Reconstructing FRC equilibria from experimental data

The magnetic structure of FRCs cannot be measured directly by existing diagnostics. A new tool finds the structure based on field measurements at the vessel wall. The first step is data conditioning, finding smooth fits to the data, i.e. the excluded flux radius and wall magnetic flux, both as functions of the axial coordinate. Distilled from these are six parameters, three each from the excluded flux and wall flux profiles. The second step is the equilibrium finder, assuming a static equilibrium (Grad-Shafranov, “GS” equation). The inputs to GS system are the pressure vs flux function and the wall-flux boundary condition. The pressure is expressed as one function family and the wall flux as another. Both families have three adjustable parameters for a total of six. Finally, a two-level iteration finds the solution: the inner loop is a standard relaxation algorithm that updates the flux function; the outer loop iterates the six adjustables, targeting the six parameters distilled by data conditioning. The result is the 2D structure of the flux variable. Extracted from this are various properties of interest, e.g. trapped flux, fraction of plasma current flowing inside the separatrix, as well as stability indices for interchange and tearing.