Scenario Planning in Tokamaks by Integrating Free-boundary Equilibrium and Fast Transport Solvers into a Model-based Optimization Scheme

Model-based optimization in tokamaks has the potential of successfully generating feedforward-control policies capable of achieving an advanced scenario characterized by weak magnetic shear, electron internal transport barriers (e-ITBs), and an unfavorable plasma configuration. The optimization scheme integrates free-boundary equilibrium (FBE) and fast transport (FT) solvers, enabling efficient trajectory planning for the powers of available heating and current drive systems (H&CDs) and the currents of the poloidal-field (PF) coils. In the FBE solver, the toroidal current density is parameterized by using polynomials based on the normalized poloidal flux function. This parameterization is constrained by the plasma current prescribed by the designer and the poloidal beta computed by the FT solver. The FT solver, utilizing different transport and source models while leveraging the equilibrium configuration computed by the FBE solver, provides solutions for the electron heat transport equation (EHTE) and the magnetic diffusion equation (MDE). The optimization scheme takes into account limitations imposed on actuators and the plasma state, including the requirement to maintain q_min above specific thresholds to avoid associated MHD instabilities. Optimized evolutions are determined for the PF-coil currents and the H&CD powers of the EAST tokamak to illustrate the effectiveness of the proposed method.