Kinetic theory for a short-wavelength lasing plasma

A kinetic analysis is made of a reacting plasma dominated by three-body recombination and ionization, together with collisional and radiative excitation and de-excitation of atomic states. The plasma includes excited atoms, ions, electrons and photons. The kinetic theory yields rate equations for these species, together with explicit expressions for relevant rate coefficients. In the limit of spatial homogeneity and assuming atom and electron densities are close to equilibrium, an explicit form is obtained for the radiation absorption coefficient per unit length. A criterion is then constructed for population inversion. Application to a helium-like active medium (e.g. Al⁺¹¹) and hydrogen-like passive medium (e.g. A1⁺¹²), at electron temperature of 300 eV, reveals that population inversion ensues at electron densities in excess of 10²⁰ cm^-3. Algebraic solution of atomic state rate equations demonstrates that the absorption coefficient grows insensitive to photon-atom interactions with increasing electron density.