{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-simple-and-fast-approach-for-computing-the","title":"A Simple and Fast Approach for Computing the Fusion Reactivities with Arbitrary Ion Velocity Distributions","arxiv_id":"2302.09753","date":"2023-02-20","proceeding":null,"authors":["Huasheng Xie"],"abstract":"Calculating fusion reactivity involves a complex six-dimensional integral of the fusion cross section and ion velocity distributions of two reactants. We demonstrate a simple Monte Carlo approach that efficiently computes this integral for arbitrary ion velocity distributions with a time complexity of $O(N)$, where $N$ is the number of samples. This approach generates random numbers that satisfy the reactant velocity distributions. In cases where these numbers are not readily available, we propose using Gaussian random numbers with weighted factors. For cases where only a small number of $N$ samples are available, a $O(N^2)$ method can be used. We benchmarked this approach against analytical results for drift bi-Maxwellian distributions and provided examples of drift ring beam and slowing down distributions. Our results show that the error can be less than 1\\% with $N\\sim10^4$ samples for our standard approach.","url_abs":"https://arxiv.org/abs/2302.09753v2","url_pdf":"https://arxiv.org/pdf/2302.09753v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-simple-and-fast-approach-for-computing-the","repo_url":"https://github.com/hsxie/fusionreactivity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}