Numerical assessment of a novel technique for the reconstruction of 3D magnetic fields in tokamaks

In this paper, we aim at numerical validating a novel technique for 3D reconstruction of magnetic fields in tokamaks from a discrete set of magnetic measurements. The identification is based on the solution of a classical inverse problem, after modeling the direct problem by using a well-tailored expansion for the plasma and the other field sources. Suitable boundary conditions are defined on two virtual nested surfaces, one inside the plasma, the other surrounding the plasma and including the magnetic sensors. Some a-priori information on the problem, as the expected major periodicity of 3D effects and the known poloidal field sources, are also taken into account for the field evaluation. An influence matrix is calculated, to get the measurement values due to each basis function and then a classical pseudo-inverse procedure identifies the coefficients in the expansion. The reconstructed magnetic field is then available to trace the plasma boundary with conventional methods. In this way, accurate 3D plasma shape identifications are available, at affordable computational cost. A significant set of magnetic configurations is adopted as test-bed for validating the technique, allowing in particular to separately evaluate the efficiency in catching the intrinsically 2D effects and the fully 3-D ones.