Studying the effects of magnetic island (MI) on the micro-turbulence are important for understanding the turbulent transport and confinement in the presence of MI. The impact of thin island on slab ion temperature gradient (ITG) mode instability has been investigated[1]. In this work, we have investigated the influences of static MI on electrostatic toroidal ITG mode. The ions are described by gyro-kinetic equations including MI[2], and adiabatic approximation is used for electrons. The eigen-equation for short wavelength toroidal ITG mode in Fourier-ballooning representation is derived based on quasi-neutrality condition, and eigen-value as well as mode structure is given. The flattening effects of MI on plasma pressure and E×B flow around MI separatrix[1] are considered. The main results are as follows: (1) The flattening effects of MI can stabilize ITG mode as compared to the case without MI. While, the effective drive of toroidal ITG mode is enhanced by MI scale E×B  flow, which even results in higher growth rate than the case without MI. This indicates that the E×B flow induced by MI destabilizes the toroidal ITG mode; (2) When MI is taken into account, the radial profile of mode structures at MI phase ξ=0 , ξ=±π  show different characteristic length, which can be clearly observed from the 2D contour plot of mode structure. This reveals that the mode structure is asymmetric about MI phase. The mode structure is unsmooth at the MI phase ξ=±π2 , which may be caused by numerical integration problems.



[1]     H. R. Wilson and J. W. Connor, “The influence of magnetic islands on drift mode stability in magnetized plasma,” Plasma Phys. Control. Fusion, vol. 51, no. 11, 2009.

[2]     K. S. Fang and Z. Lin, “Global gyrokinetic simulation of microturbulence with kinetic electrons in the presence of magnetic island in tokamak,” Phys. Plasmas, vol. 26, no. 5, 2019.