标题： MAST-U上静态前向自由边界Grad-Shafranov问题的多重解 显示英文标题

标题： Multiple solutions to the static forward free-boundary Grad-Shafranov problem on MAST-U

摘要： 广义-沙夫拉诺夫（GS）方程是一个非线性椭圆型偏微分方程，用于描述托卡马克等离子体的理想磁流体力学平衡。先前的研究表明，在理想几何形状下，当简化等离子体电流密度分布和边界条件时，GS 方程存在多个解。直到现在，关于在更复杂的电流密度分布和积分自由边界条件下（这些条件常用于生产级平衡代码中），真实世界托卡马克几何形状中是否存在多重平衡的问题仍未得到解答。在这项工作中，我们使用经过验证的演化平衡求解器 FreeGSNKE 和排斥连续算法，在 MAST-U 托卡马克几何形状中发现了静态前向自由边界 GS 问题的多个解。通过改变 GS 方程中的等离子体电流、电流密度分布系数或线圈电流，我们识别并表征了不同的平衡解，包括深陷和较浅约束的等离子体状态。我们认为，即使存在更多平衡的可能性，也可能受到积分自由边界条件的限制，该条件在全球范围内耦合了计算边界上的环向磁通与内部的磁通。最后，我们讨论了这些发现对更广泛的平衡建模的影响，并强调需要探索其他平衡代码和托卡马克中是否存在多个解，以及它们对依赖于 GS 平衡的下游模拟可能产生的影响。 显示英文摘要

摘要： The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when solved in idealistic geometries with simplified plasma current density profiles and boundary conditions. Until now, the question of whether multiple equilibria might exist in real-world tokamak geometries with more complex current density profiles and integral free-boundary conditions (commonly used in production-level equilibrium codes) has remained unanswered. In this work, we discover multiple solutions to the static forward free-boundary GS problem in the MAST-U tokamak geometry using the validated evolutive equilibrium solver FreeGSNKE and the deflated continuation algorithm. By varying the plasma current, current density profile coefficients, or coil currents in the GS equation, we identify and characterise distinct equilibrium solutions, including both deeply and more shallowly confined plasma states. We suggest that the existence of even more equilibria is likely prohibited by the restrictive nature of the integral free-boundary condition, which globally couples poloidal fluxes on the computational boundary with those on the interior. We conclude by discussing the implications of these findings for wider equilibrium modelling and emphasise the need to explore whether multiple solutions are present in other equilibrium codes and tokamaks, as well as their potential impact on downstream simulations that rely on GS equilibria.