Equilibrium Reconstruction Codes
Reconstruction codes fit a Grad-Shafranov equilibrium to experimental magnetic and internal measurements, inferring the plasma state that best explains the data.
Inference, not prediction
Equilibrium reconstruction is an inverse problem. Given magnetic probe signals, flux loops, and where available internal constraints such as motional Stark effect pitch-angle data or pressure profiles, a reconstruction code finds the free functions p'(psi) and FF'(psi) and the total plasma current distribution that produce an equilibrium consistent with all measurements in a least-squares sense.
This differs from a predictive free-boundary code: reconstruction is anchored to a real or synthetic dataset and reports uncertainties on the inferred profiles.
The fitting loop
The code parameterizes the source profiles with a basis (polynomials or splines), computes the predicted diagnostic signals via Green's functions, and minimizes the weighted residual between predicted and measured signals. Because the Grad-Shafranov source depends on psi, the fit and the equilibrium solve are nested and iterated to joint convergence.
Constraints and regularization
Magnetics alone constrain the boundary and total current well but the internal current profile weakly. Internal measurements break that degeneracy. Regularization or physics priors, such as forcing the bootstrap current to match neoclassical theory, stabilize the ill-posed interior inference.
Role in the workflow
Reconstructed equilibria are the starting point for nearly all interpretive analysis: transport, stability, and heating studies all begin from a reconstruction. For a design-stage device like the Hyperion breeder, reconstruction tools are exercised against synthetic diagnostics to size the magnetic sensor set and verify that the planned diagnostics will constrain the equilibrium adequately once the machine operates.
- Solves an inverse Grad-Shafranov problem
- Fits to magnetics plus optional internal data
- Reports uncertainties on inferred profiles
- Foundation for all interpretive analysis