Modeling the Effects of Cluster Size on X-ray Amplification at $\sim $3 {\AA} in Strong Laser Field -- Xe Cluster Interactions

An extensive xenon time-dependent ionization dynamic (TD-ID) model that includes a complex set of lumped excited states in the Ni-, Co- [1], and Fe-like ionization stages, as well as 3 single hole states in Co-like xenon and 16 single and 9 double hole states in Fe-like xenon that are self-consistently coupled to the ionization dynamics. The TD-ID model receives input on the cluster's electron and ion temperatures and densities from a 3D Relativistic Molecular Dynamics Model in which electrons and ions are treated classically according to a coupled set of relativistic equations of motion. One of the important effects found in MD calculations, not seen in hydrodynamic descriptions of laser-matter interactions, is the fast ion heating that occurs during the cluster's explosion. The combined model enables us to study the influence of cluster size and laser intensity (10$^{18}$-10$^{20}$ W/cm$^{2})$ on the cluster's amplified x-ray emissions when they are subject to a 248 nm laser field.\\[4pt] [1] Tz. B. Petrova, \textit{et.al.}, J. Phys. B \textbf{43} (2010) 025601.