A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications
This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.