Resistive instabilities in general toroidal plasmas with neoclassical bootstrap currents

In this work, linear neoclassical resistive instabilities are investigated in general toroidal plasmas using standard perturbation theory. Using a neoclassical fluid model, we derive the singular layer equations modified by bootstrap currents and also obtain the dispersion relation of the resistive interchange mode and the neoclassical tearing mode (NTM), respectively. Additionally, we determine the stability criteria D-R(bs) and Delta(bs)(c) for bootstrap current-modified resistive modes. The resistive interchange mode is stable when D-R (bs)< 0 and the NTM is stable when Delta ' < Delta(bs)(c), where Delta ' is the stability index of the tearing mode. It is found that, in tokamak plasmas with a positive magnetic shear, bootstrap currents have a destabilizing effect on resistive interchange modes, which not only increases the value of the stability criterion (D-R(bs)) but also enhances the growth rate. In addition, bootstrap currents have a stabilizing effect on the growth rate of the NTM in a low growth rate region. However, bootstrap currents can also decrease the critical value Delta(bs)(c). In plasmas with negative magnetic shear, the opposite holds. Furthermore, the coupling effect between bootstrap currents and Pfirsch-Schl & uuml;ter currents via magnetic field curvature is determined for the first time in this work. This coupling always has a stabilizing influence on the resistive interchange mode and can increase the value of Delta(bs)(c). The coupling is also independent of the sign of the magnetic shear and can be enhanced in low-aspect-ratio tokamaks (such as spherical tokamaks) or in plasma regions with low magnetic shear (as used in ITER hybrid scenarios). Our results are valid for low-n resistive instabilities in toroidal plasmas with arbitrary aspect ratios and beta, where n is the toroidal mode number and beta represents the ratio of the plasma pressure to the toroidal magnetic pressure. Overall, this investigation has broad parametric applications and deepens our understanding of the physical mechanisms underlying the influence of neoclassical effects on resistive instabilities.