We will now examine the influence of turbulent pulses on the optical quality of a medium without allowance for the potential effect of turbulent mixing in the presence of an inhomogeneous averaged temperature field. It is obvious that taking this effect into account [10] will not improve the optical characteristics.

The refractive index dependence, n, for the gases under consideration is quite accurately imparted by the equation

n = 1 + Cnp, (9.20)

where Cn is the constant for a gas of this type. Using Eq. (9.13) for the refractive index pulses in the smallest-scale inhomogeneities, we obtain

-3/2

An0 — Cnp(v/Л)1/2 — (9.21)

u2

Correlation (9.21) corresponds to definition (9.10) for pressure pulses. However, if dependence (9.15) is used instead of Eq. (9.10), the corresponding expression for estimating the Дп0 value takes the form

Дп0 — Cnp(v/Л)1/4 —r. (9.22)

u2

According to Eqs. (9.11) and (9.20), the expression for refractive index pulses in the largest inhomogeneities with a typical scale of Л can be written as

Дnm — CnP-2/u2- (9.23)

Estimates for helium based on dependence (9.21) using the numerical parameter values previously assigned at U = 10 m/s yield Дп01~10~10, while based on dependence (9.22), Дn02~10~9. According to Eq. (9.23), Дnm ~6 x 10~9; at a velocity of U = 100 m/s, we get Дп01~5 x 10~9, Дn02~6x 10~8, and Дnm ~6 x 10-7.

Refractive index pulses cause energy dissipation in a coherent light beam passing through a turbulent medium. In an optically active medium, the dissipated energy lost during diffraction on inhomogeneities can be viewed as a coherent beam loss, i. e., as a kind of absorption [14, 15]. In order to calculate the absorption constant (see refs. [15—17] for example), use was made of the results that Sutton

[14] obtained under the following assumptions: a turbulent medium with a dimen­sion of L, is homogeneous and isotropic; the light wave front at the medium inlet is planar; and consideration is given to the effective value averaged over time intervals that exceed the turbulence time scales.

The absorption constant that reflects the effect of turbulent pulses is determined by the formula [14]

aT = 2k{ An2) Л, (9.24)

where kx is the wave number, and (An2) is the mean-square pulse of refractive index.

The aT coefficient can be estimated by replacing (An2) with (Anm)2. Because, in point of fact (An2) < (Anm)2, this replacement can only lead to the overstatement of the absorption coefficient. We assume that Л ~ 1 cm. Placing kx = 2л/Х into Eq. (9.24) (for certainty’s sake, we assume that X = 1.73 qm [18, 19]), together with the Anm values found above, we obtain aT~2 x 10-7 cm-1 at U = 10 m/s and aT~2 x 10-3 cm-1 at U = 100 m/s. For comparison: the gain in NPLs based on rare gas mixtures is вк~ 10-3-10-2 cm-1 [20].

According to ref. [14], the dependence of coherent beam intensity upon the distance traversed, x, is determined by the law

I(x) = l0exp{(Pk — aT)xg.

Here, if D/Л ~ 1 (where D is the transverse dimension of the beam), and

aTL, < < 1, (9.25)

the diffraction pattern in the far-field zone then virtually replicates the diffraction pattern from the inlet following the traversal of a homogeneous medium that does not contain turbulent pulses, and the noticeable attenuation of the laser beam is absent. Thus, if condition (9.25) is satisfied, turbulent pulses in density should not exert a direct influence on the shaping of laser beam power and angular parameters. Only statistically averaged density inhomogeneities identical to those originating in sealed laser cells, or in the presence of laminar flows, will affect these character­istics (see ref. [10] for an example of the determination of this average).

Based on inequality Eq. (9.25), we will estimate the permissible gas flow velocities at which turbulent pulses in density do not necessarily exert a direct influence on the optical quality of a medium. Deliberately reducing the permissible gas-flow velocity values, we will replace (An2) with (Anm)2, then from Eqs. (9.24) and (9.25), we obtain

(Дnm)2 << {2kjALt)

Placing Eqs. (9.23) into (9.26), we obtain

We note that in inequality Eq. (9.26), in which the U velocity value enters the biquadrate, must be strictly executed; therefore, in order to estimate the permissible U values, it is not obligatory to require that the “much less” condition in Eq. (9.27) be satisfied: it is sufficient that its left side be roughly two to three times smaller than its right side. In order to facilitate estimates of the upper limit of the gas-flow velocities at which the effect of turbulent pulses on the optical quality of a medium is small, we will transform Eq. (9.27) into the inequality U < U*, where

During estimates of permissible gas-flow velocity based on formula (9.28) in an amplification regime, the Lt quantity is used (the geometric dimension of the medium along the optical axis, which equals the distance between the amplifier’s end windows.) During estimates of gas-flow velocity in the lasing regime, L, should be replaced with Lp (the effective photon path in the resonator, Lp = ctp, where c is the light velocity in the medium under consideration and tp is the photon lifetime in the laser cavity). The latter can be determined by means of the formula [21]:

tp = clnrm(1 — Rd)] . (9:29)

Here, La is the length of the active amplifying section of the gas medium that fills the cavity (which can be taken to equal the size of the uranium layer in the direction of the optical axis); RD is the share of diffraction and other losses; and rm is the reflectivity of the output mirror (the reflectivity of the second mirror is taken to equal unity).

The permissible gas-flow velocities, U*, for mixtures based on He (P0 = 2 atm) and Ar (P0 = 0.5 atm) at LA = 1 m, L, = 1.4 m, Л = 1 cm, RD = 0, and rm = 0.9 obtained using formulas (9.28) and (9.29) are presented in Table 9.1.

In addition to the direct influence examined, turbulence can have a strong indirect effect. Actually, medium turbulization, as is generally known, leads to an increase in heat conduction process efficiency. Effective turbulent thermal diffu — sivity coefficient noticeably exceeds conventional thermal diffusivity coefficient in a stationary medium. As a result, the averaged temperature and density profile

equalization rate increases. When conditions are present that favor the origination of a passive region in a gas within which lasing is absent, this phenomenon can lead to a perceptible increase in the subject region’s dimensions as compared to the laminar flow mode.

An approximate estimate of turbulent thermal diffusivity coefficient can be derived from the following considerations. Temperature equalization time in the scales characterized by linear dimensions on the order of the maximum turbulent pulse scale is determined by correlation Eq. (9.18). On the other hand, assuming that the heat exchange process within macroinhomogeneities between individual smaller inhomogeneities has the same mechanism as during conventional molecu­lar heat exchange in a stationary medium (i. e., individual migrating inhomogene­ities play the role of molecules during the turbulent mixing process), the temperature equalization time can be estimated from the correlation

TTm — Л2/ат, (9.30)

where aT is the effective turbulent thermal diffusivity coefficient. Comparing Eqs. (9.18) and (9.30), we obtain

ат — AU. (9.31)

This expression is commensurate with the well-known correlation ат ~ Л x Дu

[4] , where Ди is the typical variation of large-scale pulse velocity at distances on the order of Л (under specific conditions, it can be comparable to U).

The average time required for a portion of the gas to traverse a section of a laser channel with a length of x comes to t — x/U. Assuming that the dependence of passive zone development upon gas residence time in the channel comes in accordance with dependence (8.3), then for the size of this zone within the channel part involved in the turbulence at a medium thermal diffusivity coefficient, aT, that conforms to Eq. (9.31), we get I — л/Ax. Thus, the passive zone will involve almost the entire width of the channel, d, after the gas traverses a turbulent section with a length of x~ d 2/Л, which, assuming that Л~d, yields x~d <<bL.

Of course, these are only approximate estimates; however, they illustrate some of the difficulties that would possibly be faced during the development of NPLs with longitudinal gas flowing and that it would require considerable effort to overcome. This situation was one of the reasons for seeking alternative solutions.

The gas mixture SF6-H2 with a non-chain chemical reaction was used as the active media. This mixture was studied previously at VNIIEF with excitation by a relativistic electron beam at a 40 ns pulse duration [19, 20].

One of these experiments [17] used a 480-cm long cylindrical laser cell 11 cm in diameter without a laser cavity. The cell was filled with a SF6-H2 (9:1) mixture at 2.1 atm. The angle between the propagation direction of the у-radiation and the optical axis of the cell was about 10°. Therefore, longitudinal excitation of the laser media was achieved in practice. Under these conditions, the divergence of the laser beam was determined by the geometric dimensions of the cell. To reduce the divergence, the section of the cell near the у-source was comprised of closely placed channels, 60-cm long and 3-mm in diameter, which formed beam directivity in the remaining part of the cell.

The distribution of the specific energy deposition along the length of the cell is shown in Fig. 12.1. The average energy deposition by volume was about 1 J/cm3 at a y-pulse duration of 18 ns at the base. This experiment obtained the following parameters for the laser radiation: the energy density at the output of the cell was 4.4 J/cm2; the half-amplitude pulse duration was 8 ns (Fig. 12.2); and the beam angular divergence was 7 x 10~3 rad.

The results of the experiment were analyzed based on a theoretical model developed by the authors [17]. This model is a one-dimensional transport equation for direct and reverse light waves at the vibrational-rotational transitions of the HF molecule (A = 2.7-3.0 ^m). It follows from the calculations that approximately 90 % of the radiation is in the forward direction corresponding to the direction of the initialization wave. Figure 12.2 shows the calculated shape of the laser pulse when energy is removed from the main volume of the cell as a result of the amplification of the narrow-band radiation from the former. Calculations also show that under experimental conditions, the energy of the narrow-band radiation from the cell is 20-25 % of the potential laser energy.

A significantly higher laser output, about 70 kJ, was obtained in an experiment with about 6 m3 of active medium [18]. The active medium and the conditions for pumping it (average specific energy contribution and y-pulse length) were the same

as in the previous work [17]. The experiments whose schematics are shown in Fig. 12.3 used a cylindrical laser cell, 130 cm in diameter and 480 cm long, without a laser cavity. Laser radiation distribution in the beam cross-section was measured using bolometric wire-netting calorimeters.

As in the work [17], to reduce the angular divergence of the beam, a 60-cm long former of radiation directivity was used that consisted of elongated channels 3-mm in diameter. The inner volume of the main part of the cell was divided into long partitions to reduce energy loss due to amplification of the spontaneous emission in the transverse direction. The average energy density in the cross­
section of the laser beam at the cell output was 5.1 J/cm2, and the shape and duration of the laser pulse were about the same as in Fig. 12.2.

Thus the maximal specific power deposition of gas NPLs is no more than 5 x 103 W/cm3 and is achieved in experiments using pulsed reactors at the maximal possible thermal-neutron flux densities of ~1017 cm-2 s-1. Such a pumping level is substantially lower than when electron and ion beams are used, or in a pulsed gas discharge. [Note that while the pump power density is low, the NPL has a tremen­dous opportunity to achieve enormous energy densities if proper metastable species can be found. This led some later searches to consider lasers involving states like singlet-delta oxygen, 02([1]Д)]. This circumstance hampers the search for laser transitions for NPLs, especially in the visible and ultraviolet spectral ranges, because the unsaturated gain of the laser medium is directly proportional to X[2]. If one considers that the frequency of realization of experiments with pulsed reactors as a rule does not exceed one pulse per day (~100 pulses/year), and pulsed reactors are unique and potentially dangerous, then experiments to find and study active media for NPLs are a complicated and expensive proposition.

Significant assistance in the preliminary selection and study of active media for NPLs is provided by experiments using other, more accessible and safer sources of ionizing radiation operating at high frequency: high current electron and ion accelerators [77, 78], and accelerators with large cross-section beams that have been developed for laser pumping [79]. The kinetics of plasma processes in laser media excited by various types of ionizing radiation (y radiation, fission fragments, and other products of nuclear reactions, fast electrons, and ions) are practically identical, so that laser characteristics depend not on the type of ionizing particles, but on the energy deposition to the laser medium.

At present, electron and ion accelerators operate in a wide range of pulse durations from ~10 ns to stationary mode with electron and ion energies from ~0.1 MeV to ~100 MeV. The specific power depositions of gas media in pulsed mode can reach 109 W/cm1 2 [3] [4] [5] [6] [7] [8] [80], and in stationary mode 10 W/cm3 [81], which makes it possible to model NPL pumping in a wide range of conditions, from nuclear explosions to stationary nuclear reactors.

From investigations with the use of electron and ion beams related to NPLs, one should note the study [10], in which pumping of lasers with mixtures of He-Ne, He-Xe, Ne-Xe, and Ar-Xe at atmospheric pressure by ionizing radiation was carried out for the first time (in this case with an electron beam), as well as studies performed at FIAN [82—84], the Institute of High Current Electronics of the SO RAN [85—87], the Scientific Research Center for Technological Lasers [88, 89], and the Institute of Electrophysics of the Ural Division of the Russian Academy of Sciences [90, 91]. Abroad, the most interesting research was carried out in the United States [92—95], Germany [81, 96], and The Netherlands [97, 98]. A detailed description of gas lasers excited by electron and ion beams is not the purpose of this book. Nonetheless, in the following chapters, in the discussion of NPL character­istics, data acquired using electron and ion beams will be cited as needed.

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

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.

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.

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].

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.

With expansion and deepening of investigations into the NPL lasing mechanism, as well as the specific features of onset and development of optical inhomogeneities in them, the question of how to determine the share of fission energy which is transmitted directly to the gas became increasingly more critical. Despite some differences in approaches, all of the calculation and theoretical work yields similar quantitative results. But in experimental investigations, lower values of efficiencies є were obtained, in comparison with calculations. And the results of different authors differed markedly from one another [27—33]. The greatest discrepancy between experiment and calculation (by roughly double) was obtained in studies [30, 31]. If such a great difference did indeed occur, it could lead to the need for adjustment of the efficiency values, and possibly the kinetic models of the NPL (see Chap. 5). Therefore, analysis of the causes of the spread of the experimental results on the efficiency of the energy deposition by fission fragments and their discrep­ancy from the calculated values is very important. Apart from that, this parameter plays a significant role in calculations of the energy and mass-dimension properties of reactor-laser facilities.

A simpler variant of an RL with minimal critical mass parameters does not use coolant and excess heat is absorbed inside the core. In this case, the operating time of the RL is limited by the permissible temperature of the core.

An RL with energy release in the core <10 MW/m3 has a simple construction (Fig. 10.5) if the laser cell (1) is carried out according to the schematic in Fig. 10.2a. Beryllium (or beryllium oxide) is used as the neutron moderator (2) as it is the

substrate for the uranium layer. With the output laser power at ~200 kW, the RL core contains almost 300 cells that are 2-m long (the core is cylindrical with a 2-m diameter). The central channel contains reactor control devices (5). The inside of the core may be supplied with auxiliary mechanisms and gas-intake devices. In addition, the cavity of the central channel may have an initiating small-scale pulsed reactor intended to accelerate output of the device to the given power level and to simply operations with control devices at this output. A neutron reflector (3) is used (the beryllium thickness ~100 mm) to vary the neutron flux round core volume. The entire structure is placed in a cylindrical metal enclosure (4) with optical elements

(6) . To reduce the flowing velocity of the laser medium, the core may be formed in sections in the axial direction as shown in Fig. 10.5.

The energy release in one startup (that is the operation time at the given power) of the core is limited by the thermal capacity of the core. If the permissible rise in the core temperature is accepted to be at most 500 °C, then stationary operation is ~100 s (with other power levels, this time changes accordingly). After this time, downtime of approximately 1 h is needed for forced cooling of the core. The startup frequency may be ~5 min with forced cooling of the core.

The NPL allows a laser system with an extremely large excitation volume and a “built-in” energy source. This unique possibility could lead to a wide variety of applications that require high power sources. Here, two examples are discussed: space applications and laser fusion.

The power demand for future space missions will significantly increase in the twenty-first century, especially for such missions as establishing lunar and Mars

bases, creating space industrialization, and developing new propulsion systems. NASA-Langley and University of Illinois researchers have considered the use of NPLs to provide a cost-effective, enabling technology that could beam power in the form of a laser beam to remote users in space [78]. These users could then convert the laser energy into either electricity or propulsion. The space-based reactor power station could be placed in a high nuclear-safe orbit (as illustrated in Fig. 13.5).

The Laboratory Microfusion Facility (LMF), shown in Fig. 13.6, has been proposed to study inertial confinement fusion (ICF) targets with an MJ-scale laser

to obtain reactor-grade gains. An advanced solid-state laser is the prime candidate as the driver for the LMF. However, researchers at the University of Illinois have developed a preliminary conceptual design for an alternate approach using NPLs [70, 71]. In this concept, a pulsed fission reactor is used to excite an O2([11] [12]A)-I2NPL. An important potential advantage of the NPL driver is that projected costs are significantly lower than for a conventional solid-state laser. Another key advantage is that the LMF NPL experiment would provide a direct path to the development of a high-efficiency commercial reactor using the neutron feedback NPL driver approach [71]. In that case, the fission reactor would be eliminated with neutrons from the target implosion directly driving the NPL. This approach and a variant on it using D-3He instead of conventional D-T targets are discussed in [78].

Acknowledgments As indicated by the references, many people have made significant contri­butions to NPL research in the United States. This chapter was largely adapted, with some additions (especially regarding theoretical advances) from a prior review in the Journal of Laser and Particle Beams [2], and a presentation at the ANS Conference on Fifty Years with Nuclear Fission authored by Miley, R. DeYoung, D. McArthur, and M. Prelas [1].

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[2] K. Thom, R. T. Schneider, Nuclear Pumped Gas Lasers. AIAA J. 10(4), 400-406 (1972)

[3] N. W. Jalufka, Direct nuclear-pumped lasers. NASA Technical Paper, 2091, 1983

[4] E. Matovich, In pursuit of a pulsed homogeneous nuclear laser. IEEE J. Quantum Electron. QE-4(5), 379 (1968)

[5] V. E. Derr, G. T. McNice, P. M. Rushworth, Application of nuclear radiation to the pumping of lasers, in Radioisotopes for Space. Part 2: Systems and Applications, (Plenum Press, 1966), pp. 309-346

[6] A. A. Sinyanskiy, Research on continuous-action nuclear-laser devices at VNIIEF (Issledovaniya po sozdaniyu yaderno-lazernykh ustroystv nepreryvnogo deystviya vo VNIIEF). Proceedings of the 2nd International Conference Physics of Nuclear-Excited Plasma and Problems of Nuclear-Pumped Lasers, Arzamas-16, 1995, vol. 1, pp. 16-36

[7] T. A. Babicheva, A. M. Voinov, L. Ye. Dovbysh, L. M. Pavlovskaya, A. A. Sinyanskiy, Nuclear- pumped lasers with liquid active media (Lazery s yadernoy nakachkoy na zhidkikh aktivnykh sredakh). Proceedings of the Specialist Conference Physics of Nuclear-Excited Plasma and Problems of Nuclear-Pumped Lasers (Fizika yaderno-vozbuzhdayemoy plazmy i problemy lazerov s yadernoy nakachkoy), vol. 3, (Obninsk, 1993), pp. 146-155

[8] A. N. Sizov, Propagation of light through a liquid excited by fission fragments (Rasprostraneniye sveta cherez zhidkost, vozbuzhdayemuyu oskolkami deleniya). Proceed­ings of the 2nd International Conference Physics of Nuclear-Excited Plasma and Problems of Nuclear-Pumped Lasers, Arzamas-16, 1995, vol. 1, pp. 397-398.

[9] A. M. Voinov, L. E. Dovbysh, V. N. Krivonosov, S. P. Melnikov, A. A. Sinyanskii, A study of nuclear-pumped lasers operating on rare gas atomic transitions. Proc. 17th Int. Quantum Electronics Conf., Anaheim, USA, 1990, pp. 348-350.

[10] S. P. Melnikov, A. A. Sinyanskiy, On the ultimate efficiency of nuclear-pumped lasers (O predelnom KPD lazerov s yadernoy nakachkoy). Proceedings of the Specialist Conference “The Physics of Nuclear-Excited Plasma and the Problems of Nuclear-Pumped Lasers,” Obninsk, 1993, vol. 2, pp. 133-148

[11] G. H. Miley, D. McArthur, M. Prelas, R. DeYoung, Fission Reactor Pumped Lasers: History and Prospects. Fifty years with nuclear fission (American Nuclear Society, La Grange Park, IL, 1989), p. 333

2. G. H. Miley, Overview of nuclear-pumped lasers. Laser Part. Beams 11(3), 575 (1993)

3. D. R. Neal, W. C. Sweatt, J. R. Torczynski, D. A. McArthur, R. J. Gross, W. J. Alford, G. N. Hays, Application of high speed photography to time-resolved wavefront measurement. Proc. SPIE 832, 5256 (1987)

4. D. R. Neal, W. C. Sweatt, J. R. Torczynski, Resonator design with and intracavity time-varying index gradient. Proc SPIE 965, 130 (1988)

5. J. K. Rice, D. R. Neal, D. A. McArthur, G. N. Hays, W. J. Alford, D. E. Bodette, W. C. Sweatt, Reactor pumped laser research at Sandia National Laboratories, 1987, In Proceedings of the International Conference on Lasers ‘86, (STS Press, McLean, VA, p. 571)

6. D. A. McArthur, G. H. Miller, P. B. Tollefsrud, Pumping of high-pressure CO2 laser media via a fast-burst reactor and electrical sustainer. Appl. Phys. Lett. 23, 303 (1973)

7. D. A. McArthur, P. B. Tollefsrud, Observation of laser action in CO gas excited only by fission fragments. Appl. Phys. Lett. 26, 187 (1975)

8. D. A. McArthur, G. H. Miley, R. DeYoung, M. Prelas, Report SAND76-0584, (Sandia National Labs., Albuquerque, NM, 1977); reprinted November 1983

9. D. A. McArthur, G. N. Hays, D. R. Neal, J. K. Rice, Recent results from nuclear-pumped laser studies: gain and measurement in XeF, in Laser Interaction and Related Plasma Phenomena, ed. by H. Hora, G. H. Miley, vol. 8 (Plenum Press, New York, 1988), p. 75

10. K. Thom, R. Schneider, Nuclear pumped gas lasers, AIAA, 10(4), (1972)

[12] G. H. Miley, Review of nuclear pumped lasers, in Laser Interaction and Related Plasma Phenomena, ed. by H. Schwarz, H. Hora, vol. 4a (Plenum Press, New York, 1977), p. 181

12. R. T. Schneider, F. Hohl, Nuclear-pumped lasers, in Advances in Nuclear Science and Techno­logy, ed. by J. Lewins, M. Becker (Plenum Publishing, New York, 1984), p. 123

13. G. H. Miley, Review of nuclear pumped lasers, in Laser Interactions and Related Plasma Phenomena, ed. by H. Hora, G. H. Miley, vol. 6 (Plenum Press, New York, 1984), p. 47

Presently, known gas NPLs radiate in a wide band of the optical spectrum of 390­5,600 nm using approximately 50 transitions of atoms Xe, Kr, Ar, Ne, C, N, Cl, O, Hg, Cd, and I; the ions Cd+, Zn+, and Hg+; the molecule CO; and the molecular ion Nj.

3.1 IR Lasers Operating on Transitions of the Xe, Kr, and Ar Atoms

Nuclear-pumped lasers operating on transitions of Xe, Kr, and Ar atoms have been studied in greatest detail and have the maximal energy parameters of NPLs studied to date. Primarily, uranium fission products and nuclear reaction products 3He(n, p)3H were used to excite these lasers. Diagrams of the energy levels of atoms Xe, Kr, and Ar with laser transitions are shown in Fig. 3.1. Lasing occurred in the IR range of the spectrum, and the most intensive laser lines belong to the transitions nd-(n + 1)p of Xe, Kr, and Ar atoms (n = 5, 4, 3 for Xe, Kr, and Ar respectively).

Experimental investigations of NPLs operating on IR transitions of Xe, Kr, and Ar atoms in Russia were done chiefly at VNIIEF and VNIITF, and elsewhere at the Sandia Laboratories (United States).

Let us examine in more detail the possible processes of populating of upper laser levels (see Table 5.3). The first models [19, 20] for NPLs operating on mixtures 3He-Xe and 3He-Ar were based on preferential populating of nd levels of Xe and Ar atoms as a result of the process of collisional-radiative recombination: B+ + e + e —— B*(nd) + e (B+ = Xe+, Ar+) (process (1)). Individual characteristics of lasers were calculated in [19, 20]; a detailed comparison with experimental results was not made. Process (1) was also included in kinetic models developed later for lasers

operating on the mixtures He-Xe [29, 30, 32] and He-Ar [31], the supposition was made that up to 60 % of the total reaction flux (1) may come to the nd levels. As is known (see [10], for example), process (1) is not selective, so as a result it is possible for atoms to appear in different excited states. In this regard, the assump­tion of a significant contribution of process (1) to populating of the nd levels of atoms Xe and Ar, advanced in studies [19, 20, 29—32], is doubtful. Moreover, the rate constant kcr of process (1) greatly depends on the temperature of the electrons (kcr ~ Te—4,s), so that He-Xe(Ar) lasers are hardly able to operate in a wide range of experimental conditions in the case of populating nd levels through this process.

In study [23], other populating mechanisms of upper laser levels were proposed for Ar-Xe NPLs: a) process (5), energy transfer in inelastic collisions Ar* + Xe —— Xe*(5d) + Ar; b) process (6), populating of 5d levels of the Xe atom by electron impact from states 6 s. Process (5) was also included in the kinetic models [25, 27—30, 32], and process (6) in models [28—30, 32]. Process (5) cannot provide efficient pumping of 5d levels, since as a result of this process, highly excited Xe levels are formed initially (states 7d, 8d, etc.), while populating of 5d levels is possible only as a result of subsequent radiative-collision processes with a proba­bility of a few percent [40]. In this regard, the assumption of [28—30, 32] regarding populating of 5d levels of the Xe atom through process (5) with a probability of 20­30 % is too optimistic. As for process (6), experimental studies [41, 42] show that there is no marked contribution of this process to populating of the nd levels.

The hypothesis regarding populating of nd levels of the Xe, Kr, and Ar atoms through dissociative recombination of heteronuclear molecular ions of ArXe+ or

HeB+ (B = Xe, Kr, Ar) with electrons is the most widespread. In a number of models (see [21, 22, 24], for example), this process is viewed as the only one, while in others [27—32] it is viewed as one of the main ones, with a populating probability of up to 40 % [28, 29]. In the majority of studies [22, 24, 27—32], it was proposed that populating of nd levels occurs directly as a result of process (3). Study [21] proposes for the Ar-Xe mixture a more complex two-stage mechanism of populat­ing of the 5d levels of the Xe atom—formation, in the process of recombination ArXe+ + e, of high states 7p, 7s of the Xe atom, with subsequent collisional transitions Xe*(7p,7 s) + Ar(Xe)! Xe*(5d) + Ar.

In binary A-B mixtures, heteronuclear molecular ions AB+ are formed in three — body collisions:

B++ B + A! B+ + A (5.3.a)

B++ B + A! AB+ + B; (5.3.b)

B++ A + A! AB+ + A. (5.4)

and are destroyed as a result of the processes:

AB+ + A! B++ 2A. (5.5)

AB+ + B! B+ + A. (5.6)

AB+ + ! B++ A + e. (5.7)

Information about rate constants of processes (5.3)-(5.7) is extremely limited. The rate constants for these ions used in various models (see, for example, information for the ArXe+ in Table 4.11) are estimates, sometimes quite rough, so that it is virtually impossible to predict the contribution of dissociative recombination of ions AB+ to population of nd levels. Unknown constants most often were estimated in the process of fitting the results of calculation of NPL characteristics to the experimental data.

The destruction of heteronuclear ions largely depends on their bond energy, which decreases with an increase in the difference in masses of the atoms making up the ion [43, 44], and equals 0.14, 0.050, 0.030, and 0.027 eV for ArXe+, HeXe+, HeKr+, and HeAr+, respectively [44]. The estimates cited in study [10] provide the following values for the rate constants of process (5.5): for ArXe+ ions, k55«5 x 10-11 cm3/s, while for the HeB+ ions (В = Xe, Kr, Ar), k55 > 10-10 cm3/s. Heteronuclear ions are also destroyed by plasma electrons as a result of process (5.7); moreover, the rate constants of such processes can reach 10~7-10~6 cm3/s [10].

The characteristic time of process (5.5), for example for HeXe+ ions when the atmospheric pressure of the He-Xe mixture is ~ 3 x 10~10 s, while the characteristic time of the process of dissociative recombination of this ion under the most favorable conditions (Te = 300 °K, ne < 1015 cm~3) will be > 10~7 s. Consequently, heteronuclear ions HeB+ are effectively destroyed as a result of collisional processes, so their recombination cannot make a marked contribution to formation of excited atoms. The latter circumstance is confirmed by the results of spectro­scopic research on dissociative recombination of heteronuclear ions in the after­glow of gas-discharge plasma, in which “despite the large number of studies of these particles, it has not yet been possible to discover the formation of excited atoms associated with their recombination” [10].

An additional argument against a significant contribution from dissociative recombination of heteronuclear ions to the population of the upper laser levels comes from the results of experiments studying the influence of the medium temperature on laser characteristics. It follows from Table 3.7 (see Chap. 3, Sect. 3.1) that the temperature at which the output laser power decreases by half differs insignificantly for the mixtures Ar-Xe, He-Xe, and He-Ar, and is 350-450 °K. If populating of the upper laser levels occurred with the participation of the heteronuclear ions ArXe+ (mixture Ar-Xe) or HeXe+, HeAr+ (mixtures He-Xe, He-Ar), for the mixtures He-Xe and He-Ar, the reduction in energy parameters would have to occur at substantially lower temperatures than for the mixture Ar-Xe, owing to the more efficient destruction of HeXe+ and HeAr+ ions as the temperature increases due to reaction (5.5). In addition, in experiments [45, 46] with mixtures He-Xe and He-Ar, the specific energy depositions were ~ 1 J/cm3 per pulse, and the temperature of the medium by the end of the pumping pulse reached 800-1,000 °K, but lasing occurred throughout the entire pulping pulse (see Fig. 2.10, for example).

Thus construction of the models [22, 24] based on the reaction of dissociative recombination of ions HeB+ with electrons, or its insertion in models [29—32], where the contribution of this reaction to populating of nd levels is estimated at 15­25 % [31], is invalid.

In the majority of kinetic models, the process of dissociative recombination of molecular ions B2+ with electrons was viewed as a loss channel, populating the lower laser (n +1) p levels. This assumption was initially based on the results of spectroscopic investigations (see review [10] and the literature cited there), which registered intensive radiation from (n +1)p levels. However, it should be noted that spectroscopic investigations were carried out in the spectral range of X < 1,000 nm using photoelectric multipliers for registration, so IR transitions nd-(n + 1) p could not be observed. Consequently, one can assume that the radiation from (n +1) p levels registered in these studies is the consequence of preliminary IR transitions nd-(n + 1) p.

In study [47], based on the measured intensities of spectral lines, a conclusion was drawn regarding preferential population as a result of the process Xe^ + e of level 6p[5/2]2 in comparison with level 5d[3/2]10 which are the lower and upper levels of the laser transition respectively, with X = 1.73 pm (see Fig. 3.1). The authors [47] drew this conclusion from calculation of the ratio of the recombination fluxes Г, populating these levels:

^ r5d I5dA6pA5dT6p (5 8)

Г6р 16pA5pA6pT5d

where hd and I6p are the intensities of the 1.73 ^m and 0.992 ^m spectral lines measured in [47] > A5d and A6p are the wavelengths of these lines, A5d and A6p are the probabilities of radiative transitions, and T5d and T6p are the lifetimes of the levels. In [47] it is assumed that т 5d is equal to the radiative lifetimes of the level 5d [3/2] 10, which is about 200 ns. With these assumptions, the authors of [47] obtained Y < 0.2 for PXe _ 5-10 Torr.

Study [48] reevaluated correlation (5.8), taking into account the processes of collisional quenching. From results of experiments [49], it follows that quenching of the level 5d [3/2]10 by Xe atoms in ground state already become noticeable at PXe ~ 0.1 Torr. This means that for PXe « 0.1 Torr, the radiative lifetimes of level 5d[3/2]10 are roughly equal to the lifetimes of this level through the process of collisional quenching. Hence, it follows that the rate constant of the quenching process is~2 x 10~10 cm3/s-1 (similar values of this constant were obtained in kinetic models [21, 25]). Therefore, for PXe _ 10 Torr, taking into account colli­sional quenching, T5d ~ 10 ns, and accordingly, the ratio у ~ 5. Thus if one allows for the reduction in the lifetimes of the level 5d[3/2]10, then based on the spectral lines measured in [47], one can infer the opposite to the conclusion drawn by the authors [47]: the level 5d[3/2]10 is populated primarily due to the dissociative recombina­tion Xe2 + e.

This inference is confirmed by the information of study [50], which concludes, based on experimental investigations of the process Xe^ + e, that there was prefer­ential populating of the 5d level of the Xe atom in comparison with the 6p levels. A significant role of the process Xe^ + e in populating levels 5d is also noted in study [51]. And finally, analysis [52] of the kinetics of an Ar-Xe laser (A_ 1.73 ^m) showed that the probability of populating of the level 5d [3/2] 10 through the process Xe)~ + e can reach 90 %.

In 1979, VNIIEF offered the hypothesis of selective populating of nd levels of Xe, Kr, and Ar atoms through dissociative recombination of molecular ions B2 + e! B *(nd) + B(B _ Xe, Kr, Ar), published later in [33]. Based on this hypothesis, kinetic models were developed for calculation of NPL characteristics [34—39]. Populating of nd levels of Xe and Ar atoms through the processes of dissociative recombination of molecular ions B2l with electrons was also taken into account (along with other processes) in kinetic models [27—32]. The efficiency of populating of nd levels was taken as equal to 15-20 % with regard to the total pumping flux.

A somewhat different lasing mechanism, proposed in the study [25] for Ar-Xe NPLs and later used in a kinetic model of a He-Xe NPL [26], was based also on preferential populating of the 5d levels of the Xe atom as a result of dissociative recombination of molecular ions Xe^. However, in this case dissociative recombi­nation of the ion (XeJ) * in an excited state (electronic or vibrational) was proposed as the basic populating channel. According to this model, the excited (XeJ) * ions are formed in the reaction ArXe+(HeXe+) + Xe! (Xe2) * + Ar(He), while the Xe2 in the ground state are a result of the reaction Xe+ + Xe + Ar(He)! Xe2 + Ar(He). Authors of [25, 26] proposed that recombination of the Xe2 ion in the ground state leads to populating of the levels 6p and 6p’. To test the reliability of this model, which contains a large number of unknown constants, additional research is nec­essary, particularly calculations of the characteristics of a Xe laser in various experimental conditions.

Thus the most efficient populating of the nd levels of Xe, Kr, and Ar atoms, which are the upper laser levels in rare gas mixture NPLs, most likely occurs through the processes of dissociative recombination B2 + e! B * (nd) + B (B = Xe, Kr, Ar). Unfortunately, direct experimental proof of such inference is still absent, except perhaps for the information contained in study [50]. To resolve this problem, spectral-luminescence studies are needed, analogous to those performed using the single-photon spectrometry method in the visible and UV spectral ranges [53, 54]. However, IR photodetectors of the same high sensitivity as photoelectronic multipliers are needed in order to carry out such investigations.

Investigations revealed that if the initial thermal neutron flux value is on the order of, or higher than, Ф0 = 1013 cm_2-s_1, passive zone development is then followed by a regularity of the type described in (8.3)

I « A/Pa (8.35)

not only at l << r1, but also at l < 0.3 r1, with an accuracy no worse than 20 %. If gas thermal diffusivity, a, in this instance is assumed to equal its value at the initial moment in time, the proportionality factor, Ah will then fluctuate within limits of a few units. So, for a cell with planar layers (see Fig. 8.12), A/ = 3.24 for Ar and Ai = 2.75 for He. Here, expression (8.35) describes the l(t) dependence derived from an accurate calculation all the way up to l« 0.25d, with an error no higher than 6 %. For a cylindrical cell, Al = 4.61 for Ar and Al = 3.04 for He, with this same accuracy.

Calculations of different excitation alternatives demonstrated that at l < 0.3r1, the Al factor is most highly dependent upon cell geometry (planar or cylindrical), and to a lesser extent, upon the shape and intensity of the exciting neutron pulse, uranium layer thickness, and gas mixture thermophysical properties, despite the fact that mixture characteristics are partially taken into account by the thermal diffusivity in correlation (8.35). This Al factor behavior is explained by the fact that passive region development is determined not only by heat removal to the cell wall, but also by the gas motion, during which the occurrence of thermal and

Fig. 8.15 Dependence of the active region’s outer boundary upon pumping power rise time:

(1) D0 = 0.1; (2) D0 = 0.5; 3.) D0 = 1

gas-dynamic processes is dependent upon the power and spatial distribution of the energy release sources in the gas at any given moment in time.

The regularity noted makes it possible for the initial stage of passive zone development in cells with identical geometries to establish the approximate rela­tionship between their dimensions and the thermal diffusivities of the gases filling the cells

/,~l

If two identical cells irradiated by identical neutron pulses are filled with mixtures that have identical compositions, but different initial densities, it then follows from the latter correlations that

(8.36)

Here, the determination of thermal diffusivity is used, a = kg/cvp.

The calculation results for the moment in time at which the fluence reaches 3 • 1013 cm~2 are presented in Fig. 8.15 for a cylindrical cell with r1 = 1 cm, filled with helium at different pressures, and irradiated by an exponentially rising neutron flux (8.34). Because the moment in time, t, and the fluence, ф, are linked by the formula t = т1п(1 + фФ0т), the т value at given Ф0 and ф corresponds to specified t value. The data in Fig. 8.15 confirm the existence of approximate dependence

(8.36) for the values of I < 0.3r1.