A novel optimal control strategy has been formulated to enhance plasma stability within tokamak fusion devices. This approach leverages incompressible, viscous, electrically conducting magnetohydrodynamic (MHD) fluid equations to model plasma behavior. The objective is to identify control inputs that steer the plasma towards a desired stable state, minimizing deviations and preventing disruptions. The mathematical framework addresses the inherent complexities of plasma dynamics, aiming for precise real-time adjustments to magnetic field configurations and heating profiles.

The presented work builds upon established MHD theories, which describe plasma as a conducting fluid interacting with magnetic fields. This continuum model simplifies the kinetic complexities of individual particles, allowing for the analysis of macroscopic plasma phenomena such as turbulence and instabilities. By treating the plasma as a viscous fluid, the model incorporates dissipative effects that are crucial for understanding energy transport and the potential for plasma cooling, which can lead to disruptions. The electrical conductivity ensures that the plasma responds to and influences applied electromagnetic fields.

The presented work builds upon established MHD theories, which describe plasma as a conducting fluid interacting with magnetic fields.

Previous research in tokamak control has often relied on simplified plasma models or empirical approaches. While these methods have achieved significant operational milestones, they can struggle with the highly nonlinear and dynamic nature of fusion plasmas. The development of advanced control algorithms, informed by more comprehensive physical models, is essential for achieving sustained high-performance plasma regimes. This research aims to bridge the gap between theoretical plasma physics and practical engineering challenges in fusion reactor operation.

The proposed optimal control problem is framed as a minimization of a cost functional, which quantifies deviations from the target plasma state. This functional typically includes terms related to plasma confinement, temperature, density, and stability margins. The control inputs, such as external coil currents or heating power, are then optimized to minimize this cost over a given time horizon. The solution involves solving complex differential equations, often requiring advanced numerical techniques and computational resources to implement in real-time control systems.

Future work will focus on validating this control framework through numerical simulations using more realistic tokamak geometries and plasma profiles. Investigating the robustness of the control strategy against uncertainties in plasma parameters and external perturbations will be critical. Furthermore, exploring the integration of this optimal control approach with other plasma control techniques, such as feedback control based on diagnostic measurements, could lead to more resilient and efficient fusion reactor operation.