A Closed-form Solution for Source-term Emission of Xenon Isotopes from Underground Nuclear Explosions

Yunwei Sun,Souheil Ezzedine,William Cassata,Tarabay Antoun,Yue Hao,Charles Carrigan

doi:10.1007/s11242-021-01650-x

Yunwei Sun, Souheil Ezzedine + Show 4 more

Open Access

https://doi.org/10.1007/s11242-021-01650-x

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Abstract

Isotopic ratios of radioactive xenons sampled in the subsurface and atmosphere can be used to detect underground nuclear explosions (UNEs) and civilian nuclear reactors. Disparities in the half-lives of the radioactive decay chains are principally responsible for time-dependent concentrations of xenon isotopes. Contrasting timescales, combined with modern detection capabilities, make the xenon isotopic family a desirable surrogate for UNE detection. However, without including the physical details of post-detonation cavity changes that affect radioxenon evolution and subsurface transport, a UNE is treated as an idealized system that is both closed and well mixed for estimating xenon isotopic ratios and their correlations so that the spatially dependent behavior of xenon production, cavity leakage, and transport are overlooked. In this paper, we developed a multi-compartment model with radioactive decay and interactions between compartments. The model does not require the detailed domain geometry and parameterization that is normally needed by high-fidelity computer simulations, but can represent nuclide evolution within a compartment and migration among compartments under certain conditions. The closed-form solution to all nuclides in the series 131–136 is derived using analytical singular-value decomposition. The solution is further used to express xenon ratios as functions of time and compartment position.

Highlights

Isotopic ratios and ratio correlations of radioactive xenon isotopes 131mXe, 133mXe, 133Xe, and 135 Xe were proposed as possible indicators for detecting and discriminating underground nuclear explosions (Bowyer et al 1998; Saey and De Geer 2005; Kalinowski and IM release number: LLNL-JRNL-817302.1 3 Vol.:(0123456789)Pistner 2006; Kalinowski et al 2010; Saey et al 2010; Kalinowski 2011; Galan et al 2018)
We simulated the evolution of all 43 nuclides in the cavity, melt puddle, and host-rock compartments, calculated xenon fluxes from the cavity to host rock, and calculated xenon isotopic ratios for discriminating nuclear explosions and civilian nuclear applications
We derived a closed-form solution to a multi-compartment system coupled with complex radioactive decay/ingrowth networks

Summary

Introduction

Isotopic ratios and ratio correlations of radioactive xenon isotopes 131mXe, 133mXe, 133Xe, and 135 Xe were proposed as possible indicators for detecting and discriminating underground nuclear explosions (Bowyer et al 1998; Saey and De Geer 2005; Kalinowski and IM release number: LLNL-JRNL-817302.1 3 Vol.:(0123456789)Pistner 2006; Kalinowski et al 2010; Saey et al 2010; Kalinowski 2011; Galan et al 2018). To mitigate the difficulty and high computational expense of solving the coupled PDEs and ODEs of transport and the complex decay/ingrowth networks necessary in evaluating details of the linkage between the physical and chemical evolution of the cavity, closedform solutions may be developed. Such an approach may be critical to rapidly developing predictive source terms for interpreting xenon-ratio observations

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