Collisional effects on global gyrokinetic particle-in-cell simulations of ITG and TEM instabilities in tokamaks

摘要

Particle and heat transport in tokamaks exceed the neoclassical prediction. This anomalous transport is produced by turbulence which is probably caused by microinstabilities such as ion and electron-temperature-gradient (ITG/ETG) and trapped-electron-mode (TEM). This work studies the effects of collisions on these instabilities by using the 3D global gyrokinetic PIC code EUTERPE. In this code, the distribution function of each species evolves according to the set of gyrokinetic equations, where C(f) is a collision operator, for example the Fokker-Planck operator. The guiding center trajectories (characteristics) for the collisionless case are: The code utilizes the δf method [1] in which, for each species, the distribution function is divided into a background equilibrium distribution function and a perturbed part f = f_0 + δf. This makes it possible to compute only the time evolution of the perturbation, which reduces the statistical noise as compared with the full-f method. Since EUTERPE has been extended to include collisions and multiple species, a generalized collisional δf scheme was implemented. This is known as the two-weight scheme [2,3,4]: with collisions, the weight evolution of the Monte-Carlo markers cannot be solved directly by the method of characteristics, because the diffusive particle motion causes the "characteristic line", along which the convective derivative of the weight is to be evaluated, to be stochastic. To overcome this problem, it is better not to define the weight in terms of the local of, but to treat the weight as another variable, in addition to the usual dimensions of χ - v space. By taking the moments of the new kinetic equation in the extended phase space, it is possible to choose the weights to be consistent with the original of equation. By doing so, one finds that the evaluation of the marker density becomes difficult, unless a second weight is added to the extended phase space. In the cases we have studied, however, (C(f_0) = 0 and zeroth order of df_0/dt = 0) the second weight does not evolve, which is equivalent to having a one-weight scheme.