In a groundbreaking discovery that could reshape our understanding of tokamak plasmas, researchers have found multiple solutions to the static forward free-boundary Grad–Shafranov (GS) problem in the MAST-U tokamak geometry. This finding, published in the journal *Nuclear Fusion* (translated to English), challenges long-held assumptions and opens new avenues for plasma physics and fusion energy research.
The GS equation is a cornerstone of tokamak plasma modeling, governing the ideal magnetohydrodynamic equilibrium. Previous studies had hinted at the possibility of multiple solutions, but these were limited to idealized geometries and simplified conditions. The new research, led by K. Pentland of the United Kingdom Atomic Energy Authority, demonstrates that multiple equilibria can indeed exist in real-world tokamak geometries with complex current density profiles and integral free-boundary conditions.
Using the validated evolutive equilibrium solver FreeGSNKE and the deflated continuation algorithm, Pentland and his team varied parameters such as plasma current, current density profile coefficients, and coil currents. This approach revealed distinct equilibrium solutions, including both deeply and more shallowly confined plasma states. “The existence of multiple equilibria suggests that our understanding of plasma behavior in tokamaks may be more nuanced than previously thought,” Pentland explained. “This could have significant implications for equilibrium modeling and downstream simulations.”
The restrictive nature of the integral free-boundary condition, which globally couples poloidal fluxes on the computational boundary with those on the interior, likely limits the number of possible equilibria. However, the discovery raises important questions about the uniqueness of solutions in other equilibrium codes and tokamaks. “We need to explore whether multiple solutions are present in other scenarios and understand their potential impact on fusion energy research,” Pentland added.
The findings could have profound implications for the energy sector, particularly in the development of fusion energy as a clean and sustainable power source. By uncovering multiple equilibria, researchers can gain deeper insights into plasma behavior and optimize tokamak designs for more efficient and stable operation. This could accelerate the commercialization of fusion energy, bringing us closer to a future powered by clean, limitless energy.
As the field continues to evolve, the discovery of multiple solutions to the GS problem serves as a reminder of the complexity and potential of plasma physics. It underscores the need for continued research and innovation in fusion energy, paving the way for a brighter, more sustainable future.