R. M. Thomson

Calculations on output pulse shapes, gain pulse profiles, and gain limitation in the CO2 TEA laser

An eight‐equation kinetics model for the CO2‐N2‐He‐CO system has been developed to predict the output power pulse shapes from laser oscillators and the small‐signal gain from laser amplifiers. The model takes into account CO2 dissociation into CO, variation in the ambient temperature, as well as the possibility that the lower laser vibrational level is not in equilibrium with the other vibrational levels of the CO2 symmetric stretch mode. Theoretical predictions are compared with experimental data and show good agreement. Calculations have been carried out to determine the factors underlying the limitation of gain at specific input energies.

Plasma Chemistry Models of Gas Lasers

In a laser cavity containing primary species CO2, N2, He, H2, and CO, low-energy electrons are used to excite the vibrational modes of N2 and CO2. These same electrons also react with the primary species to form secondary species. The various types of reaction, with an example of each, are given below.

A General Plasma Model

We consider a plasma containing Natomic and molecular species and electrons. f iα (v, x, t), i = 1, N, is the distribution function in position and velocity space, defined such that f iα (v, x, t)d 3 v d 3 x is the number of molecules (atoms) of species i in vibrational (atomic) state a at time t in a volume element of size d 3 v at v in velocity space and in volume element d 3 x at x in position space. Electronically excited species, as well as distinct vibrational modes and positive and negative ions, are regarded as distinct species. In the same way we have f e (v,x, t), the distribution function for electrons.

The Haas Approximation to the General Model

In this chapter we shall derive Haas’ plasma model from the general model of Chapter 5 and, following Haas,(70) obtain the perturbed equations required for a stability analysis.

Stability Analysis of Laser Plasmas

In practice many physical systems are continually subject to small amplitude perturbations. In a plasma, for example, there will be local fluctuations of the plasma variables (species, number densities, etc.) as well as noise generated by flow turbulence and power-supply ripple.

Electron Excitation Rates

In Eq. (2.74) the electron–molecule excitation rates X i were expressed in terms of the relevant cross section Q i (v) and the electron velocity distribution function f (that is, for i representing a mode of CO2 or a species): (3.1) where f is a function of the gas temperature T,the applied field E,and the relative velocity of the electron and molecule, and is obtained by solving the relevant Boltzmann equation. This equation is derived in the following section.

Relaxation Phenomena in Gases

A theoretical model of a gas laser consists of a set of equations for the number densities, or energy densities, of the relevant excited states of the constituent gases of the laser, together with equations for the gas temperature and the intensity of the radiation within the laser cavity. The process by which energy is transferred between excited molecular states is called relaxation. In this chapter we shall study relaxation phenomena as a prerequisite to the formulation of laser models discussed in Chapter 2.