The three-dimensional (3D) piston model provides a convenient framework for investigating the growth of implosion asymmetries. In the conventional approach, the imploding shell is discretized into multiple small conical pistons, each constrained to move radially and coupled through an isobaric core. However, this method is susceptible to numerical instabilities and entails complex input‑output dependencies, which limit its broader applicability in asymmetry analysis.
To address these limitations, the 3D piston model is reconstructed using a spherical-harmonic expansion, through which the original governing equations are reduced to a set of ordinary differential equations describing the time-dependent coefficients of each mode. This reformulation explicitly characterizes the coupling mechanism between the evolution of low-mode asymmetry perturbations and the primary quasi-one-dimensional implosion dynamics, while also improving numerical stability. Analytical solutions, including zeroth- through second-order perturbative terms, are derived and subsequently validated against numerical integrations performed with a high-order Runge–Kutta solver, thus confirming the reliability of the reconstructed model.