| Tools for extending our understanding of microinstability turbulence in magnetized toroidal plasmas are developed through two analytic calculations. First, temporal evolution equations for the density, temperature and magnetic field are presented under the gyrokinetic ordering. To achieve these results, we present a systematic ordering of the Fokker-Planck equation using the native spatial and time scale separation inherent in gyrokinetic turbulence. We show the close link between collisional heat transport and entropy production, emphasizing the need for simulations to include collisions in a nonlinear code to produce consistent results. Second, we examine the electron temperature gradient (ETG) instability with the gyrokinetic equation in a regime where k⊥rhoe is much less than the peak value of the growth rate spectrum. In this limit, the eigenvalue solution is derived with a numerical solution demonstrating proper convergence. The growth rate and real component of the frequency are mapped out over the available parameter space after benchmarking against the solution of the code GYRO [CW03a]. The results of this stability analysis are considered in relation to the convergence of nonlinear ETG simulations. |
