Abstract: We present a compact semi-analytic framework that couples solid-target energy-deposition physics with two-temperature plasma hydrodynamics to model the earliest stages of a fission-driven fireball. Starting from spherically symmetric conservation laws, the approach replaces cold-matter constitutive closures with a two-temperature equation of state that explicitly includes ionization enthalpy and radiative energy loss, and systematically reduces the full PDE system to a thin-shell ODE model for the shell radius and mean ionization fraction. The manuscript documents the step-by-step asymptotic reduction, derives closed-form limits, and quantifies model uncertainty through analytic sensitivities and example-propagated bounds. A stability study of the reduced dynamics includes analytic results for the ionization subsystem and numerical recipes for instantaneous eigenvalues, finite-time multipliers, and Lyapunov exponents useful for experimental design. Representative parameter sweeps reveal rapid ionization (sub-picosecond) and nanosecond-scale hydrodynamic expansion, characterized by velocities on the order of 106 m·s⁻¹. Comparisons with classical blast scaling solutions and recommended validation pathways (radiation-hydrodynamic benchmarks and targeted laser-plasma experiments) demonstrate the model’s value as a fast, efficient, and physically grounded tool for parametric studies, uncertainty quantification, and experiment planning.

Keywords: Thin-shell model, Two-temperature plasma, Ionization kinetics, Radiative losses, Uncertainty quantification, Stability analysis, Nuclear fireball dynamics, Reduced-order modeling

Pages: 86-102