Nonlinear verification of the resistive-wall boundary modules in the and 3 magneto-hydrodynamic codes for fusion plasmas

A nonlinear verification benchmark is reported between the three-dimensional magneto-hydrodynamic (3D MHD) codes SPECYL [Cappello and Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [Chacón, Phys. Plasmas, 15, 056103 (2008)]. This work substantially extends a former successful verification study between the same two codes [Bonfiglio et al., Phys. Plasmas, 17, 082501 (2010)] and focuses on the verification of thin-shell resistive-wall boundary conditions, recently implemented in both codes. Such boundary conditions feature a thin resistive shell in contact with the plasma and an ideal wall placed at a finite distance, separated from the resistive shell by a vacuum region, along with a 3D boundary flow consistent with Ohm's law. This setup allows the study of MHD modes that are influenced by the plasma magnetic boundary, such as external kink modes. The linear growth and nonlinear saturation of external kink modes are studied in both the tokamak and reversed-field pinch magnetic configurations, demonstrating excellent agreement between the two codes. For the tokamak, we present a comparison with analytical linear stability results for the external kink mode, demonstrating remarkable agreement between numerical and analytical growth rates.