A fast, magnetics-free flux surface estimation and q-profile reconstruction algorithm for feedback control of plasma profiles

The flux surfaces' layout and the magnetic winding number q are important quantities for the performance and stability of tokamak plasmas. Normally, these quantities are iteratively derived by solving the plasma equilibrium for the poloidal and toroidal flux.In this work, a fast, non-iterative and magnetics-free numerical method is proposed to estimate the shape of the flux surfaces by an inward propagation of the plasma boundary shape, as can be determined for example by optical boundary reconstruction described in Hommen (2010 Rev. Sci. Instrum. 81 113504), toward the magnetic axis, as can be determined independently with the motional Stark effect (MSE) diagnostic. Flux surfaces are estimated for various plasma regimes in the ITER, JET and MAST tokamaks and are compared with results of CRONOS reconstructions and simulations, showing agreement to within 1% of the minor radius for almost all treated plasmas.The availability of the flux surface shapes combined with the pitch angles measured using MSE allow the reconstruction of the plasma q-profile, by evaluating the contour-integral over the flux surfaces of the magnetic field pitch angle. This method provides a direct and exact measure of the q-profile for arbitrary flux surface shapes, which does not rely on magnetic measurements. Results based on estimated flux surface shapes show agreement with CRONOS q-profiles of better than 10%. The impact of the shape of the flux surfaces on the q-profile, particularly the profiles of elongation and Shafranov shift, and offsets in plasma boundary and the magnetic axis are assessed.OFIT+ was conceived for real-time plasma profile control experiments and advanced tokamak operation, and provides quickly and reliably the mapping of actuators and sensors to the minor radius as well as the plasma q-profile, independent of magnetic measurements.