For understanding the transport mechanism in toroidal plasmas, the statistical feature of the plasma turbulence have been investigated by experimental observations. It was found in CHS plasma that the fractional dimension characterizes the attractor of the turbulence and the largest Lyapunov exponent is positive [1]. It was also shown that the difference of the plasma heating methods affects the degree of freedom in turbulent plasma. However, the parameters to control the dimension has not been understood well. There are still several physical problems to be clarified, such as the dependency of the statistical feature on the characteristic plasma parameters.
In this research, the transport in the presence of turbulence such as the sheared slab electron temperature gradient (ETG) mode has been simulated by the three-dimensional gyro-fluid model developed by Li and Kishimoto [2]. The statistical values such as the correlation dimension and the Lyapunov exponent have been analyzed for the electric field. To evaluate the fractal dimension, the correlation dimension can be calculated with Grassberger-Procaccia algorithm [3] by taking correlation integral of time series data. The embedding theorem is used for the evaluation of the correlation dimension and Lyapunov exponent. The primitive results show the enhancement of correlation dimension for larger electron temperature gradient η_e (η_e = d ln T_e / d ln n). It is found that the formation of the zonal flows causes the reduction of the correlation dimension to about half even if the characteristic parameters are the same except the zonal flow component. After the excitation of KH mode by the zonal flow [2], the correlation dimension is also found to be reduced to less than half.

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