Bluemira is an integrated design framework for fusion power plants. The design space of many physics and engineering aspects of a power plant concept can be rapidly explored using automated workflows. Bluemira workflows include a free-boundary plasma equilibrium solver with coil optimisation of position and current, that is subject to geometrical and engineering constraints.
An equilibrium poloidal field configuration has contributions from both the plasma and the coilset. Normally, when we optimise the coilset contribution, we must also re-solve the non-linear Grad-Shafranov equation for the equilibrium to find the plasma contribution. However, we can exploit the premise that the equilibrium solution will not change if the coilset contribution in the region occupied by the plasma is kept the same (Bardsley et al., 2024). This means that we do not need to re-solve the Grad-Shafranov equation, which is advantageous as we can reduce the computational complexity of the optimisations used in our coilset and divertor magnetic field configuration design.
The magnetic field in a toroidal region can be described by a scalar quantity using toroidal harmonic functions. In this work, we make use of these functions to describe the coilset contribution to the equilibrium poloidal magnetic flux within the region containing the plasma. We then select the most significant harmonics and fix their amplitudes to create a small (typically about 5 amplitude values) set of constraints to use while performing coilset optimisation. We explore the use of toroidal harmonic constraints on both single and double null designs and compare our method to optimisations using a set of fixed poloidal flux points to constrain the LCFS shape while re-solving the Grad-Shafranov equation. We present the implementation of the toroidal harmonic constraint method in the bluemira framework and demonstrate the advantages of its application on magnetic field design using equilibria from demonstration power plant concept designs.