A Quantum Data Fitting Approach to Parametrize Dependences of ICF Implosion Asymmetries*

A quantum data fitting algorithm was developed to characterize the correlations between measured core asymmetries and the sources of nonuniformities in laser-driven inertial confinement fusion (ICF) implosion experiments. This approach constructs an ICF experimental observable as a superposition of quantum many-body wave (QWF) functions in terms of Legendre polynomials. The multi-parameter correlations are explored by analyzing the behavior of the corresponding density matrix that stores a minimal set of QWF eigenstates. The objective is to quantify the mapping relationship between measured core asymmetries and their sources. This machine learning algorithm will be ultimately applied to develop a real-time symmetry control system to improve the fusion energy output by minimizing the low-mode asymmetry. The quantum data fitting model was applied to construct mapping relationships for a wide range of experimental observables in OMEGA implosions. The model performs well in fitting ICF implosion metrics, including fusion yields and areal densities, and asymmetries observed in nuclear and x-ray image measurements. A decent correlation was found between hot-spot flow velocities and target positioning, beam pointing, and beam-to-beam laser power balancing. By parameterizing the dependencies of core asymmetries, the causality of low modes can be identified, guiding future efforts to mitigate the impact of low-mode nonuniformities on ICF implosions.