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 ($k_\theta \rho_i > 1$) for standard parameters and with adiabatic electrons. These modes have a maximum amplitude at a poloidal angle $\theta$ that is shifted away from the low field side ($\theta \ne 0$). 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 ($\theta \ne 0$) 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 $\theta \ne 0$ can be important also for $k_\theta \rho_i < 1$ close to the threshold of the ITG. In fact, modes with $\theta \ne 0$ can exist for normalised temperature gradient lengths below the threshold of the ITG obtained for $\theta = 0$

On seed island generation and the non-linear self-consistent interaction of the tearing mode with electromagnetic gyro-kinetic turbulence

The multi-scale interaction of self-consistently driven magnetic islands with electromagnetic turbulence is studied within the three dimensional, toroidal gyro-kinetic framework. It can be seen that, even in the presence of electromagnetic turbulence the linear structure of the mode is retained. Turbulent fluctuations do not destroy the growing island early in its development, which then maintains a coherent form as it grows. The island is seeded by the electromagnetic turbulence fluctuations, which provide an initial island structure through nonlinear interactions and which grows at a rate significantly faster than the linear tearing growth rate. These island structures saturate at a width that is approximately $\rho_{i}$ in size. In the presence of turbulence the island then grows at the linear rate even though the island is significantly wider than the resonant layer width, a regime where the island is expected to grow at a significantly reduced non-linear rate. A large degree of stochastisation around the separatrix, and an almost complete break down of the X-point is seen. This significantly reduces the effective island width.Comment: Joint Varenna - Lausanne International Worksho