Characterizing nonlinear stopping power in warm dense matter with time-dependent density functional theory

Electronic stopping power underlies the heating mechanism of fast ignition fusion concepts and drives hotspot self-heating in inertial confinement fusion. Commonly used linear-response models assume stopping power scales quadratically with the projectile's nuclear charge Z, but slow ions can capture electrons from the host material that screen further electronic excitations. Here, we investigate the Z-dependence of stopping powers using real-time time-dependent density functional theory (TDDFT) calculations for warm dense aluminum and carbon. By comparing TDDFT predictions for alpha-particle and proton stopping powers, we benchmark available effective charge models, including their sensitivity to density, temperature, and ion velocity. To directly probe the linear-response regime, we also compute stopping powers for fictitious fractionally charged projectiles. We find modest deviations from Z² scaling even for Z<1, suggesting that even proton stopping powers exhibit nonlinear effects. These results challenge typical assumptions of stopping power models based on linear-response theory and carry practical implications for accurately parameterizing simulations of fusion experiments.