Gas ionization in the initial stage occurs directly by charged particles and secondary electrons. A picture of the electron energy distribution in the gas is shown in

Fig. 4.2 [11], where fe is the energy distribution function of the electrons, normal-

1

0

electron energy range can be divided into three regions:

fe( Ee)

1. The region of the ionization cascade Vt < ee < e0 (e0 is the particle initial energy, Vi is the ionization potential of the gas atoms and molecules), in which the energy of the electrons is sufficient for ionization of gas particles, and is expended for ionization and excitation of particles.

2. The region Im < ee < Vi (Im is the minimal threshold of electron, or vibrational excitations) in which the energy of the electrons is reduced, primarily due to excitation of electron and vibrational states of the gas particles. In this region, as in the previous one, electrons lose energy in comparatively large “portions,” equal to or greater than Im (for helium, Im = 19.8 eV is the energy of the lowest 23S state; for molecular gases Im is substantially lower and can be ~1 eV).

3. In the subthreshold region (ee < Im), electrons lose energy in small “portions” due to elastic collisions with gas particles, and the share of energy lost by an electron in one collision, Sea = 2me/Ma (where me and Ma are the masses of the electron and atom, respectively). This process is sometimes called electron thermalization.

An estimate of the characteristic time of energy loss by electrons in the high — energy region (ee > Im) for gases at atmospheric pressure gives Tne1 ~ (Meffex[A])_1 ~0.1 ns [2], where ue ~108 cm/s is the electron velocity, aex ~10-17 cm2 is the characteristic cross section for inelastic processes, and [A] is the concentration of gas particles. In study [12], the Monte Carlo method was used to calculate the time required to slow primary electrons jointly with secondary electrons of an ionization cascade from an initial energy of e0 to Im. This time Tex was calculated for He, Ne, Ar, Kr, and Xe on the assumption that an electron beam pulse constitutes a S function at the moment of time t = 0 (Fig. 4.3). Calculations

show that Tex increases with growth in £0 and for £0 = 1 MeV, at atmospheric pressure Tex varies from 25 ns (xenon) to 250 ns (helium). It should be noted that the time to slow the secondary electrons (ts), which have lower energies and accordingly higher cross sections of inelastic interaction with the gas atoms, is much lower than Tex, and amounts to ts > 0.01 ns atm [12]. These are the times that are realized when fast electrons excite a gas volume of small size (on the order of a few centimeters).

Calculations of the high-energy part of fe for argon (£e > Im = 11.6 eV) showed that stationary distribution is established rather quickly in times of <0.1 ns after switching on the electron beam [13]. The time to establish stationary distribution increases with the growth in the initial energy of the electrons: from ~0.001 ns at £0 = 1 keV to ~0.1 ns at £0 = 1 MeV. These results agree with calculations conducted in study [14] on temporal evolution fe(£e > Im) when £0 = 10 keV for neon (4 atm) and xenon (1 atm). The time required to reach stationary mode for xenon is roughly an order of magnitude less than for neon, and amounts to ~0.001 ns, which is explained by the higher cross sections of inelastic processes.

For electrons with energies £e < Im, the mechanism of energy loss is related to the processes of elastic scattering with gas particles. The characteristic time of this energy-loss process Tel~ (ueoea8ea[A])~l where ueoea ~10~9 cm3/s is the rate con­stant of the elastic process for rare gases [2]. With an average energy of plasma electrons £e~1 eV and at atmospheric pressure, Tel > 100 ns, which greatly exceeds Tnel. Measurements of the characteristic times of the electron thermalization pro­cesses at an initial energy of 0.15 eV and a gas temperature of Tg = 300 K, carried out using microwave methods in study [15] for Ar (0.4 atm), Kr (0.15 atm) and Xe (0.14 atm), showed that the products Tel • Р = 1,050 ns • atm, 240 ns • atm, and 260 ns • atm, respectively.

Experimental data for He and Ne obtained in study [16] with an initial electron energy of around 1 eV and Tg = 300 K are 4.8 ns • atm and 120 ns • atm, respectively.

The time to establish stationary distribution fe in the subthreshold region £e < Im considerably exceeds the analogous time for the high-energy region. From the calculations of fe(£e < Im), obtained as a result of a numerical solution of the Boltzmann non-stationary kinetic equation for He [6], Ne [17], Ar [18, 19], and Xe [19] in the case of ionization by electron beams, it follows that the time required to reach stationary mode at atmospheric pressure is 5-10 ns.

To a significant extent, the electron energy distribution function in the sub­threshold range is determined by the frequency of electron-electron collisions, which depends on the degree of plasma ionization Z = ne/[A] (ne is the electron concentration). From the data shown in Fig. 4.4 [17] for the mixture Ne-Xe-HCl, it follows that the influence of electron-electron collisions on the formation of the electron energy distribution function is great even for a comparatively low specific power deposition q = 2 kW/cm3 (Z < 10~6). The complicated structure of the distribution shown in Fig. 4.4, calculated without taking electron-electron collisions into account, is explained by the influence of vibrational excitation of HCl molecules.

Fig. 4.4 Calculation of stationary electron energy distribution in the low-energy region for a Ne-Xe-HCl mixture (596:3:1) at a pressure of 4.9 atm, excited by an electron beam, without taking into account (1) and with taking into account (2) for electron-electron collisions [17]

For a low degree of plasma ionization, the electron energy distribution in the subthreshold region (ee < Im) can differ from the Maxwell distribution. To establish the Maxwell energy distribution for slow electrons at temperature Te, it is necessary for the frequency of the electron-electron collisions to greatly exceed the frequency of energy loss in elastic electron-atom collisions. This constraint can be written as follows [2]:

where oea is the cross section of elastic electron scattering on the atoms; e is the electron charge; and Л is the Coulomb logarithm. For helium, which is frequently used in NPL gas media as the buffer gas, uea ~5 x 10~15 cm~2; ee~0.15eV; Л ~10; me/Ma = 1.4 x 10~4; and consequently, Z ^ 10~6. We note that in experiments with pulsed reactors for atmospheric pressure NPLs, q < 5 kW/cm3 and the degree of ionization Z < 10-5, so that the condition (4.1) is fulfilled only in the case of maximal possible power deposition for NPLs.

Methods of calculating electron energy distributions are considered, for exam­ple, in studies [11,20]: the use of the continuous slowing down model, in which it is presumed that a fast electron loses energy in the degradation process continuously; modeling of the process of electron energy exchange by the Monte Carlo method, as

well as numerical solution of the Boltzmann kinetic equation. The continuous slowing down model is applicable primarily to calculate the electron energy distribution with energies ee > Im. For precise determination of electron energy distribution in the region of subthreshold and thermal energies, numerical solution of the Boltzmann kinetic equation is necessary.

For analysis of the kinetics of plasma processes in NPLs, information about the electron energy distribution for He, Ne, or Ar is the most interesting, because these are the gases that are used as the basic component (buffer gases) in nearly all known gas NPLs. It should be noted that all the data relating to electron energy distribu­tions in rare gases were obtained by computation except for study [21], where such distributions were found using spectroscopic and probing measurements for He and Ar during excitation by 235U fission fragments (Figs. 4.5 and 4.6) in a pressure range of 0.03-1 atm (q~0.01 W/cm3 at a pressure of 1 atm, ne~1011 cm~3, Z ~ 10~8). For comparison, Fig. 4.5 also shows the results of the calculation [22] for helium excited by a particles.

Information about the electron energy distributions for helium with excitation by fission fragments at an energy of 85 MeV and protons with an energy of 0.6 MeV (PHe = 0.4 atm; q = 1 kW/cm3) is contained in study [6], where these data were obtained as a result of solving the non-stationary kinetic equation. It follows from Fig. 4.7 that the electron energy distributions for two methods of excitation in the region ee < Im virtually coincide and are close to the Maxwell distribution.

Fig. 4.5 The electron energy distribution in helium excited by fission fragments [21]:

Р = 0.07 atm (1);

0.H3 atm (2) and 1 atm (3); (4) calculation results [22] with excitation of helium by a particles; dotted line is the Maxwell distribution

Fig. 4.6 Electron energy distribution in argon excited by fission fragments [21]: PA = 0.4 atm (1); 0.6 atm (2); 0.8 atm (3) and 1 atm (4); dotted line is the Maxwell distribution

Fig. 4.8 Electron energy distribution in argon (PAr = 3 atm) excited by an electron beam [18]. The dotted line is the Maxwell distribution when Te = 1.5 eV

The authors are not aware of any computational or experimental data on the electron energy distributions in neon during excitation by nuclear particles.

Information on electron energy distributions for plasma excited by electron beams is more extensive. Calculations by the Monte Carlo method for He, Ar and Xe in a range of initial electron energies £0 = 20-10,000 eV showed that the electron energy distribution in the subthreshold region (ee < 20 eV) does not depend on £0 for £0 > 300 eV [23].

The electron energy distribution for Ar (PAr = 3 atm) during excitation by an electron beam with a duration of 5 ns and £0 = 200 keV (q = 1.5 MW/cm3; ne = 2 x 1015 cm~3, Z = 2.5 x 10~5) is shown in Fig. 4.8 [18]. From the data cited, it follows that for electrons with £e < 10 eV, the electron distribution roughly corresponds with the Maxwell distribution. This circumstance is more clearly illustrated by the data in Fig. 4.9, which shows the ratio of the electron distribution to the Maxwell distribution for three different pressures of Ar [18]. With higher £e, these functions differ: the number of electrons in the region £e = 10-30 eV is less, while for £e > 30 eV it is greater than the Maxwell distribution. From a comparison of the data of Figs. 4.6 and 4.8, one can conclude that the shape of the distribution for argon under significantly differing conditions of excitation is roughly equal.

Calculation of the electron energy distribution for Ne was carried out in the studies [14, 17] for the following conditions: an electron beam with £0 = 200 keV, PNe = 4 atm, q = 200 kW/cm3, ne « 5 x 1014 cm~3, Z ~ 5 x 10~6. For neon (as for argon), the electron distribution function in the low-energy region (£e < Im) also

Fig. 4.9 Ratio afm of the electron energy distribution to the Maxwell distribution at argon pressures of 1 (1), 3 (2), and 10 (3) atm [18]. The excitation conditions are the same as in Fig. 4.8

coincides with the Maxwell distribution, while for ee > 40 eV the number of electrons significantly exceeds the equilibrium value (Fig. 4.10).

From the data cited it follows that in the range of conditions in which atmospheric-pressure gas NPLs were studied in experiments using pulsed reactors with excitation by nuclear reaction products (q < 5 kW/cm3, Z < 10~5), the electron energy distribution consists of two parts. The chief quantity of plasma electrons are concentrated in the subthreshold region, ee < Im, and their energy distribution is

similar to the Maxwell distribution, with a certain characteristic temperature Te = 2jsefe(ee)de/3k = 2 ee/3k. The electron energy distribution function in the region ee < Im is virtually independent of the type of charged particles. The low-energy electrons of this region participate in processes of great importance in the kinetics of populating and relaxation of lasing levels of NPLs: electron-ion recombination, “quenching” of excited states, the processes of attachment to electronegative atoms and molecules, and excitation and ionization in collisions with gas particles that are in excited states.

For ee > Im, the distribution function decreases as a consequence of the effective inelastic electron-atom collisions and differs from the Maxwell distribution. The electrons in this region scarcely participate in the recombination processes, and this region itself is a source of electrons for the subthreshold region.

Clearly, in the case of non-symmetrical periodic inhomogeneities, including two-dimensional (that is, depending on two spatial coordinates), the maximal reduc­tion in the energy deposition must be manifested when there is a rectangular profile of these non-uniformities. Let us examine the influence of the presence of craters with vertical walls and an arbitrary base (Fig. 7.8) on the efficiency of the energy deposition. Let us introduce the dimensionless parameters of the inhomogeneities:

Let D1(8+ + 😎 be the depth of the craters; a the area of their base; and S the equivalent area of the surface of the elementary cell of the active layer containing one crater, defined as the ratio of the total surface of the active layer to the total number of craters. As in the one-dimensional model, we shall assume that the maximal deviation of the thickness of the active layer from its average value does not exceed the range R1 by an order of magnitude (that is, 8±D1 < 1), and the distance between the nearest craters markedly exceeds the fragment range in the layer material:

S1/2 » R1. (7.16)

From the conservation of the average thickness of the active layer (S — a)8+D1 = a8-D1 it follows that:

8+ = 2 S 8; 8- = 2 ^ 8.

If D — = 0, that is, the depth of the craters reaches the substrate, then 8- = 1. Hence

in accordance with the second equation (7.17) we find that for a given ratio of areas ff/S, the value of the parameter S cannot exceed

and the minimal value which the ratio ff/S can assume for a given S is

The effective energy deposition in the two-dimensional case is determined by an equation analogous to Eq. (7.14), in which integration is performed over the area of the equivalent cell active layer surface S. For the crater model in question, this equation boils down to the simple expression

Figure 7.9 shows the results of calculations for the model of craters with vertical walls when D0 = 0.5 in a system comprised of two plane parallel plates.

Let us transform Eq. (7.19) using Eqs. (7.15) and (7.17):

є = є^-)[1 — 2(1 — ff/S)S]ff + є^+)(1 + 2Sff/S)(1 — ff/S).

S

Substituting the value of Smax from Eq. (7.18), which clearly corresponds to the minimal possible value of є, we get emin = ^D+). Thus the limit minimally possible value of є for a non-uniform layer is equal to the value of є which has a uniform layer with a normalized thickness equal to the maximal thickness of the non-uniform layer. Such correlations are also not hard to write for the model of

Fig. 7.9 Dependence of the share of energy of fission fragments efficiently transmitted to the gas on the relative area of the craters: (1)D1 = 0.5; (2)D1 = 1; the solid line is S = 0.5; the dotted line is S= 1

Fig. 7.10 Cross section of the layer of uranium oxide — protoxide: (1) substrate of aluminum; (2) layer of uranium oxide-protoxide; (3) epoxide resin

active layers with two-dimensional projections having vertical walls, which give results analogous to the crater model.

Of course, the models we have discussed are only an illustration of the signif­icant influence of inhomogeneities; they cannot serve as a method providing precise results of calculation of e, because the spectrum of possible configurations of real inhomogeneities, even for one specific layer, is hard to convey mathematically. Figure 7.10 shows photograph [24] enlarged roughly 1,000 times of the cross section of one of the layers of the uranium oxide-protoxide used in NPL experi­ments at VNIIEF. The best method of allowing for the influence of inhomogeneities in determining e is evidently to introduce the corrective multiplier e = fie(pi), which is found from a comparison of the experimentally determined efficiency of energy deposition to the gas with the computed efficiency e(D), obtained on the assumption of uniformity of the active layer, D1 = D1.

The circumstance that a maximal reduction in the energy deposition occurs for inhomogeneities having a rectangular profile in the cross section of the active layer makes it possible to determine the lower limit of the possible drop in the energy deposition to the gas, and to select acceptable values of the amplitude of the inhomogeneities. Analysis conducted on the results of calculations showed that if the amplitude of fluctuations of the inhomogeneities does not exceed one half the thickness of the active layer, then the maximal possible reduction in the energy deposition will be no more than 10 %. However, it should be noted that this conclusion is valid provided that the conditions (7.12) and (7.13), or (7.16), are met. Otherwise, a reduction in the energy deposition can prove more significant. The reason for a marked reduction in the energy deposition could be, for example, screening of the escape of fragments to the gas by the inhomogeneities themselves, when h < R1.

In study [21], in several specific examples, the influence of periodic one-dimensional inhomogeneities of the active layer, determined by inhomogene­ities of the surface of the substrate on which this layer was deposited, was examined computationally. The inhomogeneities had a rectangular profile. The width of the projections of the non-uniformities is equal to their height, while the period of the non-uniformities is equal to twice their height.

The surface of the uranium turned toward the gas was considered ideally smooth. Calculations of the energy deposition of the fragments were carried out by the Monte Carlo method, which automatically led to allowance for the screening factor of substrate projections in the active layer. As the material of the active layer, uranium dioxide UO2 was considered (R1 ~ 8 qm), and the substrate material was Al and W. The height of the inhomogeneities was varied within the limits of 2-10 qm. The results of these calculations agreed with the results discussed above: with the growth in amplitude of the inhomogeneities, the efficiency of the energy deposition drops, and when the amplitude corresponds to S = 1 in Eq. (7.11), it decreases by ~50 %. This last evidently testifies to a relatively weak influence of screening (at least for the examples considered).

In contrast to direct numerical calculations for a specific geometric profile of the active layer and its composition, the methods of (7.14) and (7.19) in the limits of the constraints (7.12) and (7.13) have greater universality. These methods used the formulas (7.11) and (7.14)-(7.19) and the methods of calculations from studies [14—16], in which the efficiency of the energy deposition of both Є and e(D1) are determined by means of the normalized thickness of the active layer D1 = SU/R1. Because the range R1 is inversely proportional to the density of the decelerating medium, in the utilized approach, the inhomogeneities of the normalized thickness of active layers include both the inhomogeneities of the real thickness, provoked by roughness of the geometric surfaces bounding these layers, and the inhomogeneities of density of the layer material.

To support stationary operation of a NPL with transverse gas flow through the laser channels, the gas flow velocity must be >100 m/s. Chapter 9 shows that, at these circulation speeds, the gas flow is turbulent and gas density fluctuations emerge, which negatively affect the optical quality of the medium and, consequently, on the characteristics of the laser radiation. The calculations show that the gas velocity at which turbulent density fluctuations do not have a direct influence on the laser parameters should be <30 m/s for helium-based laser media and <10 m/s for argon — based.

Velocities ~10 m/s may be realized with transverse circulation (see Chap. 9, Sect. 9.3). In this case, the RL core consists of separate laser channels with transverse (with respect to the optical axis) circulation of the gas medium [13, 14]. A single laser channel with a rectangular profile contains a ~10-cm wide flat layer of uranium deposited to the internal surface of the side walls parallel to the direction of gas flow. A cross section of this channel is shown in Fig. 10.2b (see also Figs. 9.1 and 9.2). To cool the mixture heated in the channel, a radiator is placed at its output. The next laser channel can be placed beyond the radiator output, which serves as its input and so on. Thus, a chain of laser channels can be built that is combined in a single gas loop. The gasdynamic and thermophysical characteristics of the laser channel, their relationship with laser parameters, and also the optimal operation modes for this channel in the case of transverse gas flow are examined in detail in Chap. 9.

The RL core should contain a sizable (~1,000) number of laser cells. Due to design, manufacturing, and operational considerations, this system is conveniently implemented in sections consisting of functionally complete modules.

A possible schematic for the RL is given in Fig. 10.4. The device does not have a special enclosure. This function is fulfilled by the reactor matrix together with a hard support layer made of a solid neutron moderator (4) and biological shielding

(5) . The reactor matrix may be produced with graphite blocks and zirconium tubes containing nuclear reactivity regulators (2) of the reactor (boron carbide rods) and devices for monitoring nuclear-physical parameters (3). The matrix contains replaceable laser modules (1) forming, in total, the RL core.

A variety of concepts for combining an NPL and fission reactor into a compact efficient NPL system have been considered [6, 10, 70—74]. For example, as previ­ously mentioned, work at the University of Missouri involved an aerosol reactor concept called Aerosol Reactor Energy Conversion System (ARECS) proposed as a nuclear-driven flash lamp [75—77]. The ARECS concept is potentially attractive for several applications, including photolytic lasers, photochemical production, and photoelectric or photo-electrochemical generation of electricity. These processes can be achieved at both high efficiency and high temperature. Consequently, this approach could serve as a topping cycle for an integrated reactor energy conversion system.

The pulsed nuclear reactors listed in Table 2.1 were used outside of the USSR to search for and to study the characteristics of NPL active media. The bulk of the studies were done in the United States, at the Sandia Laboratory (reactors SPR-II, SPR-III) and the University of Illinois (TRIGA reactor).

Fig. 2.20 Schematic view of the SPR-II reactor [2]:

(1) support column for upper half of reactor core,

(2) upper half of reactor core, (3) flange of protective tube in cavity, (4) shielding enclosure, (5) axial cavity for irradiation, (6) lower half of reactor core

A report concerning the first successful experiment outside of the USSR in a pulsed reactor to pump a laser with nuclear radiation appeared in 1975: a molecular CO-laser (к = 5.1-5.6 qm) was pumped by uranium fission fragments in experiments using SPR-II reactor [18, 60]. Figures 2.20 and 2.21 show a diagram of the fast neutron-pulsed reactor SPR-II [2] and the scheme of experiments on this reactor with a CO-laser [60]. The cylindrical reactor core consists of six annular discs and four rods made of uranium alloy (93 % enriched 235U) with molybdenum (10 %). The external diameter and height of the reactor core are 20.3 cm and 20.8 cm, respec­tively, and the total mass of the uranium-molybdenum alloy is 105 kg. Detailed characteristics of the SPR-II reactor can be found in monograph [2].

The laser cell was placed at a distance of around 20 cm from the reactor core. The neutron flux density at the reactor pulse maximum was 1 x 1017 cm~2 x s_1. Excitation of the CO at a pressure of 0.13 atm was carried out with uranium fission fragments emerging from the cylindrical 235U3O8 layer. The specific power depo­sition was around 200 W/cm3. A specific feature of these experiments was the necessity of cooling the carbon monoxide to a temperature of 77 K. The laser radiation receivers (calorimeter and Ge:Au photoresistor) were disposed beyond the biological shielding at a distance of around 15 m from the laser cell. In subsequent experiments with the SPR-II reactor with CO laser, a laser cell with a multipass cavity was used (see Fig. 2.2a).

Significantly more experiments with various NPLs were carried out at the Sandia Laboratories with the SPR-III pulsed reactor, which was put into operation in 1975

Fig. 2.21 Diagram of experiments to pump a CO-laser with uranium fission fragments [60]:

(1) SPR-II reactor core,

(2) output coupler, (3) CaF2 window at Brewster angle,

(4) aluminum tube,

(5) 235U3O8 layer,

(6) polyethylene neutron moderator, (7) 100 % reflectivity mirror,

(8) Dewar flask with liquid nitrogen, (9) region with vacuum, (10) laser radiation receivers

[2]. The reactor has a cavity 17 cm in diameter and 35-cm long that passes through the reactor core; it can be used to irradiate quite large objects. For example, this cavity accommodated a cell enclosed with polyethylene, which could be used to experimentally measure the gain in the mixture 3He-Xe-NF3 (X = 351 nm) [20]. Under such conditions, it was possible to obtain a specific power deposition of around 5 kW/cm3, the maximum possible using pulsed reactors.

In most of the experiments with the SPR-III reactor, the laser cell was positioned close to the surface of the reactor core (see studies [19, 61]). Most often a rectangular laser cell of 60 x 7 x 1 cm3 was used, placed inside a polyethylene neutron moderator (Fig. 2.22). The cell walls were coated with a layer of 235UO2 that was 3-^m thick. To register the shape of the thermal neutron pulse, a 1-m long cobalt-based neutron detector was placed inside the moderator. The distribution of the fluence of the thermal neutrons (specific energy deposition) along the 60-cm length of the cavity is non-uniform. At the ends of the moderator (30 cm from the center), the fluence of the thermal neutrons is around 25 % of the maximal value in the central part.

To study NPLs operating on the transitions of rare gas atoms, which can operate at lower specific power depositions of <100 W/cm3, the pulse duration of the SPR-III reactor was increased to several milliseconds. For this purpose, a “pulse

extender”—several grams of 235U—was placed in a cavity inside the reactor core in a polyethylene moderator with a wall thickness of a few centimeters. This device increased the effective lifetime of the neutrons in the reactor core, resulting in a threefold increase in the pulse duration [19].

To study the NPL characteristics, as a rule the experimental configurations shown in Fig. 2.23 were used [62]. Using these configurations, NPLs were studied

Fig. 2.24 Configuration of laser experiments on the TRIGA reactor [2, 30, 45]: (1 and 5) instruments registering the characteristics of the laser radiation, (2) system for supplying laser cells with the gases being studied,

(3) protective plug,

(4) thermal column (arrangement for withdrawal the beam of thermal neutrons),

(6) experimental chamber, (7 and 9) cavity mirrors,

(8) laser cell, (10) neutron detector, (11) reactor core, (12) graphite neutron reflector, (13) concrete shielding

at the transitions of atoms Ne (X = 585.3, 703.2, 724.5 nm), Ar (X = 1.27, 1.79 ^m), and Xe (X = 1.73, 2.03 |im).

The laser pulse energies were measured with calorimeters, while the shape was measured using silicon or InAs photodiodes. The energy deposition to the gas medium was determined from the jump in pressure, measured using a piezoelectric pressure sensor. To transport the laser radiation to and from the cell over a distance of around 20 m, lightguides—tubes with a diameter of 2.54 cm with a gold reflective coating—were used. Luminescent radiation emerging through the side surface of the cell was withdrawn beyond the biological shielding using a quartz optical fiber and was registered using a photodiode or a multichannel spectrometer with a registration range of 450-750 nm. Auxiliary lasers—a tunable F-center laser excited by radiation from a solid-state YAG:Nd3+ laser or a gas discharge laser— were used to measure the gain of the NPL.

TRIGA reactors are thermal neutron pool-type reactors, whose cores are made of the triple alloy UZrHx. These reactors are the most common of the research pulsed reactors—the number of their modification in the world in 1987 was 53 [2].

One of the reactors of the TRIGA family, namely the TRIGA Mark II, was used for many years to study NPL problems at the University of Illinois [29, 30]. The characteristic parameters of TRIGA pulsed reactors are: total number of fissions in the reactor core ~1 x 1018 fissions (~30 MJ), half-height pulse width ~10 ms, neutron fluence at the reactor center (0.5-1.0) x 1015 cm-2 [2]. The reactor can operate in stationary mode at a power of up to 1.5 MW with a thermal neutron flux density of 3 x 1012 cm-2 x s-1 [42].

The configuration of experiments on the TRIGA reactor is shown in Fig. 2.24. The typical length of the laser cell is 70-100 cm. The gas mixtures He-CO(CO2)

(X = 1.45 urn), Ne-N2 (X = 862.9; 939.3 nm), Ar-Xe (X = 1.73 |im), and 3He-Ne-H2 (X = 585.3 nm) were pumped by the nuclear reaction products 10B(n, a)7Li or 3He(n, p)3H. Various types of instruments were used to register the laser radiation (photomultipliers, photoresistors, monochromators, and power meters).

Apart from the studies of NPLs with direct pumping of active media by nuclear radiation, the TRIGA reactor was used to pump a photodissociation iodine laser (X = 1.31 um) with radiation of excimer molecules XeBr*, which are formed upon irradiation of the mixture Xe-CHBr3-3He by the neutron flux [29].

Lasers on Infra-Red (IR) transitions of Xe, Kr, and Ar atoms have the highest energy parameters among the NPLs (see Chap. 3, Sect. 3.1). Apart from high efficiency (n < 2-3 %), the chief merits of these lasers are the low laser thresholds, the full restoration of the medium after radiative influence, and the possibility of obtaining lasing over a wide range of the spectrum (1-3.5 ^m). The record holder in terms of advantages is the laser operating on transitions 5d-6p of the Xe atom (A = 1.73, 2.03, and 2.65 ^m).

From the survey of results of experimental investigations provided in Sect. 3.1 of Chap. 3, one can draw the following conclusions:

1. All the most intensive laser lines belong to the transitions nd-(n + 1)p of atoms Xe, Kr, and Ar (n = 5, 4, and 3 for Xe, Kr, and Ar, respectively). Analogous results in laser spectrums are also obtained with electron beam excitation.

2. Maximal energy parameters were registered for an Xe laser at the 1.73, 2.03, and 2.65 qm lines, which start from the common upper laser level 5d[3/2]10 ; these lines are the most powerful when using various buffer gases (He, Ar, or He-Ar and Ne-Ar mixtures).

3. For lasers operating on transitions of the Xe, Kr, and Ar atoms excited by nuclear radiation and electron beams, one observes a qualitative similarity of experi­mental dependencies of energy parameters on the mixtures’ pressure and composition.

4. For the most intensive laser lines at excitation by nuclear radiation and electron beams, efficiencies were obtained that are close to ultimate values, which testify to the high populating selectivity of the upper nd levels.

Considering these circumstances, as well as the similar structure of energy levels of the Xe, Kr, and Ar atoms (Fig. 3.1), one can conclude that the basic processes of populating nd levels are similar or even identical, so that NPLs operating on IR transitions of Xe, Kr, and Ar atoms should be viewed as one family.

The characteristics of IR NPLs operating on transitions of rare gas atoms were investigated in detail for roughly 40 years in a wide range of experimental condi­tions (see Chap. 3, Sect. 3.1), and a large number of studies [19—39] were dedicated to their theoretical modeling. The processes leading to depopulating of the lower laser (n +1) p levels can be considered well established: collisional quenching during collisions with atoms of the active medium and electrons (at high specific power depositions). However, to date the discussion on the mechanisms for popu­lating the upper laser levels is not yet concluded. The variety of proposed mecha­nisms for populating nd levels (see Table 5.3) is explained by difficulties in registering and researching radiation in the IR range of the spectrum, uncertainties in the rate constants of many plasmochemical reactions, and by significant differ­ences in the experimental conditions in which these lasers were studied.

Laser output intensity is linked to the size of the working gas’s active region that takes part in lasing: reducing the size of the passive zone in a gas mixture can increase laser emission intensity.

The typical temperature equalization time in a gas mixture with a transverse dimension of r1 is

tt ~ rja. (8.33)

If a laser cell is irradiated by a time-varying neutron flux, the typical rise time of which is t < tt, it can then be anticipated that a similar procedure would make it possible to slow passive zone development. The time dependence of this type that is the simplest one actually feasible, and that is the most convenient for numerical and theoretical investigations, consists of an exponentially rising neutron flux density

Ф() = Ф0^=т. (8.34)

The capabilities of this method were investigated based on the example of a helium-filled cylindrical cell with an internal radius of r1 = 1 cm and a wall thickness of Sw = 1 mm (the wall material during the calculations was zirconium). During all the calculations, it was assumed that Ф0 = 1013 cm-2 s-1. The reduced transverse dimension values of the cell’s metallic uranium layer and the tube were selected as D1 = 0.5 и D0 = 0.5 (which corresponds to 5U = 2.775 x 10~4 cm and P0 = 2.88 atm) at an initial temperature of T0 = 300 K. The calculated temperature profiles in the laser cell for several successive moments in time at a power deposition rise time of t = 10 ms are represented by the solid lines in Fig. 8.13. The passive zone involves the region between the cylindrical surface, r = rA, on which the maximum temperature is reached and the cell’s inner surface, r = r1.

The dependences of the radial coordinate of the active region’s outer boundary, rA, upon the thermal neutron flux rise time, t, and fluence, ф, which equals the

Fig. 8.14 Dependence of the radial coordinate of an active region’s outer boundary upon the thermal neutron flux rise time, t, and its fluence, ф, at D0 = 0.5: Curves 1-6 correspond to the values ф = (0.5, 1, 2,

3, 4, and 5) x 1013 cm~2 integral of expression (8.34), that were obtained as a result of calculations are shown in Fig. 8.14. Here, by way of comparison, it seems appropriate to recall that the fluence in the center of the laser cell during experiments performed on a VIR-2 M reactor reached 1.4 x 1013 cm~2 [2, 5—7,14]. For the sake of convenience in comparing the results obtained, the relationship between the pumping power rise time, t, thermal neutron fluence, ф, and the moment in time, t, by which this fluence is reached is reflected in the time scales in Table 8.4.

The results obtained make it possible to reach a conclusion: in order for at least half of the gas mixture volume in a cell with the parameters selected (which correspond to rA « 0.7 cm) to be an active region, the neutron flux rise time must be no higher than t = 7.5 ms. Here, the time that an active region with this volume exists does not exceed 0.1 s.

There is no information in the literature about semiconductor lasers excited by nuclear radiation although the possibility for pumping them, for example, with reactor y-ray radiation, is discussed in article [35]. To pump semiconductor lasers,

electron beams are another type of ionizing radiation that is widely used. Numerous studies in this area have produced semiconductor lasers based on CdS, InSb, InAs, GaAs, etc. that radiate within a broad spectral range, 0.33-30 qm, and have very different operation modes: continuous-wave mode with excitation by a focused electron beam, a picosecond pulsed mode with a repetition frequency in the several tens of gigahertz, and a pulse-periodic mode with an average power in the tens of watts and intrinsic efficiency of ~10 % [36].

In addition to electron beams, semiconductor lasers were pumped using the bremsstrahlung of pulsed electron accelerators. In experiment [37], by pumping monocrystal CdS (A«500 nm) with the bremsstrahlung of a pulsed electron accelerator, 5 kW lasing was achieved with a pulse duration of about 20 ns.

CO Laser

A molecular CO laser was the first laser to be pumped with nuclear radiation in experiments outside Russia with a pulsed reactor [143]. As with gas-discharge CO lasers, lasing was observed on vibrational-rotational transitions of the CO molecule with X = 5.1-5.6 qm. The pumping of carbon monoxide at a pressure of 0.13 atm and temperature of a 77 K was carried out using uranium fission fragments. The neutron source was an SPR-II pulsed reactor (see Chap. 2, Sect. 2.7). The output laser power was 2-6 W; the efficiency, determined in [143] with respect to the energy deposition to the volume of the principal mode, was 0.1-0.3 %. The small — signal gain at transitions 10-9, 9-8, and 7-6 of the CO molecule reached 5 x 10-3 cm-1 [144]. Study [51] reports that later on, the authors of [143, 144] obtained output power of around 100 W for CO NPLs using a multiple-path cavity with a 120-cm active length (see Fig. 2.2a).

Lasing at X ~ 5 qm of the CO molecule was also obtained in study [145] on exciting the mixture 3He-CO with nuclear reaction products 3He(n, p)3H. The output power at a mixture pressure of 3 atm was >200 W from an active volume of 300 cm3. The laser threshold was reached at ФгА = 3 x 1016 cm-2 s-1.

In Chap. 2 we examined rather simple NPL designs for searching for and studying characteristics of laser active media, but there are also more complex nuclear laser devices. As a rule, they are structural elements of multichannel reactor lasers operating in stationary or pulsed modes, and are intended to study the specifics of their operation. This chapter examines some of these devices, whether in operation or still being designed.