Fluid simulations of tokamak turbulence in quasiballooning coordinates

A set of coordinates for simulations in toroidal magnetic geometry, called quasiballooning coordinates, is proposed and implemented. Quasiballooning coordinates are straight-field-line coordinates in which one of the coordinate directions is as close as possible to that of the magnetic field consistent with the near-parallel grid lines meshing exactly (without interpolation) as they cross the boundaries of the simulation region. This allows the true periodicity conditions in the toroidal-poloidal plane to be satisfied in a straightforward and seamless way, even for sheared magnetic fields. Quasiballooning coordinates are useful in the simulation of instabilities and turbulence of interest in fusion plasmas since the number of grid cells needed to represent structures that are elongated along the magnetic field with a given resoluton is greatly reduced compared with toroidal-poloidal or other nontwisting coordinates. For explicit codes, they allow shorter time steps, and it is anticipated that for particle codes, their use will naturally minimize the numerical noise. The key details necessary for the implementation of quasiballooning coordinates, both in finite-difference and pseudospectral fluid codes are presented, and a fluid code has been written. The advantages of quasiballooning coordinates are demonstrated by applying this code to turbulence driven by the ${\mathrm{\ensuremath{\upsilon}}}_{\mathrm{\ensuremath{\Vert}}}^{\ensuremath{'}}$ instability.