Analytical theory of the optical gain associated with H–ion transitions in a freely expanding plasma

A theoretical analysis is made of the optical gain associated with H-ion transitions in a fully ionized cylindrical plasma (a plasma column) freely expanding into a vacuum. A formula is proposed which gives the recombination heat deposited in a multiply charged plasma as a result of one three-body nuclear recombination event. An analytical expression is obtained for the time dependence of the gain during the expansion of the plasma, taking into account the recombination heating of the electrons. It is shown that for the maximum gains to be realized, the initial values of the electron density and temperature and also the plasma radius must satisfy a definite relationship. Lowering the initial plasma density leads to some increase in the gain with a substantial reduction in the input energy. An analysis of the time dependence of the gain shows that the 3–2 transition is a promising one. When the initial plasma parameters are N₀= 10²⁰cm^–3, R₀ = 10μ, and Z = 6, the expected value of the maximum gain is κ≈ 1 cm^–1.