Multishock compression of dense deuterium-helium mixtures with varying helium abundance up to megabar pressures: Assessing the role of the nonideal mixing effect

Hydrogen and helium constitute the main components of Jovian planets. Under the warm dense conditions inside gas giants, helium droplets settle deeper into the planet, forming a helium gradient. Consequently, thermodynamic properties, such as the equation of state (EoS) and sound speed, of hydrogen-helium mixtures with varying atomic helium mole fractions $({x}_{\mathrm{He}})$ under warm dense conditions are crucial for evaluating EoS models used in astrophysical modeling. To this end, we conducted multiple reverberation compression experiments on gaseous deuterium-helium $({\mathrm{D}}_{2}\text{\ensuremath{-}}\mathrm{He})$ mixtures with two distinct ${x}_{\text{He}}$ of 0.14 and 0.60. The multishock pressures reached 110 GPa, and reshock temperatures reached 7620 K, conditions directly relevant to planetary interiors. The obtained EoS and sound velocity are used to evaluate ${\mathrm{H}}_{2}\text{\ensuremath{-}}\mathrm{He}$ EoS models constructed with or without taking into account nonideal mixing (NIM) effects. It is found that the state-of-the-art $\mathrm{CMS}19+\mathrm{HG}23$ EoS model, which incorporates NIM effects for arbitrary ${x}_{\text{He}}$ values, can reasonably reproduce the measured pressure-density EoS for both mixtures but underestimates the shock temperature of the ${x}_{\text{He}}=0.14$. First-principles molecular dynamics (FPMD) simulations reveal that the NIM effect, arising from the strengthening effect of helium on deuterium molecule bonds, is more prominent for the mixture with ${x}_{\text{He}}=0.60$. Our findings impose new constraints on the EoS models applicable to the mixtures with arbitrary ${x}_{\text{He}}$, which are crucial for modeling the structure and evolution of gas giants.