This study describes an efficacious setup for producing lasing plasma which utilizes a thin solid film for the purpose of collisional x-ray lasers. For analyzing this setup, a simple atomic kinetic model of multiple charged high Z ions is developed. The model based on screened hydrogenic approximation is improved to reproduce a level structure of Ar-like to Pd-like ions. The time dependent ion abundance is calculated in plasmas produced from a thin foil irradiated by a short pulse laser. Calculations show the optimum heating pulse duration for attaining a large abundance of Ni-like ions in the expanding plasma. Combined with excitation by the second short pulse laser, this plasma can be an effective medium for producing a transient gain of electron-collisional excited x-ray lasers.