An inverse equilibrium tool to define axisymmetric plasma equilibria

In this paper, a numerical tool, called the inverse equilibrium tool (IET), for the solution of the inverse equilibrium engineering problem is presented. IET is developed in a MATLAB environment and allows for the computation of the coil currents needed to obtain a predetermined plasma shape with well defined plasma global parameters (i.e. total plasma current and total poloidal magnetic flux at the boundary) by solving a constrained minimization problem. IET can be used for the characterization of an existing plasma boundary or for the full design of a new one. Thus, it can be used to generate families of equilibrium configurations and to determine if the desired plasma shape is within the engineering capabilities of the device. The typical features of IET can be summarized as follows: (a) the plasma shape can be arbitrarily defined or characterized by means of a compact analytical functional form; (b) the fixed boundary plasma equilibrium solver allows the user to arbitrarily define the plasma current density profile for both tokamak and reversed field pinch magnetic configurations; (c) the minimization problem for the computation of the equilibrium coil currents is solved with both single and multi-objective optimization approaches. IET was validated considering both limiter and lower single null ITER-like plasma configurations and an upper single null experimental plasma in the RFX-mod tokamak. For all the cases under analysis, IET leads to accurate results for determining the currents that are able to reproduce the direct equilibrium reconstruction. The accuracy of the solution and the simplicity of both user interface and computational algorithm are the key features of the IET computational tool.