Theory of the pulsed molecular nitrogen laser

It is shown that laser action at 3371 A terminates in times t < (tau(32)(-1) + Y(3))(-1), where tau(32) is the lifetime of the transition of C(3)pi(u) --> B(3)pi(g) and Y(3) is the electron depopulation rate of the upper laser level. Following Gerry but including electron impact mixing of laser levels, rate equations, coupled to the circuit equation, were solved under saturation approximations. Assuming a Seaton excitation cross section between laser levels, with an effective Gaunt factor of 0.25, power and pulse width were in good agreement with Shipman's values. The rate equations were also solved without recourse to the saturation approximation yielding excellent agreement with the saturation method during most of the pulse and indicating the existence of an early oscillation which is not predicted by the saturation approximation method. Finally, the inclusion of the electron impact ionization of he nitrogen molecule from the excited state C(3)pi(u) brings the pulse width to still better agreement with Shipman's values.