A theoretical model for quantifying the imprinting sensitivity of direct-drive inertial confinement fusion implosions

To quantify the sensitivity of diverse implosion designs to laser imprinting, we developed an equivalent perturbation model that maps laser imprinting as the target surface perturbation. By incorporating imperfections in target fabrication and thermal smoothing in the plasma, the model shows a reduced implosion sensitivity on laser imprinting, extending the analysis beyond geometric irradiation. The imprint sensitivity threshold is defined as $\delta h_{\rm las}/\delta h_{\rm tar}= 0.1$. When the imprinting amplitude $\delta h_{\rm las}$ is less than one-tenth of the target perturbation amplitude $\delta h_{\rm tar}$, target perturbations dominate. Radiation-hydrodynamics simulations confirm that when $\delta h_{\rm las}/\delta h_{\rm tar}\le 0.1$, variations in nonlinear onset time and entropy remain within 12\% of those observed with target perturbations alone. Moreover, the imprinting sensitivity is supported by OMEGA experiments. These results indicate that joint control of laser and target perturbations, improving target quality when $\delta h_{\rm las}/\delta h_{\rm tar}<0.1$ and laser smoothing otherwise, can support stable implosions for high-gain direct-drive inertial confinement fusion.