The toroidal flux and separatrix effects in tokamaks

Abstract: The toroidal magnetic flux enclosed by magnetic surface has remarkably little prominence in the tokamak literature. Nevertheless, it is required to properly interpret Faraday's Law, which gives the slippage of the poloidal relative to the toroidal magnetic flux through the loop voltage. The toroidal flux also simplifies and makes more precise the equilibrium conditions when a tokamak plasma is bounded by a separatrix. This paper illustrates the effect of a separatrix on equilibria using an analytic model in which the $z$ Cartesian coordinate is assumed to define a periodicity direction. Using 95\% of the poloidal flux between the axis and the separatrix to define the edge rotational transform, $q_{95}$, gives the definition an unnecessary sensitivity to the current profile in the central part of the plasma. The required avoidance of disruptions places great importance on identifying parameters that can be both measured and controlled in tokamak power plants. This identification would be clarified by the use of the toroidal rather than the poloidal flux as the radial coordinate.