Instantaneous charge state of Uranium projectiles in fully ionized plasmas from energy loss experiments

Abstract: The instantaneous charge state of uranium ions traveling through a fully ionized hydrogen plasma has been theoretically studied and compared with one of the first energy loss experiments in plasmas, carried out at GSI-Darmstadt by Hoffmann \textit{et al.} in the 90's. For this purpose, two different methods to estimate the instantaneous charge state of the projectile have been employed: (1) rate equations using ionization and recombination cross sections, and (2) equilibrium charge state formulas for plasmas. Also, the equilibrium charge state has been obtained using these ionization and recombination cross sections, and compared with the former equilibrium formulas. The equilibrium charge state of projectiles in plasmas is not always reached, it depends mainly on the projectile velocity and the plasma density. Therefore, a non-equilibrium or an instantaneous description of the projectile charge is necessary. The charge state of projectile ions cannot be measured, except after exiting the target, and experimental data remain very scarce. Thus, the validity of our charge state model is checked by comparing the theoretical predictions with an energy loss experiment, as the energy loss has a generally quadratic dependence on the projectile charge state. The dielectric formalism has been used to calculate the plasma stopping power including the Brandt-Kitagawa (BK) model to describe the charge distribution of the projectile. In this charge distribution, the instantaneous number of bound electrons instead of the equilibrium number has been taken into account. Comparing our theoretical predictions with experiments, it is shown the necessity of including the instantaneous charge state and the BK charge distribution for a correct energy loss estimation. The results also show that the initial charge state has a strong influence in order to estimate the energy loss of the uranium ions.