Ions and excited atoms can occur both directly in the processes of collisions between a primary charged particle and gas atoms, and during the collision of atoms with secondary electrons. As a rule, computational methods are used to determine the actual contribution of the primary and secondary processes to the formation of ions and excited atoms.

Figure 4.11 shows the results of computation in [24] of the energy that is expended for the formation of ions, excited atoms, and subthreshold electrons during excitation of helium (PHe = 0.53 atm) by a proton beam with an energy of 4 MeV. The absorbed energy on a proton path length of 1 cm was taken as the baseline; it amounted to 9.1 keV. It is evident from Fig. 4.11 that the percentage of

Fig. 4.11 Channels for conversion of absorbed energy during excitation of helium (PHe = 0.53 atm) by a proton beam with an energy of 4 MeV [24]

Рне, Ton-

the primary ionization is 52 %, and the percentage of excited atoms formed as a result of primary processes is 31 %. According to the data of study [5], the percentage of the primary ionization for Ne and Xe is 15-20 % when excited by a beam of fast electrons. When excited by fission fragments the percentage is 30-50 %. The authors of [5] attribute the difference to the harder, more severe spectrum of electrons formed as a result of primary ionization by an electron beam.

It appears that the only study in which the ratio of the primary and secondary inelastic processes was determined experimentally was study [25], in which spectroscopic methods were used to study the excitation processes during ioniza­tion of He by uranium fission fragments. The ratio rfe of the number of excited atoms formed directly by fission fragments to the number of excited atoms formed by secondary electrons of the ionization cascade is shown in Fig. 4.12. With a helium pressure of 25 Torr, the ratio rfe « 1, while at a pressure of 100 Torr, the contribution of secondary electrons to the formation of excited helium atoms is twice as great as for fission fragments. At helium pressures of around 1 atm, the contribution of fission fragments to direct formation of excited atoms may be ignored.

Frequently, the energy cost of the elementary process is used to characterize the rates of the inelastic processes of ionization and excitation in gas media. The energy cost of the jth inelastic process occurring with a gas particle of the type s constitutes the ratio of the specific excitation power to the frequency of the occurring actions of this process [26]:

j(eeW ^Ee/mefe (єе) dee

where [As] the concentration of atoms of the type s; asj, Esj are the cross section and energy threshold of the jth inelastic process. The expression (4.2) is applicable to determine the energy costs of ionization and excitation both in the case of single­component gas media, and of gas mixtures.

The simplest method of determining the energy expended on ionization and excitation of atoms is to use the semi-empirical Platzmann formula [27], which relates the energy cost of formation of an ion-electron pair w; to the ionization potential of an atom, V;.

wi = Ei + (Nx/Ni)Ex + Ee = 1.71 Vi, (4.3)

where Ei = 1.06V;- is the average energy expended on ionization; Ex = 0.85 V;- is the average energy expended on excitation; Ee = 0.31 V; is the average kinetic energy of a subthreshold electron; and Nx/N; = 0.4 is the ratio of the number of excited atoms to the number of ionized atoms, which is roughly identical for all rare gases.

The expression (4.3) was obtained for rare gases excited by a and p particles. For fission fragments, the value w; is somewhat higher than for a and p particles. In this case, the Platzmann formula has the same form, but the ratio Nx/N; = 0.53 and w; = 1.82V; [28]. Using w;, it is possible to determine the formation rates of ions f+ and excited atoms f* per unit of volume.

f+ = q/wi f * = (Nx/Ni)f, (4.4)

where q is the specific power deposition of the gas medium.

Table 4.2 shows the results of calculation of w; by formula (4.3) for light particles and fission fragments, the results of numerical calculations at ionization of rare gases by electron beams, as well as the results of experiments for rare gases excited by a and p particles and uranium fission fragments. From the data of Table 4.2, it is possible to draw the following conclusions. (a) precise numerical calculations and calculations by formula (4.3) of values of w; agree with one another with an accuracy of no worse than 10 %; (b) a and p particles are virtually equivalent to one another from the standpoint of energy expenditures for the formation of an ion-electron pair (ratio wi(a)/wi(P) = 1 with an accuracy no worse than ±2 % [27]); (c) the value of w; for fission fragments is 6-7 % greater than for light particles [29]; (d) the maximal differences between the results of different authors is observed for the ratio Nx/N;, which is evidently associated with differences in the excitation cross sections included in the calculations.

For calculations of the plasma kinetics and characteristics of NPLs, it is neces­sary to know not only the percentages of energy that are expended on ionization and excitation, but also the distribution of absorbed energy between excitation states.

Table 4.2 Energy cost of formation of an ion-electron pair (in eV) in rare gases and the ratio of the number excited atoms to the number of ionized atoms (Nx/N,) Rare gas He Ne Ar Kr Xe Ionization potential, V,, eV 24.6 21.6 15.8 14.0 12.1 Calculation by formula (4.3) Light particles w, = 1.71 V,, eV 42.1 36.9 27.0 23.9 20.1 Fission fragment wi = 1.82 V,-, eV 44.8 39.3 28.8 25.5 22.0 Numerical calculations Electron beam 46.8 [12] 36.5 [12] 27.3 [12] 23.6 [12] 20.9 [12] 45.9 [23] 38 [14] 25.4 [13] 21 [14] 22 [14] 46.2 [30] 38.5 [23] 25 [14] 24.3 [23] 22.2 [23] 46.0 [31] 36.1 [26] 26.1 [23] 24.0 [31] 22.3 [26] 46.4 [32] 36.6 [31] 26.0 [26] 21.7 [31] 26.4 [31] Proton beam 46.4 [24] — — — — Experiment 14C and 63Ni в particles 42.3 [33] 36.6 [33] 26.4 [33] 24.2 [33] 22.0 [33] 210Po and 239Pu a particles 42.7 [33] 36.8 [33] 26.4 [33] 24.1 [33] 21.9 [33] 46.0 [34] 26.4 [34] 241Am a particles — — 26.5 [35] 23.9 [35] 21.0 [35] 235U fission fragments — 39.2 [29] 28.2 [29] — — Nx/N 0.65 [12] 0.45 [12] 0.51 [12] 0.53 [12] 0.60 [12] 0.64 [23] 0.54 [14] 0.44 [14] 0.32 [14] 0.38 [14] 0.66 [24] 0.55 [23] 0.45 [23] 0.56 [23] 0.70 [23] 0.68 [30] 0.51 [26] 0.57 [26] 0.39 [31] 0.51 [31] 0.54 [31] 0.33 [31] 0.32 [31] 0.55 [35] 0.60 [35] 0.77 [32] 0.52 [35]

The initial spectra of excited states in gases excited by nuclear radiation were determined as a rule by calculation, with the reliability and accuracy of the calculations depending primarily on the values of the excitation cross sections used in the calculations.

From expression (4.2) it is clear that calculation of the energy costs of the processes is closely connected with the precision of the determination of fe(ee) in the region of inelastic electron-atom interactions (ee > /m). Because in this region, the shape of electron energy distribution does not depend on the energy of the primary electrons (see the data of [13] for argon, for example), the absence of energy dependence for wsj in a wide range of electron energies is an important practical consequence. The absence of energy dependence of w, (the cost of an ion — electron pair formation) was observed in experiments [27] in the early stages of investigation, in which it was shown that such a rule is valid with an accuracy of ±2 % for p particles in an energy range of 5-60 keV.

Fig. 4.13 Dependence of the number of ions and excited atoms at 100 eV of absorbed energy asj on the initial energy of the electron e0 in helium (a), argon (b), and xenon (c) [23]: (1-4) ions A+, A2+, A3+, and A4+, respectively; (5) subthreshold electrons; (1′, 2′, 3′) excited states of atoms of helium (1′-21S and 23S; 2′-21P and 23P; 3′-3!S, 31P, 31D, 33P and 33D), argon (1′-4s; 2′-4s’; 3’­5s, 3d, 5s’ and 3d’) and xenon (1′-6s; 2′-6s’, 6p, 5d; 3′-higher levels)

As an example, Fig. 4.13 shows the dependence of the number of ions and excited atoms at 100 eV of absorbed energy rnsj (rnsj = 100/wsj) on the initial electron energy, as obtained from calculations [23] by the Monte Carlo method for He, Ar, and Xe. For all three gases, msj and, consequently, wsj — cease to depend on e0 if £0 > 500 eV. This result agrees with the computation of the ionization cascade in helium obtained in study [30] by the degradation spectrum method.

The most complete information on energy costs of inelastic processes was obtained as a result of calculations for single-component gas media. Tables 4.3, 4.4, 4.5, 4.6, and 4.7 show the calculated data for He, Ne, Ar, Kr, and Xe, respectively. It was presumed in calculations [24] that the gas medium (helium) was excited by a proton beam with an energy of 4 MeV; in all the other studies by electron beams with an initial energy of 1-2 keV.

The most detailed information about the formation of excited states in the initial stage of the processes of interaction of the primary particle and secondary electrons with the gas medium was obtained for helium, because helium has quite detailed information about the cross sections of inelastic processes. From the data of Table 4.3, we see that around 50 % of excited atoms of He are formed in the state 21P. This agrees with the results of study [36], in which, on the basis of analysis of the luminescence spectra and the kinetics of plasma processes, it was

concluded that the majority of initially excited He* atoms are formed in the states n1P, and half of them in the states 21P. The validity of the conclusion is confirmed by calculated data [24], from which it follows that when helium is irradiated with a proton beam, roughly 30 % of the absorbed energy is expended on excitation of helium atoms, and half of them are formed in the states 21P. The basic channels of destruction of the atoms He*(21P) are radiative and collisional transitions to metastable states 21S [36, 37]. The probability of radiative transition is 1.9 x 106 s-1 [38], while for the process He*(21P) + He! He*(21S) + He, the rate constant kq = 1.8-10~12 cm3/s [37]. Therefore, for PHe~1 atm, as a result of collision processes, the atoms He*(21P) are converted rather quickly to the metastable atoms He*(21S), in a time of Tq = (kq[He])-1 ~ 20 ns. Then, examining the kinetics of plasma processes in quasicontinuous helium gas NPLs, one can assume that atoms He*(21S) are the primary excited atoms.

It follows from the data of Tables 4.4 through 4.7 that in the case of heavy rare gases, 80-90 % of excited atoms are formed in lower ns and np states (n = 3, 4, 5, 6, respectively, for Ne, Ar, Kr, and Xe) roughly in an equal proportion. Excited atoms are also formed through plasmochemical reactions, such as recombination for example. However, the contribution of the initial ionization stage to the forma­tion of excited atoms in the case of heavy rare gases may be significant. Thus, an investigation of the spectral-kinetic characteristics of Ne luminescence on excita­tion by single fission fragments 252Cf showed that all ten 3p levels of the Ne atom are populated very quickly, in the time that the fission fragment passes through the gas (~4 ns) [39, 40]. This circumstance allowed the authors of [39, 40] to conclude that a significant contribution to population of the 3p levels is provided by the processes of direct excitation of the neon in the initial stage of ionization of the gas medium.

Above we looked at the energy expenditures for the formation of ions and excited atoms in single-component gas media. In the case of gas mixtures, the energy cost of the inelastic process can be represented in the form [41]:

where vs is the percentage of energy absorbed in the component s of the gas mixture, Rs is the path length of the charged particle in the component s of the gas mixture at a pressure of 1 atm. We note that the formula (4.5) is equivalent to the expression for wsj- proposed in the study [34] for binary mixtures.

Binary mixtures are most often the active media of gas NPLs, and He, Ne, or Ar are used as the main component (buffer gas). Information about the energy costs of formation, wsj, for mixtures that are of interest for NPLs is very limited and was obtained as a result of calculations for the mixtures He-Xe [12]; Ar-Kr [14]; He-Ar [34]; Ar-Xe and Ne-Xe [26]; Ar-Xe(Kr, N2) [42], and He-Cd [43]. As an example, Figs. 4.14 and 4.15 show the costs of forming ions and excited Xe* atoms for the mixture Ar-Xe [26].

Table 4.4 Energy costs wsj of inelastic excitation processes for Ne Level 3s 3P 4s, 5s, 3d Works cited Threshold energy, eV 16.7 18.6 20.1 wsj, eV 170 130 1,500 [14] 110 150 1,200 [26]

Table 4.5 Energy costs wsj of inelastic excitation processes for Ar Level 4s[3/2]2, 4s'[1/2]0 4s[3/2]1 4s'[1/2]“ 4p 3d, 5s 4d, 6s Works cited Threshold energy, eV 11.55 11.62 11.83 13.0 14.0 15.0 wsj, eV 280 640 550 — [13] 190 270 290 660 [14] 130 — 1,000 — [23] 110 800 120 500 800 — [26]

Table 4.6 Energy costs wsj of inelastic excitation processes for Kr Level 5s 5P 6s, 4d Higher levels Works cited Threshold energy, eV 10.0 11.5 12.2 12.9 wsj, eV 110 200 1,500 4,700 [14]

Table 4.7 Energy costs wsj of inelastic processes for Xe Level 6s 6s0, 6p, 5d Higher levels Works cited Threshold energy, eV 8.4 9.7 11.2 wsj, eV 130 120 910 [14] 400 90 270 [23]

For a xenon concentration of ~1 % (optimal for the most powerful IR laser operating on transitions 5d-6p of the Xe atom), the cost of forming the excited atom Xe* in the upper laser state 5d[3/2]0 is >10 keV, which is roughly two orders of magnitude greater than the cost of forming Xe* atoms in the lower lasing states 6p (Fig. 4.14), so population of the state 5d[3/2]0 in the initial stage is not significant.

From the data provided in Fig. 4.15 it is clear that when there is an increase in the xenon concentration, the cost of forming an electron in the Ar-Xe mixture smoothly decreases from the cost of ionizing pure Ar (26 eV) to the cost of ionizing pure Xe (22 eV). For a Xe concentration of around 45 %, the costs and rates of ionization of Xe and Ar atoms are roughly identical.