Events at Physics |
In this vein, computational routines are developed to support stellarator simulations with the initial-value magnetohydrodynamics (MHD) code NIMSTELL. Developments include mapping ideal MHD equilibria from the DESC code and efficient preconditioning for typical stellarator configurations. Subsequently, NIMSTELL is verified through benchmarks against initial-value reduced-MHD simulations in JOREK and full-MHD eigenvalue calculations in CASTOR3D. Linear growth rates are compared for tearing and ballooning modes in W7-A, a tearing mode in QA and a near-resonant interchange mode in QH. NIMSTELL and CASTOR3D growth rates agree to within $3%$ for most cases, verifying the accuracy of both codes. Larger deviations (∼ 10%) in JOREK growth rates are attributed to the use of a reduced-MHD model. For the QA tearing mode, the three codes demonstrate the theoretical $\eta^{3/5}$ scaling for tearing modes. Because ballooning growth rates are higher at shorter wavelengths, the challenge of spatially resolving the W7-A ballooning eigenmode is considered in detail.
Informed by the prevalence of low magnetic shear in optimized configurations, pressure-driven instabilities are investigated in the low-shear regime. Linear and nonlinear simulations with NIMSTELL indicate that such modes can severely degrade confinement, consistent with results from prior research. Following the standard analysis of ballooning modes, which is valid for magnetic shear of order unity, a modified theoretical model valid for low shear is developed using the Wentzel–Kramers–Brillouin (WKB) method. The analysis yields a system of two coupled ordinary differential equations (ODE) that constitutes an eigenvalue problem analogous to standard ballooning analysis. In contrast to the latter, the eigenvalue of the low-shear ODE system does not reduce to a three-dimensional (3D) function in the 4D phase space. This avoids the “lock-in” phenomenon and corresponding singular solutions found in standard analysis. As a result, eigenvalues of the ideal MHD normal mode equation can be determined using conventional quantization methods such as the Einstein-Brillouin-Keller (EBK) conditions. The low-shear model is verified for an axisymmetric configuration by comparing the linear growth rates given by the EBK conditions with NIMSTELL results.