Ion temperature gradient instability at sub-Larmor radius scales with non-zero ballooning angle

Linear gyro-kinetic stability calculations predict unstable toroidal Ion Temperature Gradient modes with normalised poloidal wave vectors well above one ($k_θρ_i > 1$) for standard parameters and with adiabatic electrons. These modes have a maximum amplitude at a poloidal angle $θ$ that is shifted away from the low field side ($θ\ne 0$). The physical mechanism is clarified through the use of a fluid model. It is shown that the shift of the mode away from the low field side ($θ\ne 0$) reduces the effective drift frequency, and allows for the instability to develop. Numerical tests using the gyro-kinetic model confirm this physical mechanism. It is furthermore shown that modes with $θ\ne 0$ can be important also for $k_θρ_i < 1$ close to the threshold of the ITG. In fact, modes with $θ\ne 0$ can exist for normalised temperature gradient lengths below the threshold of the ITG obtained for $θ= 0$.

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