Description
Three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium reconstruction is a central problem in magnetic confinement fusion, where complex geometry, limited diagnostic coverage, and experimental uncertainty fundamentally challenge existing reconstruction approaches. Widely used equilibrium solvers such as VMEC [Hirshman83] determine a single equilibrium by prescribing kinetic and iota profiles, while extensions such as V3FIT [Hanson09] incorporate experimental diagnostics through least-squares fitting. Although these approaches have been highly successful, their deterministic formulation does not provide a systematic framework for uncertainty quantification.
Recent advances in Bayesian equilibrium reconstruction have demonstrated that probabilistic formulations offer a principled method to address these issues. In particular, Bayesian inference for axisymmetric equilibria has established uncertainty-quantified reconstruction using multiple diagnostics as the state of the art in two dimensions [Kwak22]. At the same time, studies of three-dimensional magnetic fields have shown that even small uncertainties in external coil configurations can lead to dramatic topological changes in the magnetic field structure [Zhu19], underscoring the necessity of uncertainty-aware modeling in 3D. Extending Bayesian equilibrium reconstruction from axisymmetric to fully three-dimensional configurations therefore represents a natural and essential, but substantially more challenging, next step.
In this work, we introduce a probabilistic framework for three-dimensional equilibrium reconstruction by embedding a flux-coordinate, VMEC-compatible equilibrium representation within a Bayesian inference setting. Equilibrium-defining quantities are modeled probabilistically in flux space, while experimental diagnostics are incorporated through likelihood functions defined in real space. This separation enables physical constraints, diagnostic models, and uncertainty descriptions to be combined in a coherent and extensible manner.
The present contribution focuses on the theoretical formulation of this framework, which establishes a foundation for uncertainty-quantified 3D equilibrium reconstruction and future applications to diagnostic integration, model validation, and experimental design.
[Hanson09] Hanson, James D., et al. Nucl. Fusion 49.7 (2009): 075031.
[Hirshman83] Hirshman, Steven P., and J. C. Whitson. Phys. Fluids 26, 3553 (1983);
[Kwak22] Kwak, Sehyun, et al. Nucl. Fusion 62.12 (2022): 126069.
[Zhu19] Zhu, Caoxiang, et al. Nucl. Fusion 59.12 (2019): 126007.