A Simple and Fast Approach for Computing the Fusion Reactivities with Arbitrary Ion Velocity Distributions

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 $N\sim 10^4$ samples for our standard approach.

arXiv comment8 pages, 5 figures

References in corpus (3)

• A Unified Numerically Solvable Framework for Complicated Kinetic Plasma Dispersion Relations
• Fusion Reactivities with Drift bi-Maxwellian Ion Velocity Distributions
• Fusion yield of plasma with velocity-space anisotropy at constant energy

Cited by in corpus (7)

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• Enhancement of Fusion Reactivity under Non-Maxwellian Distributions: Effects of Drift-Ring-Beam, Slowing-Down, and Kappa Super-Thermal Distributions
• On the Upper Bound of Non-Thermal Fusion Reactivity with Fixed Total Energy
• Enhancement of fusion reactivities using non-Maxwellian energy distributions
• Generation of non-Maxwell-Boltzmann energy distributions during thermalization of interacting baths
• Dynamics of thermalization in classical three-dimensional many-body systems: Non-Maxwellian distributions and the role of anisotropic trapping
• Maximization of nuclear fusion reactivity via optimal energy distributions