Design of proton deflectometry with in situ x-ray fiducial for magnetized high-energy-density systems

We report a design and implementation of proton deflectometry with an in situ reference x-ray image of a mesh to precisely measure non-uniform magnetic fields in expanding plasmas at the OMEGA and OMEGA EP laser facilities. The technique has been developed with proton and x-ray sources generated from both directly driven capsule implosions and short pulse laser-solid interactions. The accuracy of the measurement depends on the contrast of both the proton and x-ray images. We present numerical and analytic studies to optimize the image contrast using a variety of mesh materials and grid spacings. Our results show clear enhancement of the image contrast by factors of four to six using a high Z mesh with large grid spacing. This leads to further improvement in the accuracy of the magnetic field measurement using this technique in comparison with its first demonstration at the OMEGA laser facility [Rev. Sci. Instrum. 93, 023502 (2022)].