are forced to consider all variables to describe the dynamics of the system. Simulations were performed for both ideal and resistive MHD models. In the former case, the results show that the complete ideal spectrum can be extracted accurately, viz. the magnetoacoustic waves, Alfvén and slow modes, provided a shareless background magnetic field and in presence of the (m, n) = (2, 1) interchange instability. Particularly, the behaviour near the marginal point ω —> 0 is in agreement with theoretical predictions. We emphasize the subtleties regarding the optimal choice of space discretizaton, showing that the use of quadratic and cubic finite elements avoids numerical pollution. Concerning the resistive MHD calculations, the effect of resistivity is studied for a tokamak-like equilibrium profiles. Results show that the two most unstable modes, namely the tearing and interchange instabilities, can be extracted from the code simultaneously. Moreover, the scaling relations with resistivity for both growth rates are presented, showing the ∝ η 3/5 and ∝ η1/3 dependence for the tearing and interchange modes, respectively. Nevertheless, the results are found to be valid only for small values of resistivity. In addition, the effect of resistivity on the perturbed profiles is presented. The foreseen extension of the code to study external modes is discussed.