This paper combines results from a local gyrokinetic code with analytical theory to reconstruct the global eigenmode structure of the linearly unstable ion-temperature-gradient (ITG) mode with adiabatic electrons. The simulations presented here employ the s-${ \alpha}$ tokamak equilibrium model. Local gyrokinetic calculations, using GS2 have been performed over a range of radial surfaces, x, and for ballooning phase angle, p, in the range -${ \pi} { \leq} p { \leq\pi}$, to map out the complex local mode frequency, ${ \Omega_0(x, p) = \omega_0(x, p) + i\gamma_0(x, p)}$. Assuming a quadratic radial profile for the drive, namely ${ \eta_i = L_n/L_T}$, (holding constant all other equilibrium profiles such as safety factor, magnetic shear etc.), ${ \Omega_0(x, p)}$ has a stationary point. The reconstructed global mode then sits on the outboard mid plane of the tokamak plasma, and is known as a conventional or isolated mode, with global growth rate, ${ \gamma}$ ~ Max[${ \gamma_0(x, p)}$], where ${ \gamma_0(x, p)}$ is the local growth rate. Taking the radial variation in other equilibrium profiles (e.g safety factor q(x)) into account, removes the stationary point in ${ \Omega_0(x, p)}$ and results in a mode that peaks slightly away from the outboard mid-plane with a reduced global growth rate. Finally, the influence of flow shear has also been investigated through a Doppler shift, ${ \omega_0 \rightarrow \omega_0 + n\Omega^{ \prime}x}$, where n is the toroidal mode number and ${ \Omega^{ \prime}}$ incorporates the effect of flow shear. The equilibrium profile variation introduces an asymmetry to the growth rate spectrum with respect to the sign of ${ \Omega^{ \prime}}$, consistent with recent global gyrokinetic calculations.
Categories: physics.plasm-ph