Conformal Tokamak Geometry for Turbulence Computations

Turbulence in magnetized plasma, with particle gyroradii that are small compared to the device size, consists of 2-D dynamically incompressible fluidlike turbulence in planes perpendicular to the magnetic field and of compressible wavelike dynamics parallel to it. A strong anisotropy between the perpendicular and parallel scales of motion results. The natural coordinates are, therefore, those which follow the field lines. The deformational issues which result from the magnetic shear and variation of the distance between the magnetic flux surfaces with a position are treated by judicious choices of the coordinate representation. We elucidate the methods by which, in turn, the deformation induced by the shear and, then, by the shaping is remedied. Both the physical and computational considerations are treated since the grid isotropicity best represents the small-scale turbulence and, at the same time, facilitates the multigrid solution of the elliptic equations which are part of the overall system. We present the details of the conformal coordinate system and its implementation, together with an example of its calculation for a realistic tokamak equilibrium case.