The situation is significantly more complex if a cell has large buffer volumes and the dimension of the planar uranium layers in one direction is comparable to the distance between these layers. Two such cells are a part of the LUNA-2M setup [5—7,14] (see Chap. 2, Sect. 2.4, and Chap. 7, Sect. 7.4). The cell’s transverse cross­section is presented in Fig. 8.8. The z axis coincides with the system’s optical axis and is oriented perpendicular to the plane of the figure. It is impossible to reduce calculations of the thermal gasdynamic processes of such a cell to a problem with one spatial variable. Any existing multidimensional gasdynamic program could be modified, or a special program could be created for purposes of the numerical calculations of such problems using a computer. However, large computational burden would be needed in order to perform numerical solutions; this is scarcely warranted because this type of laser cell design is far from optimum. For this reason, when conducting the numerical investigations described next, a series of model approximations based on the specific features of the experiments involving these cells was used.

Pressure. During the calculations, uranium nucleus fission density distributions and gas densities within the expanse of the uranium layers were assumed not to be dependent upon the longitudinal coordinate, z. In the presence of a cell body inside radius of R ~4 cm, the typical perturbation propagation time is тр ~ R/us, which is considerably shorter than the exciting pulse duration in the experiments mentioned above, t1/2~ 3 ms. Consequently, the pressure at any given moment in time can be regarded as homogeneous, i. e., temperature distribution determines gas density distribution as a whole.

By virtue of the distinctive features noted, the geometry of a real cell with a fission density distribution that is not dependent upon the longitudinal coordinate, in purely gasdynamic terms, is virtually equivalent to a cell with a rectangular cross-section (Fig. 8.9). The heating of the metal body of a real cell and the plates to

X

which a uranium layer has been deposited, as well as the plates in an equivalent cell with a rectangular geometry, in the presence of the energy depositions studied in this problem is negligible as compared to the heating of the gas; therefore, this factor’s effect can be ignored during the transition from one geometry to another. The volume, mass, and initial pressure of the gas in the equivalent cell, the dimensions and composition of the uranium layers, and the distance between them are the same as in the initial geometry.

In ignoring the effect of viscosity forces, the equation for the energy of the gas in an Eulerian coordinate system takes the form:

(8.27)

where u is the gas velocity, and S is the entropy of a unit mass of gas. Based on the well-known thermodynamic correlation,

together with an expression for the internal energy of an ideal gas,

E = cvT,

equation (8.27) can be written in the form

We rearrange this equation as:

after which, using the continuity equation

dp!

+ div p u = 0,

we obtain

0

cv — (pT) + cvdiv^p uTj + P div u — div(kgVT) = F. (8.28)

We integrate (8.28) over the entire gas volume. Taking into account the fact that the pressure, based on the simplifications used, is homogeneous over the volume, we rearrange the integral from the second, third, and fourth summands on the left side according to the Gauss-Ostrogradski theorem into an integral over a closed surface,

Assuming that the cell is closed, its walls are fixed, and the velocity near the inner surface of the walls equals zero, we deduce that the latter integral equals

n(t)= kgVT f, t

The integral for cell volume from the right side of equation (8.28) equals the total energy released into the gas per unit of time,

F(x, y, t)dV = eQ(t)

V

(see the designations in Chap. 7, Sect. 7.4). According to the state equation for an ideal gas, we rearrange the first term of equation (8.28) in the form

Э 1 3 ..

cvdt Ip(X;У’t)T(X;У’t)] = dtP(t).

Thus, following integration for the entire gas volume, equation (8.28) is written as
-^1 f = ее«+я«,

whence equation (7.20) ensues. A similar correlation was obtained in [45] for the pressure averaged over a cell.

Gas Density. The typical temperature equalization time in the gas between plates containing uranium is on the order of tt ~ d2/a. The thermal diffusivity for the gas mixtures used is a ~1 cm2/s. Hence, it follows that tt~1 s, i. e., tt >>tj/2. Therefore, heat exchange in the bulk of the gas volume during a neutron pulse plays a negligibly minor role, with the exception of the thin layers directly adjacent to the plates containing the uranium, where heat removal to the plates manifests itself in a noticeable manner. However, the thickness of these layers, even for the termination of a pulse with a duration of t1/2~3 ms reaches a total of I ~ 10-1 cm (see the first section of this chapter). It is heat removal from these layers precisely that determines the last summand in equation (7.20). Due to the smallness of l, even for the pulse termination, this term accounts for a total of 15-25 % of the overall volume in a cell; therefore, in approximate calculations, we will ignore heat exchange in the entire gas volume and will calculate the pressure using formula (7.21). Other authors also proceed in a similar manner (see [18, 35—38, 46] for example).

In the approximations under consideration, the spatial distribution of the tem­perature increase associated with fairly small density variations is more or less similar to the spatial distribution of specific energy sources, which is confirmed both by calculations [23, 45] and by experiments [2]:

T(x, y, t) = To + A(t)We(x, y, t), (8.29)

where A(t) is a proportionality factor that is dependent upon the integral of energy release within the cell, and We (x, y, t) is the spatial distribution of the specific sources caused by fission fragment deceleration in the gas and standardized per unit of energy released.

The density distribution of the gas between the plates varies over time. Because the fission fragment energy losses are unequivocally related to the density of the stopping medium, the We function profile is also transformed over time. In the first approximation, this factor can be taken into account by tying specific energy release to Lagrangian coordinates. In studies [18, 19], it is shown that such a technique for pulses with a duration of t1/2 ~ 3 ms at any point in the volume of a cell will not lead to noticeable gas temperature and density deviations from the corresponding values obtained during calculations if precise allowance is made for the effect of density redistribution on specific energy deposition. Bearing these results in mind, together with the fact that the fragment energy losses in the medium are proportional to its density [17], we will describe the spatial distribution of the sources using the function

efficiency in this region, but it remains constant in the model used over the entire pulse duration.

Gas density values averaged over the active volume were determined based on calculation results for several moments in time. Using these data, the corresponding energy deposition efficiencies were recalculated and the latter figures were used in conjunction with equations (7.21), (8.31), and (8.32) to estimate possible errors in the calculation of the A(t) factors and density changes, Дp*. The relative error values, Др*/Др where Дp is the density variation in the center of the cell obtained during calculations using the procedure described above, are presented in Table 8.3 for moments in time that correspond to the excitation pulse peak (t = 8 ms) and pulse termination (t« 11 ms).

Analysis revealed that the seepage effect increases noticeably over the course of irradiation. This effect is most intensely manifested if a heavier gas (such as argon) is used. Therefore, it only makes sense to talk about the quantitative agreement of the calculation results with the real processes occurring in similar laser cells for time intervals up to the exciting pulse peak. Past the peak, the calculation results may have a perceptible divergence from real gas behavior.

Fig. 8.11 Normalized gas a density distribution for He 1

(Р0 = 2 atm) in the х = 0 (a) and y = 0 (b) planes: 0.96

(1) t = 6 ms; (2) t = 8 ms; solid lines are calculated; broken lines are 0.92

experimental [2, 46]

0.88

0.84

0.8

b x

1.04

1

0.96 0.92 0.88

0.84 0.8

The calculated and experimental dependences of the variation in relative gas density in the center of a cell upon time are presented in Fig. 8.10. Gas density distribution for the helium (P0 = 2 atm) in the x = 0 (Fig. 8.11а) and y = 0 (Fig. 8.11b) planes is shown in Fig. 8.11. The calculation results are found to be in satisfactory agreement with the experimental data all the way up to the exciting pulse peak, while past the peak, the development of gas density variation over time is only qualitatively described. In addition, the calculations good enough reproduce the density gradient’s spatial dependence. This fact made it possible to successfully use this calculation technique to analyze temporal changes in the laser cavity stability with the type of cell under consideration [34] (see Sect. 5 below in this chapter).

Later, in [46], the computational modeling of the experiments [2] was carried out in two steps. In the first approximation, in fact, as during the technique described above for the gas particles which present in the active volume prior to the start of
irradiation, distribution of specific energy deposition was fixed in an unperturbed homogeneous medium, We0. Energy deposition into the gas outside the confines of this volume was ignored. Pressure was assumed to be homogeneous throughout this volume, while the gas was assumed to be nonviscous and thermally nonconductive. The distribution of fission fragment specific energy deposition was calculated using the same procedure [19, 20].

Unlike the technique described above, during which gas temperature distribution was simply assumed to be proportional to specific source distribution (here, the time-dependent proportionality factor was found by means of jointly solving equations (7.21) and (8.32)), as a starting point in [46], it was assumed that the energy absorbed by the gas mass component goes toward an increase in the internal energy of the gas and toward work based on the expansion of this component. Formally, this approach is more inherent, since it does not include a constant A(t) which does not carry a specific physical “load,”.

The average gas density in the active section of a cell’s volume was determined in the first approximation based on density space-time distribution calculation results. Specific energy deposition distribution was then recalculated for an unperturbed medium characterized by a density that equaled the average density found in the first approximation. Using this figure, density and temperature distri­bution were recalculated, but this time with a correction factor for gas heat exchange with the uranium metal substrates and the cell walls in the buffer volume. As in study [37], the thickness of the passive zone adjacent to the walls and the substrate was a priori taken to be I = fat (see also the first section of this chapter).

According to relative gas density calculation data [46], the difference in the second and first approximations comes to not more than ~5 %, though it is not always closer to the experiment. Calculation results [46] in the first approximation all the way up to the excitation pulse peak differ negligibly from the results presented in Figs. 8.10 and 8.11. The divergence becomes more noticeable past the peak. So, for helium at P0 = 2 atm at a moment in time of t = 11 ms, the divergence of results for relative density at the optical axis (x = 0 and y = 0) reaches 5 %, while for argon at P0 = 0.5 atm, this figure is 17 %.

Liquid laser media have a number of advantages as compared to solid-state media: there are no technical difficulties when making lasers with large amounts of active media, the liquids have sufficiently high volumetric optical uniformity (providing there are no temperature gradients), and the laser medium may be cooled and cleaned using flowing mode of operation.

It appears that the first experiments verifying the possibility of laser action in a liquid medium directly pumped with nuclear radiation were performed in study

[15] . These experiments used an active medium based on europium chelate: a solution of Eu3+(TTA)3TBPh in toluene. To excite the medium using fission fragments, the 235U isotope in the form of the UO2(NO3)2 compound was intro­duced into the solution. Irradiation of the solution with a neutron flux from the KEWB pulsed reactor [16] with a 1.2 ms pulse duration resulted in a rather high value for па ~ 4 % (A = 615 nm). We note that electron beam excitation of a series of europium chelate compounds resulted in an even higher value for < 10 % [17].

The experiments [15] attempted to obtain a laser effect, for which a container with the solution was placed inside the laser cavity. However, there was no lasing since the gain of the active medium, 3.3 x 10-2 cm-1, was lower than the detri­mental loss factor.

After the article [15] was published, VNIIEF [3] began studies directed to searching for liquid active media for NPLs. X-ray excitation with a 10 ns pulse duration and ~10-4 Gr dose was used for preliminary study of the specific light output and the 5D0 level lifetime of the Eu3+ ion as a function of the solvent type (Table 11.1). The specific light output could be increased by cooling the medium. For example, with an approximately 100 °C reduction in temperature, the light output of Eu3+(BA)4HP in acetone increased by ten times, and that of Eu3+- (BTFA)4HP in acetonitrile, by 1.5 times.

Next, the luminescent characteristics of europium chelate solutions were studied by irradiating them with the n, y-ray radiation of the VIR-2 pulsed reactor [16] with a pulse duration of ~4 ms as a function of the specific energy deposition and the europium concentration. The maximum dose of y-radiation was DY = 3.4 x 103 Gr, and the neutron fluence was F = 3.5 x 1014 cm-2. Evaluations have shown that

about 70 % of the specific energy deposition was provided by recoil protons that arise at elastic scattering of fast neutrons on hydrogen nuclei. Some results from these studies are given in Fig. 11.1 and Table 11.2. For reference, Table 11.2 also gives the conversion efficiency for x-ray excitation of europium chelates.

The luminescence spectrum and lifetime of the metastable level 5D0 of the Eu3+ ion did not change with the introduction of 235UO2(NO3)2 in concentrations up to 0.05 g/cm3 into the europium chelate solutions. However, in this case, the conver­sion efficiency had a sharp decrease to 0.01 %. This decrease was explained by optical losses in the medium due to the formation of gas-vapor bubbles [9] on the tracks of fission fragments and radiolysis of the europium compounds. Experiments on the VIR-2 reactor studying the transparency of the aqueous solution 235UO2SO4 (the uranium concentration was about 0.05 g/cm3) have shown that, the transmis­sion coefficient of the solution at X = 1.06 ^m slowly decreases during the reactor pulse, and with a specific energy deposition of about 30 J/cm3, the solution boils up. To decrease the influence of gas-vapor bubbles, the pressure can be increased in the liquid, or, for example, a laser cell without free space [9] can be used.

Verification of the laser action possibility when europium chelate solutions are excited with pulsed n, y-ray radiation was carried out on the TIBR reactor at Dy = 2 x 103 Gr; F = 4.7 x 1014 cm~2 and a pulse duration of about 1.5 ms [1, 3]. A cylindrical quartz laser cell, which was 30-cm long and had a 6 mm internal diameter, was filled with a solution of Eu3+(BTFA)4HDPhH in acetone (CEu = 0.02 g/cm3) and placed in the horizontal through port of the reactor (Fig. 11.2). Laser cavity was formed by two mirrors which were pressed on the ends of the cavity. These mirrors represented Ag layers on surfaces of radiation-resistant

quartz (one of the mirrors had a 1.7 % transmission). The solution was cooled to 200 K with liquid nitrogen vapor. Signals from photodetectors, when a laser cavity was used, exceeded the level of the luminescent radiation by several times. This testifies to the presence of superluminescence. The absence of lasing in these experiments was apparently related to the use of low-quality mirrors.

The first experiments to study the possibility of developing metal-vapor NPLs were carried out in 1970 using the IIN water-pulsed reactor [110]. In these experiments, using the mixture 3He-Hg at the transition 7p2P3/2-7s2S1/2 of the ion Hg+ (X = 615.0 nm), light signals that exceeded the level of spontaneous radiation were registered. The pressure of the mixture 3He-Hg was equal to 0.46 atm. These investigations were developed further in the study [111], in which, during experi­ments with the SPR-II pulsed reactor, with excitation of the mixture He-Hg (Р = 0.8 atm) using nuclear reaction products 10B(n, a)7Li, lasing was achieved and studied at the 615.0-nm line. The output laser power was ~1 mW (n~ 10~6 %), and the laser threshold was reached at ФгА ~1016 cm-2 s-1. The authors of [111] note that attempts to obtain lasing for the conditions of [110], where the mercury — vapor pressure was three orders of magnitude greater, did not yield a positive result. Study [112], based on spectroscopic investigations of the mixture 3He-Hg, con­cluded that it is not possible to obtain a high efficiency at the 615.0-nm line. This conclusion is confirmed by the calculations of [113], which show that the maximal efficiency at this line is no more than 0.03-0.04 %.

Investigations [112, 114, 115] of luminescence spectra of 3He-Hg showed a high populating efficiency of level 73S1 of the Hg atom, which is the upper of the triplet transitions 73S1-63P0210 (A = 546.1; 435.8, and 404.7 nm). The levels 63P0210 of the Hg atom are metastable, so to obtain lasing in quasi-cw or cw modes, quenching of these levels is necessary using an additional impurity, for which in [112, 114] nitrogen was proposed. However, attempts to achieve lasing in the mixture 3He-Hg — N2 at A = 564.1 nm were unsuccessful. The authors of [114] attributed the absence of lasing to the insufficient quenching influence of the N2 impurities in the presence of large quantities of helium.

The proposals to use the molecules H2 and D2 to quench the levels 63P0210 were more successful. Studies [103, 115, 116] concluded that the most promising medium for NPLs is a mixture of (He)-Xe-Hg-H2, in which Xe is a buffer gas, and He is used to cool the plasma electrons. Even before the appearance of the first lasers, Fabrikant and Butayeva in 1959 conducted research [117] into selective “quenching” of low levels of the mercury triplet with molecules of H2 in a gas discharge.

The spectroscopic investigations cited above made it possible to pump laser on the mixture He-Xe-Hg-H2 (A = 546.1 nm) using uranium fission fragments in experiments on the EBR-L setup [33, 118, 119]. For the mixture He-Xe-Hg-H2 (35:35:2:10), at an initial pressure of 0.4 atm and optimal temperature of 480 K, output laser power of 20 W was obtained (n = 0.4 %). The laser threshold was reached at ФгА«2 x 1015 cm-2 s-1. We note that pumping of the Hg laser (A = 546.1 nm) was also carried out using excitation of the active medium by an electron beam [120].

Cadmium — and Zinc-Vapor Lasers

The majority of investigations of metal-vapor NPLs were dedicated to the cadmium-vapor laser. A scheme of energy levels of the cadmium atom and ion with laser transitions is shown in Fig. 3.5. The first successful pumping of a Cd-vapor laser by nuclear radiation was carried out by MIFI associates in 1979, in experiments with the BARS-1-pulsed reactor [121, 122]. When the mixture

3He-116Cd was used, lasing was achieved at transitions 4/2F05/2,7/2- 5d2D3/2,5/2 of the Cd+ ion (A = 533.7 and 537.8 nm). The first successful experiments to pump NPLs based on metal vapors (the mixture He-116Cd, A = 441.6; 533.7 and 537.8 nm) with uranium fission fragments were carried out in 1982 by associates of VNIITF and VNIIEF on the EBR-L reactor [31].

The basic characteristics of cadmium — and zinc-vapor NPLs, which have similar lasing mechanisms, are shown in Table 3.9. There is no information about the

investigations of Cd and Zn vapor NPLs outside of Russia. Only the survey study [126], published in 1983, notes that such experiments were carried out on a pulsed reactor (probably the APRF) using the mixture 3He-Cd (Р = 0.8 atm). Intensive radiation was observed at the 533.7- and 537.8-nm lines, but reliable proofs of the presence of lasing were not obtained.

Information about high-pressure NPLs using Cd and Zn vapors may be supplemented with the results of investigations of these lasers when pumped by electron beams (see review [95] and the studies cited there). For Cd-vapor lasers, apart from the laser lines 441.6, 533.7, and 537.8 nm, registered during nuclear pumping, lasing was also obtained in the UV range of the spectrum at transitions of the Cd+ ion (A = 325.0 nm) and Cd atom (A = 361.0 nm). In the mixture He-Zn, lasing was obtained at the transition of the Zn+ ion (A = 610.2 nm), which was not observed under nuclear pumping conditions. The efficiency of Cd-vapor lasers was ~0.1 %. For electron beam pumping, lasing was also observed in the mixture He-Sr (Р = 3.5 atm) at transitions of the Sr+ ion (A = 416.5 and 430.5 nm) [127]. We note that the possibility of achieving lasing at the transition of the ion Sr+ (A = 430.5 nm) for the mixture He-Sr pumped by nuclear radiation was considered previously in the study [128].

The lasing mechanism of NPLs based on vibrational-rotational transitions of the CO molecule (A = 5.1-5.6 qm) is yet to be determined. One possible channel for populating upper laser levels is the recombination process (CO)2+ + e! CO*(v) + CO [137, 138]. The (CO)2+ ions are formed in three-body processes CO+ + 2CO! (CO)2+ + CO. However, in study [139] this mechanism of populating laser levels is called into doubt due to the lack of a time correlation between the recombination rate of (CO)2+ ions and the output laser power.

Excitation of the vibration levels of the CO molecule can occur by means of collisions between CO molecules with plasma electrons. In study [140], based on calculation of the electron spectrum formed in molecular gas under the effects of ionizing radiation, it was shown that the efficiency of a nuclear-pumped CO laser cannot exceed 0.5 %, and consequently carbon monoxide is not a promising medium for NPLs.

In a later study [141], dissociative recombination of the cluster ions CO+(CO)„ with formation of electronic-excited molecules CO* and subsequent collisions of these molecules with CO molecules in the ground state was proposed as the main mechanism for formation of CO*(v) molecules.

According to the Kolmogorov model, during turbulent motion, large vortices are broken down into increasingly smaller ones. Here, the redistribution of the turbu­lence’s kinetic energy occurs, which is transmitted from the large-scale vortices to the small-scale ones. The structure of motion on small scales (at least at distances from solid walls that are greater than the small scales [4]) is locally homogeneous and isotropic. According to ref. [9], the theory of homogeneous turbulence consti­tutes “an entirely suitable framework for analyzing the problem of scattering” of optical and acoustic waves. In this case, the proposition concerning the homoge­neity and even the isotropy of a turbulent field proves to be correct [9].

According to the model [8], a wide range of pulse length and velocity scales exists in a turbulent motion region. For the combination of the length scale, l0, and the corresponding velocity scale, u0, at which the Reynolds number takes on the order of unity

v

the turbulent motion must be damped; i. e., l0 characterizes turbulent inhomogene­ities of minimum dimensions and is called the inner turbulence scale. It is deter­mined by the correlation (see ref. [10] for example)

І0 = (v3/w)1/4, (9.6)

where w is the turbulent motion dissipation rate per unit mass, which transitions to heat at the expense of viscosity. It is fully determined by viscosity and its order of magnitude comes to

w ~ vu0/l0. (9.7)

If the Reynolds number in Eq. (9.1) for a liquid or gas flow is sufficiently large (Re > Rec), the flow loses stability. Here, vortices can be formed that have Л dimensions up to values on the order of Л ~ d, and that have a velocity, the order of magnitude of which may be close to U. According to the Kolmogorov model, the vortices under consideration are broken down into smaller ones, which are in turn broken down into even smaller ones, all the way down to inhomogeneity dimen­sions of ~l0. Thus, between the limiting values of U, u0 and Л, l0, subintervals of the variation in motion velocities, u, and typical dimensions, lt, exist. If a w parameter is identified as an average energy dissipation rate throughout the entire gas flow that is dependent upon the ~Л scale alone for the turbulent flow as a whole, and if the corresponding velocity, ~ U, is used, then for large-scale inhomogeneities, we get [9].

w — U0/K.

Over the course of vortex breakdown, energy is transmitted to the smaller-scale inhomogeneities, for which w ~ u3/lt. Energy dissipation occurs in inhomogeneities with a size on the order of the inner scale [8—10].

From Eqs. (9.5), (9.7), and (9.8), we find

lo — (Ул/и3)1/4. (9.9)

Consistent with refs. [9, 11], we will estimate the square of the sound velocity in the medium, which as is generally known, is determined by the equation

(where S is entropy), from the correlation

u2 — AP/Ap.

As was done in ref. [4, 9], the dynamic pressure for turbulent pulses can be estimated from the correlation

AP — pu2. (9.10)

Thus, for turbulent pulses that are characterized by a velocity of u and a length scale of lt, we get

Ap/p — u2/u2

It follows from Eq. (9.11) that the largest density jumps take place in inhomo­geneities that are characterized by the highest u velocity values; i. e., in inhomoge­neities with a typical Л scale that have the maximum dimensions.

Combining Eqs. (9.5), (9.7), and (9.8), we get

uo — уи3/Л, (9.12)

which, after being placed into Eq. (9.11), yields

By way of an example, we will examine helium at T = 300°K and P0 = 2 atm,

which corresponds to a density of p к 3.2 x 10~4 g/cm3 and a kinematic viscosity of v к 0.6 cm2/s. Let us suppose that d = 2 cm. The sound velocity in helium at this temperature is us к 105 cm/s. Assuming that Л ~ 1 cm and taking the velocity of gas flow to be U = 10 m/s, then from Eqs. (9.9), (9.12), and (9.13), we get l0~4 x 10~3 cm, u0~102 cm/s, and Др0~8 x 10~10 g/cm3. For maximum inho­mogeneities with a Л scale that are characterized by a velocity of ~ U, according to Eq. (9.11), we then obtain Дpm~3 x 10~8 g/cm3. At U = 100 m/s for these same parameters, we find i0~7 x 10~4 cm, u0~9 x 102 cm/s, Дp0~2 x 10~8 g/cm3, and Дpm~3 x 10~6 g/cm3.

The correlation Tt~ lt/u [9] apparently determines the typical pulse time. Then taking Eq. (9.9) into account for small-scale pulses, we get

/ 3 1/2

Tt0 — l0/u0 — уЛ/U, (9.14)

which, for the parameters we used, yields Tt0~3 x 10~5 s at U = 10 m/s and Tt0~8 x 10-7 s at U = 100 m/s.

Expression (9.10) was previously used to estimate the pressure jump in inho­mogeneities. In ref. [11], the correlation used for this estimate is

ДP — puU. (9.15)

Without entering into a discussion with the authors of refs. [9,11] concerning the correctness of a given approach, we will estimate ДР using both correlation (9.10) and correlation (9.15), because it is important for us to reflect the trend of the decrease in density jumps with a decrease in inhomogeneity scale. We will show that inhomogeneities of the maximum scale must exert a maximum effect on the optical quality of a medium, and that the process of describing the pressure jumps in small-scale inhomogeneities has no effect on the estimation of the density jumps in these inhomogeneities.

Using Eq. (9.15) instead of Eqs. (9.11) and (9.13), we obtain

Substituting the numerical parameter values we assigned yields Др0~5 x 10~9 g/cm3 at U = 10 m/s and Др0~3 x 10~7 g/cm3 at U = 100 m/s.

In previous chapters, we have reviewed pumping methods for gas-medium and condensed-medium lasers using nuclear reactors as neutron sources. We also reviewed the characteristics of these lasers and the potential to use them in different nuclear-laser devices. The highest specific power depositions for gas media (q < 5 kW/cm3) can be obtained if a laser cell that has a uranium layer or is filled with 3Не is placed inside the core of a pulsed reactor at the minimal possible pulse length for pulsed reactors, ~100 ps. However, these specific power depositions are sometimes not sufficient to reach the lasing threshold of certain active media. Precisely for this reason, attempts to achieve lasing with help of the neutron fluxes of pulsed reactors to pump excimer or chemical lasers were unsuccessful (see Chap. 3, Sect. 6).

If electron or ion beams with a ~10 ns pulse duration are used, significantly higher specific power depositions can be obtained for gas media: <107 W/ cm3 x atm and <109 W/cm3 x atm, respectively [1]. This pumping method made it possible to create many different high-pressure gas lasers (see, for example, [2]), some of which had rather significant output powers. For example, with electron- beam pumping of an excimer gas media based on the KrF (A = 248 nm) molecule, an Aurora multichannel setup measured a laser energy of about 10 kJ over 500 ns [3]. When a chemical HF laser was initiated by an electron beam on H2-F2-O2-NF3 mixture, the output energy was 4.5 kJ over 50 ns [4]. A further increase in output performance is difficult mainly due to the complexity of pumping large volumes of active media uniformly.

Investigations of high-power pulsed lasers in the nanosecond range have mainly been directed toward creating a laser driver for facilities based on inertial confine­ment fusion (ICF). In order for the facility to be economically advantageous, the gain of the thermonuclear target must be about 100 [5]. According to calculations, this gain requires laser energy of 1-10 MJ [6]. At present, the energy (power) of the most powerful operating ICF laser in Russia is 30 kJ (120 TW) [7, 8]. Outside Russia, these values are 40 + 25 kJ (60+10 TW) [9, 10]; 30 kJ (~10 TW) [11]; and 150 kJ (15 TW) [12].

© Springer Science+Business Media New York 2015 S. P. Melnikov et al., Lasers with Nuclear Pumping, DOI 10.1007/978-3-319-08882-2_12

The last two lasers are separate sections of high-power facilities under construc­tion: LMJ (240 channels) [11] and NIF (192 channels) [12]. According to calcula­tions, these facilities should have roughly identical output performance, 1.8 MJ (500 TW) at X ~ 350 nm. The commissioning of these facilities is planned for 2010­2012. Thus, building the laser driver needed for ICF facilities is a long and expensive task.

Using the y-ray radiation from a nuclear explosion as the pump source provides unique opportunities to develop high-power lasers in the nanosecond range since it excites active gas media with volumes in the tens of cubic meters at specific power depositions up to ~109 W/cm3 x atm. If a nuclear explosive device with a compar­atively low energy release (about 0.5 kt of TNT) is used, laser pumping can be implemented with an output energy of 0.1-1 MJ [13]. These lasers may find their application, for example, in the solutions for certain ICF problems.

Laser media are not yet pumped by the radiation of radioactive isotopes. Radioac­tive isotopes were previously used for an auxiliary purpose—pre-ionization of the active media of CO2 lasers [62], as well as lasers at transitions of Xe [63] and Ne [64] atoms.

In the case of the use of radioactive isotopes directly for pumping of laser media, the specific power deposition will be higher for isotopes with short half-lives, which naturally reduces the lifespan of such a laser. As data from study [65] show, the most suitable isotopes for pumping gas NPLs are the a active isotopes Po, Cm, and the spontaneously fissionable isotope 52Cf. Some characteristics of these iso­topes are shown in Table 1.3.

Calculations of specific power deposition were made in [65] for cylindrical laser cells with internal diameters of 1-8 cm, on the internal surface of which layers of isotopes were deposited with a thickness equal to one-half the particle path length in the layer material. Calculations showed that depending on the cell diameter and the

210 242

argon pressure (0.25 and 0.5 atm), for the isotopes Po and Cm, the specific power depositions vary in a range of q = 0.06-0.1 W/cm3, and for 52Cf, q < 0.02 W/ cm3. With such small specific power depositions, it is possible to achieve lasing using only the most low-threshold active media of NPLs, for example, Ar(Kr)-Xe mixtures, radiating at the infrared transitions of the Xe atom (see Chap. 3, Sect. 3.1).

Study [66] examined the possibility of radioisotope pumping of a neon laser with a He-Ne-H2 mixture (X = 585.3 nm). When a 210Po layer 65 mg/cm2 thick used, and is deposited to the internal surface of a cylinder cell with a diameter of 15 mm, it is possible to obtain q < 0.6 W/cm3. However, the conclusion of the authors of [66] regarding the possibility of achieving lasing under such conditions appears

extremely optimistic, since NPLs with He-Ne-H2 mixture have a rather high lasing threshold (see Chap. 3, Sect. 3.2).

Apart from the thin radioisotope layers, for excitation of gas media it is possible to use gaseous isotopes, for example, p radiators 42Ar, 85Kr, etc. In this case, one should consider gas media having Ar or K as their basic components (for example, Ar-Xe or Kr-Xe). Calculations [54, 63] show that the isotopes 42Ar and 85Kr can for now be used only for pre-ionization of active media of gas-discharge lasers, since in this case the specific power deposition does not exceed 0.001 W/cm3.

One of the specific features of the nuclear-excited plasma is related to the formation of tracks (or columns) of ionization with passage of heavy charged particles (fission fragments and other heavy ions) through high-pressure gases, which in turn leads to non-uniform ionization of the gas media, and as a consequence, can influence populating of laser levels in NPLs [7, 8]. Depending on the parameters of the gas media, the transverse dimensions of the tracks are 1-10 pm, and the track lifetime, or the time to establish uniform ionization through diffusion, is 0.1-1 ps [7—9]. The degree of influence of the track structure on the characteristics of the nuclear — excited plasma depends on the type of ionizing particles, the specific power deposition, and the type and pressure of the gas. The ionization non-uniformity, provoked by the formation of tracks, will be the most significant in the following cases: (a) when the gas is ionized by fission fragments and by other heavy ions; (b) for high-pressure gases with high atomic mass; (c) at low specific power deposition, when there is no overlapping of tracks.

The influence of the track nature of gas ionization on recombination processes was examined in study [9], where the recombination coefficients were measured for 3He, 4He and the mixtures 3He-CO2 and Ar-N2 on ionization by у quanta, products of the nuclear reaction 3He(n, p)3H and 235U fission fragments. In the first case, the ionization chamber was irradiated with 60Co у quanta, in the two other cases—with neutron radiation of a stationary nuclear reactor, with a neutron flux density of <1010 cm-2 s-1. The results of these measurements for several pressures of the gas media are shown in Table 4.1.

It follows from a comparison of the data in Table 4.1 that with the ionization of 4He (10 atm) and the mixture Ar-N2 (1 atm) by uranium fission fragments, the recombination coefficients are 3-4 times greater than with ionization by у quanta. It is in these two cases that the track structure of the plasma became apparent, and the so-called columnar recombination occurs, which is in accord with the calculations

performed in study [9] based on the theory of columnar recombination [10]. Also important in study [9] is the conclusion that columnar recombination becomes noticeable when there are ionization losses of в, > 107 ion pairs/cm. The optimal buffer-gas pressures at which gas NPLs operate are PHe < 3 atm, PNe < 1 atm, and PAr < 0.5 atm (see Chap. 3, Sect. 3.1, and Chap. 7, Sect. 7.5). At such pressures, в і < 106 ion pairs/cm and the influence of the track structure of the plasma on the recombination processes will be insignificant.

Fluctuation of plasma component concentrations induced by the track structure can exert some influence on the characteristics of NPLs excited by fission fragments, if the upper laser levels in these lasers are populated owing to fast charge-transfer processes, for example in the case of a He-Cd laser [7, 8]. When lasers operating on transitions of rare gas atoms are pumped by fission fragments, the influence of the plasma track structure can evidently be ignored, because the track lifetime is consid­erably less than the characteristic times of the recombination processes [8].

At high specific power deposition, the tracks are closed and the track structure of the plasma disappears. Assessments performed in study [8] show that for helium at a pressure of 1 atm, the track overlapping occurs at specific power deposition of q > 2 W/cm3.

Studies [14—16] propose determining the energy deposition of fission fragments (in particular the efficiency e) through the normalized transverse size of the gas volume D0 = d/R0 and the normalized thickness of the uranium-containing layer D1 = 8U/R1, where d is the internal transverse size of the laser cell (diameter for a cylindrical cell or distance between uranium layers for a cell with plane-parallel arrangement of the uranium layers). Such an approach is convenient, because the properties of the media are included in the values R0 and R1, so the slowing of the fragments in different media, but with an identical value of normalized sizes, must be identical. We note that since the fragment energy losses per unit of range are proportional to the density of the decelerating medium, the normalized transverse size of the cell is proportional to the initial pressure of the gas medium.

Let e(D1) be the share of fission fragment energy transmitted to the gas when the relative thickness of the active layer D1 is unchanged. The total energy released in the system is proportional to D1, while the energy absorbed in the gas, E ~D1e(D1).

Figure 7.5 shows the dependencies, calculated using formulas [14,16] of the energy deposition efficiency e and the parameter D1e(D1) on the relative thickness D1 for four values of the normalized width of the gas interval D0 in a system comprised of two plane-parallel plates, where active layers of identical thickness are deposited on two surfaces facing each other.

Let us examine a simple one-dimensional model (depending only on the x coordinate along the surface of the layer),

D1 = D1 {1 + Sf (x)}, (7.11)

whose inhomogeneities are arranged with a specific period h, that is, f(x + h) = f(x). Here D1 is the average value of relative thickness of the active layer, and S is the dimensionless amplitude of inhomogeneities.

For a uniform layer, let the number of fragments entering the gas volume from a unit of surface be equal to N. If the maximal deviation SR1D1 of the thickness of the active layer from its average value does not exceed the range R1 by an order of magnitude, that is,

SD1 < 1, (7.12)

and the distance between the nearest maxima or minima of inhomogeneities markedly exceeds the fragment range in the material of the layer

Fig. 7.6 One-dimensional model of uranium — containing layer of variable thickness

then the relative change in the number of fragments AN/N, which escape into the gas owing to the inhomogeneities (that is, screening), can be estimated by the ratio AN/N ~ a/n <<1, where а к 8RJDJ/h~R1/h. Hence it follows that the influence of the screening factor can be ignored.

The efficiency of energy deposition to the gas e(x) from a strip of thickness dx and height SU(x) (see Fig. 7.6) evidently must coincide with the energy deposition of an infinitely elongated uranium layer with a constant thickness (5U = constant) equal to the height SU(x) of the selected strip. Accordingly, the total energy transmitted to the gas from the uranium strip in question is dE(x) ~D1(x)e(x)dx.

If the flux distribution of neutrons initiating fission of the active nuclide can be considered unchanging within the limits of the spatial period of inhomogeneities, the effective value of the share of energy deposited into the gas by fragments emitted from the non-uniform layer must be determined by the expression:

h/2

Dj (x)e(x)dx

Dj(x)dx

-h /2

where e(x) is the efficiency of the energy deposition from the uniform, infinitely elongated layer of constant thickness, equal to the thickness 5U(x) of the real layer at point x.

Figure 7.7 shows the results of numerical calculations of the dependence Є on the amplitude of the inhomogeneities in a system, comprised of two flat parallel plates, for two simple models with D1 = 0.5:

(a) inhomogeneities in the form of alternating teeth of rectangular shape, the distance between which is equal to the width:

2nx
sin.

h

For cylindrical systems with an active layer deposited on the internal surface of the cell wall, the dependencies є and єD1 on D1 and D0, as well as Є on S, D1, and D0 have the same appearance as for plane-parallel systems.

Direct calculations of є for active layers with different types of periodic symmetrical one-dimensional inhomogeneities showed, as was to be expected, that the maximal reduction of the energy deposition to the gas occurs with inho­mogeneities of the rectangular shape. Here, the efficiency of the energy deposition can decrease by 50 % in comparison with the efficiency of uniform layers. Inho­mogeneities with a smoothed profile are less dangerous. Thus for inhomogeneities with a profile of the sinusoidal type, a reduction of the total energy deposition of <21 % is possible.

On the basis of calculations and experimental studies, engineering and technical examinations, and experience in the construction of domestic reactors and the operation of research nuclear reactors and laser experimental systems, the VNIIEF associates made preliminary assessments of the main energy, nuclear and physical, technical, and operational parameters for alternative RL designs operating in the time span from a fraction of a second to stationary mode.

All possible alternatives for the RL can be relatively divided into two types. The first type of RL has transverse gas flow and external cooling of the laser channels using a coolant (for example, heavy water D2O, which simultaneously plays the part of the neutron moderator) with subsequent withdrawal of the heat beyond the boundaries of the core. This type of RL can operate in stationary mode as well as in protracted pulse mode >5-s long. The second type is a heat-capacity RL. The heat released during operation of this reactor is accumulated in the core moderator. As a result, the temperature of the moderator and laser-active gas grow with time. There­fore, the second-type of RL can only operate in pulsed mode. If laser-active gas is not circulated in these RLs during the active pulse, the laser elements may be represented as extended cylinders (Fig. 10.2a) or channels formed with flat plates (Fig. 10.2b). In the latter, radiators do not have to be added to the design. The pulse duration of these RLs should be т < 0.1 s (see Chap. 8). After each pulse, forced cooling may be carried out by flowing the same gas using external pumps and blowers. For second-type of RL, the pulse durations 0.1 < т < 100 s may be obtained. In this case, the optimal RL design has rectangular laser elements with flat uranium layers. They should be joined with the radiators as shown in Fig. 10.2b and combined into one or several gas circuits, along which, the gas laser medium is circulated during the pulse.

Some RL versions have been examined in studies [15, 18]: RLs with transverse gas flow and the removal of heat energy beyond the boundaries of the core, and an RL with stored heat in the reactor core (heat-capacity mode). The main character­istics of these RLs are presented in Table 10.3, and their design and operational features are described below.