Theoretical study of effect of hyper-resistivity on linear stability of ballooning mode

Abstract

The coupling of ballooning mode and peeling mode forms the so-called peeling-ballooning mode, which is widely used in the physical explanation of the edge localized mode (ELM). The nonlinear platform simulation based on the non-ideal peeling-ballooning mode model successfully explained the ELM experimental results. Therefore, exploring the influences of various non-ideal effects on the ballooning mode in the edge transport barrier is very important in controlling the ELM in the future fusion reactors. Among the reports on non-ideal effects, there are few reports involving the effect of hyper-resistivity caused by anomalous electron viscosity on ballooning mode. It has been found that the hyper-resistivity has a destabilizing effect on the ballooning mode, but the associated physical mechanism is still unclear. Therefore, it is necessary to systematically explore the influence of hyper-resistivity on the ballooning mode theoretically by introducing hyper-resistivity into the ballooning mode model. The linear growth rate of ideal and non-ideal ballooning mode are solved by the shooting method for the derived eigenvalue equation of non-ideal ballooning mode containing hyper-resistivity, finite resistivity and diamagnetic drift effects, and the dependence of ballooning mode on hyper-resistivity is also explored under different conditions. The results show that the hyper-resistivity may destabilize the ballooning mode, and the physical mechanism is that the current diffusion effect caused by the hyper-resistivity weakens the stabilizing effect of the magnetic field line bending on the ballooning mode. When both the resistivity and hyper-resistivity are considered, they are in a competitive relationship. When the ratio of hyper-resistivity to resistivity is relatively high, hyper-resistivity plays a dominant role, and the destabilizing effect of resistivity will be shielded by hyper-resistivity, and vice versa. The destabilization effect of hyper-resistivity on ballooning modes is enhanced with the increase of the toroidal mode number. The hyper-resistivity will destabilize the original stable modes once the toroidal mode number exceeds a certain threshold. Further studies show that the threshold is inversely proportional to the ratio of hyper-resistivity to resistivity. The research results have important reference value for the control of edge localized modes in low-collisionality edge plasma in future fusion reactors.