Three-dimensional modeling and inversion of x-ray pinhole detector arrays

X-ray pinhole detectors are a common and useful diagnostic for high temperature and fusion-grade plasmas. While the measurements from such diagnostics are line integrated, local emission can be recovered by inverting or modeling the data using varying assumptions including toroidal symmetry, flux surface isoemissivity, and one-dimensional (1D) chordal lines of sight. This last assumption is often valid when the structure sizes and gradient scale lengths of interest are much larger than the spatial resolution of the detector elements. However, x-ray measurements of, for example, the strong gradients in the H -mode pedestal may require a full three-dimensional (3D) treatment of the detector geometry when the emission of the plasma has a significant variation within the field of view, especially in a high-triangularity, low aspect ratio plasma. Modeling of a high spatial resolution tangential edge array for NSTX has shown that a proper 3D treatment can improve the effective spatial resolution of the detector by 10%-40% depending on the modeled signal-to-noise ratio and gradient scale length. Results from a general treatment of arbitrary detector geometry will provide a guideline for the amount of systematic error that can be expected by a 1D versus 3D field of view analysis.