Proton deflectometry analysis in magnetized plasmas: magnetic field reconstruction in one dimension

Proton deflectometry is increasingly used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The algorithm is verified against analytic solutions and applied to example data. The virtue of a 1-D algorithm is that it is fast and can be incorporated into higher-level analysis routines and workflows, for example to scan parameters and conduct uncertainty analysis. Furthermore, working through the 1-D algorithm exposes the fundamental importance of boundary conditions and the initial proton fluence profile for an accurate reconstruction. From these considerations we propose a hybrid mesh-fluence reconstruction technique where fields are reconstructed from fluence data in an interior region with boundary conditions supplied by direct mesh measurements at the boundary.