forthcoming equations $\tau = T_i/T_e$, $\vec{v}_{\star} = \rho_s c_s \vec{y}/L_n $, $\rho_s = c_s/\Omega_{ci}$ where $c_s=\sqrt{T_e/m_i}$, $\Omega_{ci} = eB/m_i c$. We also define $L_f = - \left( d ln f / dr\right)^{-1}$, $\eta_i = L_n / L_{T_i}$, $\epsilon_n = 2 L_n / R$ where $R$ is the major radius and $\alpha_i = \tau \left( 1 + \eta_i\right)$. The perturbed variables are normalized with the additional definitions $\tilde{n} = (L_n/\rho_s) \delta n / n_0$, $\tilde{\phi} = (L_n/\rho_s e) \delta \phi /T_e$, $\tilde{T}_i = (L_n/\rho_s) \delta T_i / T_{i0}$, $\tilde{v}_{i ||} = (L_n/\rho_s) \delta v_{i ||}/c_s$ as the normalized ion particle density, the electrostatic potential, the ion temperature and the parallel ion velocity respectively. The perpendicular length scale and time are normalized to $\rho_s$ and $L_n/c_s$, respectively. The geometrical quantities are calculated in the strong ballooning limit ($\theta = 0 $, $g_i\left(\theta = 0, \kappa \right) = 1/\kappa$ where $g_i\left( \theta \right)$ is defined by $\omega_D \left( \theta \right) = \omega_{\star} \epsilon_n g_i\left(\theta \right)$) [@a31], [@a44]. The effects of safety factor and magnetic shear can also be accommodated by the factor $g_i$ [@a23]. The linear dispersion relation coming from Eqs 1, 2 and 3 is, $$\begin{aligned}
\omega^3 \left(1+k_{\perp}^2\right) + \omega^2 k_y \left(-(1-(1+\frac{10}{3}\tau)\epsilon_n 