Tokamak Turbulence Simulations With Magnetic Axis

Magnetic confinement fusion is one of the most promising approach ways to achieve controlled nuclear fusion. It is crucial to study the turbulent transport in toridal plasmas in current fusion plasma research. In recent years, the large-scale gyrokinetic parallel simulation has become a major tool to study the nonlinear physics of turbulent transport. Our work based on gyrokinteic toroidal code(GTC) in the tokomak geometry is mainly aimed to solve the singularity of flux coordinate{r,6,â– ) at the magnetic axis for the Poisson equation. As we know, the flux coordinates (e.g. Boozer coordinate, Hamada coordinate) widely used in the fusion plasma turbulence simulation are variants of the traditional cylinder coordinate^,8, z). One of the defects of this kind coordinate system is that, for some crucial differential operator, such as the Laplacian, it has a singularity at the magnetic axis. So it can not treat some MHD instability, such as internal kink mode which usually occurs around the magnetic axis. We develop an algorithm to remove this singularity at the magnetic axis for the gyrokinetic Poisson equation. First, we verify this algorithm in the cylinder coordinate system(r,8, z) for the standard Poisson equation, and get numerical results agreeing with the analytical solution. Second, we adopt this method for the Boozer flux coordinate in the GTC code. We get preliminary verification linear result by comparing with analytical solution and carry out nonlinear simulation of trapped election mode.