On how finite β and three-dimensional magnetic perturbations affect the instability of toroidal ion temperature gradient mode

The effects of finite (the ratio of plasma kinetic pressure to magnetic pressure) and three-dimensional (3D) magnetic perturbations (MPs) on the instability of toroidal ion temperature gradient (ITG) mode are studied in this work. The expression of ion magnetic drift frequency modified by the effects from both finite and 3D MPs is firstly derived based on the local 3D equilibrium model. Then, under the assumptions of adiabatic electrons and localized mode structure around the outboard mid-plane (), the dispersion equation of the long wavelength toroidal ITG mode with considering the parallel ion dynamics is derived and solved. The results show that the distribution of around the outboard mid-plane, including both and (twist parameter quantifying the degree of concave or convex of ), is the key for affecting the toroidal ITG mode instability. The diamagnetic effects from finite and the effects from 3D MPs can suppress the instability by reducing . Via reducing under the prerequisite of unchanged sign of , there also exist stabilization effects on the instability from 3D MPs and the modification of local magnetic shear by finite effects. In addition, the stabilization effects induced by reducing are closely associated with the global magnetic shear. The mechanisms for the effects of finite and 3D MPs on the instability of toroidal ITG mode revealed in this work are helpful to the comprehensive understanding of the relationship between internal kink mode induced non-axisymmetric flux surface distortion and internal transport barrier physics in tokamak plasmas.