In order to calculate the characteristics of any laser, it is necessary to know the populating rates of the upper and lower laser levels, Rj and Rt; the lifetimes of these levels Tj and Tj, with allowance for the different processes of their collisional quenching; the transition probability Aji; and the line width Дрс. The rates of populating Rj and Ri are determined from solving the system of kinetic equations which constitute a balance of the rates of formation and decay of individual components of the plasma (see Chap. 4, Sect. 4.3), with allowance for the processes of populating of the laser levels. If the above parameters of gas laser media are known, it is possible to determine the small-signal gain a0, saturation intensity Is, and output laser intensity Iout (for example, see [35, 36]):

where gj and gi are degeneracies of the upper and lower laser levels, h is Plank constant, c is light velocity, в is distributed losses, Дрс is line width, / is length of active medium, and r1 and r2 are reflectivities of cavity mirrors.

For NPLs operating on the IR transitions of Xe, Kr, and Ar atoms, the poor accuracy in determining the rate constants of a number of basic plasma processes is a serious problem when computing Rj and Ri. In some cases, such constants from different literature sources differ a few times, and sometimes they differ by an order of magnitude. Approximately the same difficulties take place for Aji, Tj, Ti, and Дрс. Let us examine the problem in more detail using the example of a xenon NPL.

Transition Probability Aji Virtually all kinetic models of xenon NPLs use calculated data on the probabilities of radiative transitions 5d-6p of the Xe atom (see Table 5.4). In a recently published study [65], an attempt was made to determine Aji from measured intensities of spontaneous radiation for the 1.73, 2.03, and 2.65 pm lines during excitation of pure xenon (PXe = 5 Torr) by a nanosecond electron beam. The precision in determining Aji was not great—values of Aji for the 1.73, 2.03, and 2.65 pm lines were equal to 4 x 105, 3.4 x 106, and 7.9 x 105 s_1, respectively.

Lifetimes Tj and Ti of Laser Levels To determine Tj and Ti, it is necessary to know the radiative lifetimes of the levels (see Table 5.4) and the rate constants of the processes of collisional quenching. The rate constants of the quenching processes of the lower 6p levels by different atoms are rather well known (see Table 5.5). For the upper 5d levels, such data are limited and frequently are estimates obtained as a result of numerical modeling. Table 5.6 provides information for the 5d[3/2]10 level, obtained on the basis of the best match of calculation results with experi­mental data [21, 23, 25, 32, 36] or from analysis of plasma processes in the

afterglow of a gas-discharge plasma [66, 67]. Study [51] was probably the only experimental study that determined a number of rate constants for quenching processes of the 5d[3/2]10 level by Xe, Ne, and Ar atoms and by certain molecules (N2, CO, H2, etc.), based on measurements of the intensity of resonance vacuum UV line 119.2 nm (transition 5d[3/2]10 ! 1S0). The results of this research for Xe, Ne, and Ar atoms are also shown in Table 5.6.

At high specific power depositions (q > 1 kW/cm3), when the concentration of electrons ne > 1013 cm-3, there may be a reduction in the lifetime and change in the populations of the excited states owing to the processes of their quenching and mixing in collisions with plasma electrons. The rate constants of such processes with the participation of excited states of the Xe atom (6 s, 6p, 5d, etc.), obtained by calculation, are contained in studies [32, 68], for example.

Line Width Дис For high-pressure gas lasers (including gas NPLs), the broaden­ing of the luminescent line is homogeneous and due primarily to collisions with gas atoms. Calculations of the parameters of xenon NPLs were carried out using values of Дрс obtained as a result of selection in the course of numerical modeling of laser characteristics [29], from calculations using the Lennard-Jones potential [69], or from the results of measurement [70, 71] (Table 5.7).

Then let us briefly examine some of the most well-developed kinetic models of NPLs operating on IR transitions of Xe, Kr, and Ar atoms, which were tested from experimental results obtained in the pumping of active media both by nuclear radiation and fast electron beams.

VNIIEF Kinetic Models VNIIEF developed “small” stationary models [33—39] to determine the lasing mechanisms of NPLs based on IR transitions of Xe, Kr, and Ar atoms and preliminary calculations of laser characteristics. As demonstrated by analysis of kinetic plasma processes, for an adequate description of the operation of lasers operating on binary mixtures He-B (B = Xe, Kr, or Ar) or Ar-Xe, it suffices to include 10-15 basic reactions in the model, which were selected beforehand as a result of analysis of the characteristic times of plasma processes (see Tables 4.10 and 4.11).

It was presumed that populating of upper laser nd levels of Xe, Kr, and Ar atoms occurs selectively, solely through reactions of dissociative recombination of molec­ular ions B2l with electrons. The percentage of recombination flux populating these

levels was determined in the process of modeling, and was taken as 100, 50, and 40 % respectively for the Xe^, KrJ, and ArJ ions. Apart from the reactions cited in Tables 4.10 and 4.11, the calculation models included the processes of collisional quenching of nd levels. For level 5d[3/2]10 of the Xe atom, the constants of the processes of collisional “quenching” by Xe, Ar, and He atoms according to the

~i /л — іл 7 О

revised data are 2 x 10- , 1 x 10- , and 2 x 10- cm /s, respectively.

The validity of the model was tested by calculations of the energy and threshold characteristics of NPLs using the mixtures He-Xe (A = 2.65 pm), Ar-Xe (A = 1.73 pm) [34—37], He-Kr (A = 2.52 pm), and He-Ar (A = 1.79 pm) [38, 39], excited by uranium fission fragments, products of the nuclear reaction 3He(n, p)3H, and electron beams as a function of pressure, mixture composition, and power deposition. The calculated curves for energy and threshold characteristics agree satisfactorily with experimental data. Table 5.8 provides a comparison of the results of calculations and experimental data in optimal modes with respect to pressure and composition.

Kinetic Models of the University of Illinois Initially the model was developed for an Ar-Xe laser (A = 1.73, 2.03, 2.63, 2.65 pm) and included around 100 plasmochemical reactions [21]. To test the model, data obtained from the pumping of Ar-Xe laser with electron beam [69, 78] and uranium fission fragments [79] were used. Later on this model was improved and was used to calculate the characteristics of NPLs using mixtures of He (Ne)-Ar-Xe (A = 1.73, 2.03, 2.63, 3.37 pm) excited by uranium fission fragments [80, 81].

A rather complex two-stage process was proposed as the main mechanism for populating 5d levels of the Xe atom. First, as a result of dissociative recombination ArXe+ + e, the states 7p and 7s of the Xe atom are populated, and then Xe atoms in the states 5d[3/2]10 and 5d[5/2]20 are formed in collisional processes Xe*(7p,7 s) + Ar(Xe). In these models it is assumed that level 5d [3/2]10 is populated during collisions with Ar atoms with an efficiency of 70 %, and level 5d [5/2]20—with Xe atoms with an efficiency of 50 % [21].

In these models, much attention is attended to processes of the so-called colli — sional mixing of levels 6 s, 6p, and 5d by plasma electrons, which reduce the population inversion of laser transitions. Calculations have shown that such pro­cesses lead to a cessation of lasing if the degree of plasma ionization exceeds some critical value (0.8-1.0) x 10-5 [82]. At atmospheric pressure, this corresponds to an electron density of about 2 x 1014 cm-3. In the opinion of the authors [21, 82], it is

Fig. 5.2 (1) Specific power deposition (1) and output power at the 1.73 pm line (2, 3) at excitation of an Ar-Xe mixture (0.68 atm; Ar:Xe = 99.5:0.5) by uranium fission fragments;

(2) experiment [79];

(3) calculation [21] these processes that cause the early cessation of lasing observed in experiments [79] (Fig. 5.2).

Associates of the University of Illinois also examined the lasing mechanism of NPLs operating on the transition of an Ar atom with X = 1.79 pm and carried out calculations of some of its characteristics [22]. It was proposed that the main process of populating of the upper laser level 3d[1/2]1 of the Ar atom in the mixture He-Ar is dissociative recombination of heteronuclear ions HeAr+ with electrons, while the processes of collisional destruction of HeAr+ ions in collisions with atoms were not included in the model. Earlier it was shown that such a populating mechanism is most likely mistaken, because of the low bond energy of the HeAr+ ion (0.027 eV [44]), which roughly coincides with the energy of thermal motion of atoms at room temperature. Therefore, HeAr+ ions will be effectively destroyed in the collisions (5.5) and (5.6).

IOFAN Kinetic Models The non-stationary models of xenon lasers [27—30, 32] developed at IOFAN are the most detailed. Their most recent modifications [29, 30, 32] include several hundred plasmochemical reactions with the participation of the ions He+, He^, He^, Ar+, ArJ, ArXe+, Xe+, XeJ, the excited atomic and molecular states He*, He2*, Ar*, Ar**, ArXe*, Ar2*, Xe2*, and all of the excited states 5d, 6p, 6 s, and 6 s’ of the Xe* atom. The numerical modeling was carried out for the mixtures He-Xe, Ar-Xe, and He-Ar-Xe, and pure Xe. As the authors of [32] state, they were able to implement complete optimization of laser characteristics of when simultaneous lasing on six lines belonging to the transitions 5d-6p occurred.

Calculations under the conditions of pumping of active media with an electron beam showed that for all laser lines, the highest energy characteristics are observed for the Ar-Xe mixture, while the maximal efficiencies (4.5 %) and specific energy
release (19 J/l) are achieved at the 1.73 ^m line. The intervals of the parameters at which such high energy characteristics can be obtained are determined.

As was shown in Table 5.3, the authors of these models assume that virtually all plasma processes ever discussed participate in populating the upper laser levels. Thus, to populate the level 5d[3/2]10, 40 % and 15 % of the fluxes of dissociative recombination of molecular ions, respectively, ArXe+ and Xe^, 20 % of excited atoms formed as a result of the Ar* + Xe reaction, and about 40 % of the reaction of three-body recombination of the atomic Xe+ ions are expended.

IOFAN associates also modeled an argon laser at the 1.27, 1.79, and 2.40 ^m lines [31]. The model was tested with experimental data on pumping a He-Ar mixture laser (A = 1.79 ^m) with electron beams (FIAN) and uranium fission fragments (VNIIEF, VNIITF, Sandia). In the opinion of the authors of [31], populating of the upper laser level occurs by means of two processes: dissociative recombination of HeAr+ ions (15-25 % of the total pumping flux) and ArJ ions (5­20 % of the total pumping flux). The model also considered processes associated with the presence of the impurities N2, O2, H2, and H2O in the He-Ar mixture, which makes it possible to more precisely consider the real experimental condi­tions. The inclusion of these impurities in the model was necessary to the authors of [31], in order to explain the behavior of experimental curves [77] in the region of partial pressures of argon < 5 Torr.