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

Abstract

The effects of finite $\beta $ (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 ${\omega _{{{di}}}}$ modified by the effects from both finite $\beta $ 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 ( ${\vartheta _{{p}}} = 0$ ), 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 ${\omega _{{{di}}}}$ around the outboard mid-plane, including both ${\omega _{{{di,0}}}} = {\omega _{{{di}}}}{|_{{\vartheta _{{p}}} = 0}}$ and $\omega _{{{di,0}}}^{{{{\prime} {\prime}}}} \equiv \left( {{{\text{d}}^2}{\omega _{{{di}}}}/{\text{d}}\vartheta _{{p}}^2} \right){|_{{\vartheta _{{p}}} = 0}}$ (twist parameter quantifying the degree of concave or convex of ${\omega _{{{di}}}}$ ), is the key for affecting the toroidal ITG mode instability. The diamagnetic effects from finite $\beta $ and the effects from 3D MPs can suppress the instability by reducing $\left| {{\omega _{{{di,0}}}}} \right|$ . Via reducing $\left| {\omega _{{{di,0}}}^{{{{\prime} {\prime}}}}} \right|$ under the prerequisite of unchanged sign of $\omega _{{{di,0}}}^{{{{\prime} {\prime}}}}$ , there also exist stabilization effects on the instability from 3D MPs and the modification of local magnetic shear by finite $\beta $ effects. In addition, the stabilization effects induced by reducing $\left| {\omega _{{{di,0}}}^{{{{\prime} {\prime}}}}} \right|$ are closely associated with the global magnetic shear. The mechanisms for the effects of finite $\beta $ 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.

Keywords

• finite β
• 3D magnetic perturbations
• ion magnetic drift frequency
• toroidal ITG mode