Reconstruction of 2D line-integrated electron density using angular filter refractometry and a fast marching Eikonal solver

Refraction of an optical probe beam by a plasma can be measured with angular filter refractometry (AFR), which produces an image containing intensity contours that correspond to curves of constant refraction angle [1]. Further analysis is required to reconstruct the underlying line-integrated electron density. Most prior efforts to calculate density from AFR data have been limited to 1D analysis or forward-fitting techniques [2, 3]. Here, we detail the use of a fast marching Eikonal solver [4] to directly invert AFR data and obtain the 2D line-integrated electron density. The analysis method is first verified with synthetic data and then applied to laser-driven experiments performed at the OMEGA EP Laser Facility of single and double plume expansion from a solid target. The calculated densities agree with 1D results and are shown to be consistent with the original AFR data via forward modeling. This technique is especially useful for studying the coronal region of high-energy-density plasmas due to its large dynamic range (10¹⁸-10²⁰ cm^-2) [1].



[1] D. Haberberger et al., Phys. Plasmas 21, 056304 (2014).

[2] J. Peebles et al., New Jour. Phys. 19, 023008 (2017).

[3] P. Angland et al., Rev. Sci. Instrum. 88, 103510 (2017).

[4] J. A. Sethian, SIAM Rev. 41, 199 (1999).