Fusion Reactivities with Drift bi-Maxwellian Ion Velocity Distributions

TL;DR

This paper derives a simplified one-dimensional formula for calculating fusion reactivity involving drift bi-Maxwellian ion distributions, enabling efficient analysis of fusion yield and ion spectra with potential reactivity enhancements.

Contribution

It unifies existing derivations into a single expression for fusion reactivity with drift bi-Maxwellian distributions, including anisotropies and drift velocities.

Findings

Reactivity can be significantly enhanced (>20%) by beam and temperature anisotropies.

The derived formula reduces computational complexity for fusion reactivity calculations.

Potential impact on Lawson gain criteria for proton-boron fusion.

Abstract

The calculation of fusion reactivity involves a complex six-dimensional integral that takes into account the fusion cross-section and velocity distributions of two reactants. However, a more simplified one-dimensional integral form can be useful in certain cases, such as for studying fusion yield or diagnosing ion energy spectra. This simpler form has been derived in a few special cases, such as for a combination of two Maxwellian distributions, a beam-Maxwellian combination, and a beam-target combination, and can greatly reduce computational costs. In this study, it is shown that the reactivity for two drift bi-Maxwellian reactants with different drift velocities, temperatures, and anisotropies can also be reduced to a one-dimensional form, unifying existing derivations into a single expression. This result is used to investigate the potential enhancement of fusion reactivity due to the combination of beam and temperature anisotropies. For relevant parameters in fusion energy, the enhancement factor can be larger than 20\%, which is particularly significant for proton-boron (p-B11) fusion, as this factor can have a significant impact on the Lawson fusion gain criteria.