Kinetics of helium bubble formation in nuclear materials

TL;DR

This paper models helium bubble formation in nuclear materials using discrete kinetic equations, providing a detailed analysis of size distribution and comparing different approximation methods for better understanding bubble growth dynamics.

Contribution

It introduces a boundary layer theory for discrete equations and compares it with numerical solutions and previous models, advancing the understanding of helium bubble kinetics.

Findings

Distribution function approximated by continuum and local expansion methods

Boundary layer theory aligns well with numerical solutions

Improved modeling of helium bubble growth in nuclear materials

Abstract

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by a discrete kinetic equations for the number densities of bubbles having $k$ atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.