The linear local gyrokinetic mode equation is numerically solved to investigate the stability of the electrostatic micro instabilities in helical systems. The mode equation with ballooning representation is free from other assumptions (1D in the space and 2D in the velocity space). Both the circulating and trapped particles dynamics are considered, and the effect of Landau resonance, magnetic drift resonance, FLR effect are involved, as is FULL code [1]. In the electrostatic regime, ion temperature gradient mode (ITG) and trapped electron mode (TEM) are expected to be driven unstable with k_⊥ρ_thi≈0.5. The electron temperature gradient mode (ETG) can also become unstable with k_⊥ρ_the≈0.5.
The linear gyrokinetic modes are assumed to be excited in the MHD equilibrium states. In particular, we consider Large Helical Device (LHD) [2] as a model configuration, whose MHD equilibrium is obtained by VMEC code [3].
The non-axisymmetric equilibrium properties of helical plasmas will affect the stability, through the curvature of field line which is mainly determined by the magnetic field strength B, and the perpendicular wave number k_⊥ which is strongly dependent on the geometry (R, Z) in the ballooning formalism. Although the linear stability of the drift modes in the helical plasmas has been investigated recently [5], it seems not to be enough clear. We will discuss these effects itself on the above various type of drift waves. The difference of these effects between the ideal MHD modes and the drift modes, and the difference from tokamak case will be also considered.

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