SCOPE: Simple Coil Optimization for Plasma and Engineering

TL;DR

The paper tackles the challenge of designing HTS tokamak coils that meet stringent engineering and plasma-shaping constraints across multiple operating scenarios. It proposes SCOPE, a two-tier optimization where an inner analytic, quadratic/quartic cost function in coil currents is embedded within an outer simulated-annealing search over coil sizes and positions, all constrained by LCFS-based plasma requirements and an inductive-drive model: $V_{\textrm{ind}}(t) = -\dfrac{d\psi_{\textrm{LCFS}}}{dt}$ and $\psi_{\textrm{ind}}(t) = -\int_0^t V_{\textrm{ind}}(t') dt' + \psi_0$, with $\Delta\psi(t) = \alpha \psi_{\textrm{ind}}(t) - \psi_0 - \psi_{\textrm{FBE,LCFS}}(t)$. Key contributions include enabling multi-scenario optimization to avoid single-point overfitting, coupling plasma, magnet, and divertor constraints for coherent design feedback, and achieving millions of evaluations within hours on modest hardware; results on the ST-E1 pre-concept design show substantial reductions in coil currents and hoop stresses while maintaining feasible flux swings. The approach provides actionable feedback for downstream cryogenics and power-supply planning, advancing integrated magnet-plasma-divertor design and enabling robust, scalable design iterations. Overall, SCOPE demonstrates a practical, high-fidelity optimization pathway for complex, interconnected tokamak coil systems with HTS technologies.

Abstract

Designing superconducting coils for a tokamak fusion device is a highly coupled, non-linear design problem. The coils have many disparate engineering requirements from structural to power electronics, as well strict limits placed on the system by the high temperature superconducting (HTS) cables. Simultaneously, the coils must be able to contain multiple plasma scenarios from inception, through ramp up, to flat top, and ramp down, all whilst applying a large, controlled, inductive voltage to drive current. In addition, we wish to optimize divertor separatrices to increase the likelihood of designing a suitable divertor strikepoint. Lastly, the physical limits of the entire tokamak must be taken into account and space reserved for support structures, access for maintenance schemes, and installation limits. The method outlined here uses a combined simulated annealing method to find optimal coil sizes and positions with a constrained quadratic or quartic optimization for the coil currents. The method is designed to optimize coils for multiple scenarios simultaneously, including ramp-ups, to avoid over optimization of a single design point. A key enabler is the efficient implementation that allows millions of evaluations to be performed in a few hours with modest computational power. This optimization method is part of a larger, iterative workflow which enables further, detailed design work to feedback on the optimization.

Figures (4)

• Figure 1: Surface plot of the typical percentage difference between the flux created by the coils from the FBE and the flux after optimization. The LCFS (red dashed) is shown with the constraint points (black crosses). At maximum the deviation of the flux recreation reaches 1.4$\%$ with 0.25$\%$ set as the average by the constraint function.
• Figure 2: Showing different flux on the LCFS for the optimization ramp up case (blue) the flux swing from METIS required for the 27.8 Vs total flux swing in time assuming no constant of integration, (red) the flux on the LCFS after optimization including a flux shift, (yellow) the value of flux on LCFS from the bare FBE that had to be cancelled and (purple) the flux from the solenoid using the infinite solenoid approximation by integrating the total flux through the solenoid bore at mid-plane.
• Figure 3: Axisymmetric of an ST-E1 pre-concept design point. A set of representative plasma LCFS (red lines) with constraint points (black crosses). The TF coils (dark blue) are the primary structural object that the coils must be designed around. The path taken by the initial PF coils (circle-lines) to the optimized coils (cross-lines) is shown. The light blue regions show the spatial constraint areas and can be added arbitrarily. Note the internal structures (black lines) are inconsistent with the plasma due to the parallel development of multiple simultaneous workflows.
• Figure 4: (Top) hoop stresses in the coils with a 30Vs LCFS flux swing centred on zero, very large central solenoid stresses can be seen at the end of the swing due to confinement of a large plasma at the end of the ramp. (Middle) hoop stresses with a LCFS flux swing shifted by (+33Vs) creating greatly reduced stresses. (Bottom) Idealised solenoid flux, ie the total flux through the centre of the solenoid, for the symmetric and shifted flux swing. While the flux swing on the plasma may be symmetric, we can see that the optimal solenoid swing is not and vice versa.