of the scope of the present paper [@a25]. In this section the linear regime of the ITG mode will be discussed and the basic equations are given by;

$$\begin{aligned}
\frac{\partial \tilde{n}}{\partial t} - \left(\frac{\partial}{\partial t} - \alpha_i \frac{\partial}{\partial y}\right)\nabla^2_{\perp} \tilde{\phi} + \frac{\partial \tilde{\phi}}{\partial y} - \epsilon_n g \frac{\partial}{\partial y} \left(\tilde{\phi} + \tau \left(\tilde{n} + \tilde{T}_i \right) \right) + \frac{\partial \tilde{v}_{i ||}}{\partial z} = \nonumber \\
- \left[\phi,n \right] + \left[\phi, \nabla^2_{\perp} \phi \right] + \tau \left[\phi, \nabla^2_{\perp} \left( n + T_i\right) \right] \\
\frac{\partial \tilde{T}_i}{\partial t} - \frac{5}{3} \tau \epsilon_n g \frac{\partial \tilde{T}_i}{\partial y} + \left( \eta_i - \frac{2}{3}\right)\frac{\partial \tilde{\phi}}{\partial y} - \frac{2}{3} \frac{\partial \tilde{n}}{\partial t} = \nonumber \\
- \left[\phi,T_i \right] + \frac{2}{3} \left[\phi,n \right] \\
\frac{\partial \tilde{v}_{i ||}}{\partial t} = - (\frac{\partial \tilde{\phi}}{\partial z} + \tau \frac{\partial (\tilde{n} + \tilde{T_i})}{\partial z}) - \left[ \tilde{\phi}, \tilde{v}_{i ||} \right].\end{aligned}$$

Here $\left[ A ,B \right] = (\partial A/\partial x) (\partial B/\partial y) - (\partial A/\partial y) (\partial B/\partial x)$ is the Poisson bracket with the additional definitions $\tilde{n} = \delta n / n_0$, $\tilde{\phi} = e \delta \phi /T_e$, $\tilde{T}_i = \delta T_i / T_{i0}$ as the normalized ion particle density, the electrostatic potential and the ion temperature respectively. In the 