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

TL;DR

This paper introduces a simple, efficient Monte Carlo method for calculating fusion reactivities with arbitrary ion velocity distributions, significantly reducing computational complexity while maintaining high accuracy.

Contribution

It presents a novel Monte Carlo approach that computes fusion reactivities with arbitrary distributions in O(N) time, improving efficiency over traditional methods.

Findings

Achieves less than 1% error with about 10,000 samples.

Validates approach against analytical results for drift bi-Maxwellian distributions.

Demonstrates applicability to various distributions like drift ring beam and slowing down 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 $N\sim10^4$ samples for our standard approach.