A divertor tokamak plasma equilibrium solver based on flux coordinates
A divertor tokamak plasma equilibrium solver based on flux coordinates
In the pursuit of controlled nuclear fusion, precise modeling of plasma behavior within a tokamak is critical. One of the most challenging and essential aspects of this process is solving for plasma equilibrium—especially in configurations that include a divertor, which is used to manage heat and particle exhaust. This work presents an advanced plasma equilibrium solver that leverages flux coordinates, enabling accurate, efficient, and stable simulations of magnetically confined plasmas in a divertor tokamak configuration.
The equilibrium of a tokamak plasma is governed by the Grad-Shafranov equation, a nonlinear partial differential equation that describes the balance between magnetic pressure, plasma pressure, and current density. Incorporating flux coordinates—where magnetic flux surfaces are treated as coordinate surfaces—offers substantial advantages. These include improved numerical stability, natural alignment with magnetic field lines, and simplification of complex boundary conditions near the separatrix and X-point regions typical of divertor-equipped tokamaks.
The solver employs a highly adaptive grid system aligned with poloidal magnetic flux, which enhances resolution near critical features such as the X-point and divertor leg. It ensures free-boundary equilibrium, allowing for flexible boundary shaping and accurate simulation of plasma-facing component interactions. By integrating an efficient numerical scheme, the model supports rapid convergence, making it well-suited for coupling with real-time control systems or integrated tokamak modeling suites.
This equilibrium solver contributes significantly to the optimization of tokamak design, divertor placement, and operational scenarios. It is particularly beneficial for current and next-generation fusion devices like ITER and DEMO, where precise control of magnetic geometry directly impacts performance and plasma-facing component durability.
By combining rigorous computational techniques with advanced coordinate systems, this solver paves the way for deeper understanding and improved predictability of tokamak behavior under realistic operating conditions. It provides a robust foundation for further developments in edge physics, transport modeling, and plasma control.
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