Geometric formulas for system codes including the effect of negative triangularity

Formulas for the volume, poloidal and toroidal surfaces, poloidal length, plasma current, and hence average poloidal field, are determined using global parameters of tokamak plasmas. Previous formulas did not include systematically the effect of triangularity and in particular are inaccurate for negative triangularity cases. Since tokamaks with negative triangularity can be attractive for DEMO reactors cite{Kikuchi, Medvedev}, it is important to have updated formulas. It is also shown that the combined effect of finite triangularity and inverse aspect ratio was not correctly taken into account. Previous formulas were also using shaping parameters at the 95% poloidal flux surface. It is shown that this is misleading and the new formulas use the effective parameters, $kappa, delta, R_{{ m geom}}, epsilon$, of the relevant flux surface, in this case of the last closed flux surface. Only the value of the safety factor, $q$, is ill-defined at the plasma edge for divertor cases, thus $q_{95}$ is still being used. A new global parameter, $w_{07}$, related to the radial width of the plasma shape at 70% of the maximum height is introduced to take into account the squareness present in most plasma shapes, in particular single-null diverted ones. We also provide a simple formula for the trapped fraction which includes the effects of triangularity. The trapped fraction is required for evaluating the neoclassical conductivity and bootstrap current in particular.