Tokamak coordinate conventions: COCOSCOCOS

Dealing with electromagnetic fields, in particular current and related magnetic fields, yields “natural” physical vector relations in 3-D. However, when it comes to choosing local coordinate systems, the “usual” right-handed systems are not necessarily the best choices, which means that there are several options being chosen. In the magnetic fusion community such a difficulty exists for the choices of the cylindrical and of the toroidal coordinate systems. In addition many codes depend on knowledge of an equilibrium. In particular, the Grad–Shafranov axisymmetric equilibrium solution for tokamak plasmas, ψψ, does not depend on the sign of the plasma current IpIp nor that of the magnetic field B0B0. This often results in ill-defined conventions. Moreover the sign, amplitude and offset of ψψ are of less importance, since the free sources in the equation depend on the normalized radial coordinate. The signs of the free sources, dp/dψdp/dψ and dF2/dψdF2/dψ (pp being the pressure, ψψ the poloidal magnetic flux and F=RBφF=RBφ), must be consistent to generate the current density profile. For example, RF and CD calculations (Radio Frequency heating and Current Drive) require an exact sign convention in order to calculate a co- or counter-CD component. It is shown that there are over 16 different coordinate conventions. This paper proposes a unique identifier, the COCOSCOCOS convention, to distinguish between the 16 most-commonly used options. Given the present worldwide efforts towards code integration, the proposed new index COCOSCOCOS defining uniquely the COordinate COnventionS required as input by a given code or module is particularly useful. As codes use different conventions, it is useful to allow different sign conventions for equilibrium code input and output, equilibrium being at the core of any calculations in magnetic fusion. Additionally, given two different COCOSCOCOS conventions, it becomes simple to transform between them. The relevant transformations are described in detail.