In the y = const planes, gas density, and accordingly, the refractive index in the bulk of a flowing laser’s gas volume decrease in an almost linear manner with an increase in x; only within the fairly short channel inlet and outlet parts near to edge of a uranium layer and further outside its confines the gas density not dependent upon the x coordinate. The latter results from a noticeable decrease in power deposition in direct proximity to the edges of the uranium layers and outside their confines. In any x = const plane, refractive index distribution (with the excep­tion of a near-wall passive zone) is satisfactorily described by a negative parabola. The parabola’s curvature increases in a linear manner with the x distance value. It reaches a maximum value near the edge of a uranium layer, x = b, and subsequently remains unchanged.

A conventional two-mirror cavity was used in the LM-4 apparatus [26, 41] that consisted of planar and spherical (with a radius of curvature of 20 m) mirrors. However, the two-dimensional stable-unstable cavity proposed in refs. [22, 24] is more convenient for a similar NPL with gas pumping. It should be unstable in the longitudinal direction in the y = const planes and stable in the transverse direction in the x = const planes. The latter can be achieved, for example, using mirrors with a predetermined radius of curvature in these planes.

The distinctive features noted above for gas density distribution in gas flowing NPLs do not make it possible to obtain a solution to the equation describing a light beam propagation that is suitable for studying cavity stability using the ray matrix technique in a channel’s entire volume, as was done for a sealed NPL in refs. [56, 57]. However, an obviously simplified approach can be used to derive stationary mode criterion for estimating the permissible gas heating from an analysis of stability in the x = const plane. So, the infringement of the stability condition in the space immediately past the right edge of a uranium layer is examined in ref. [58] (the gas is pumped in the direction of the x axis). In this region, the refractive index distribution has a parabolic shape

n(y) = no0) — 2«(b)y2, (9.rn)

where the parabola coefficient, a, is maximal and equals the value reached in direct proximity to the edge of the uranium layer. This coefficient increases with an increase in the power deposition in the gas, and accordingly, its overheating. If it exceeds the value at which the cavity becomes unstable in the x = const plane in the x > b region, it is then natural to assume that the instability in the transverse direction relative to x will be shifted into the x < b region with a further increase in the power deposition.

As previously demonstrated, with the exception of the thin near-wall passive zone layers, heat exchange in the bulk of the gas volume can be ignored. Because the pressure in the channel is almost homogeneous, density and temperature distribution is determined by the distribution of specific fission fragment power deposition. The fission fragment energy losses per unit path are proportional to the medium’s density [59]. We will ignore the edge effects, which have a compara­tively minor influence on integral energy deposition in the gas as it passes through the channel when the dimension of the uranium layers is sufficient. Therefore, along each flow line that a particular gas particle traverses, the power deposition per unit mass of gas, f, can be roughly regarded as constant. This approach is equivalent to the one used in refs. [57, 60] to represent the distribution of specific power deposition in the form F(r) = F0(r)p(r)/p0, where F0(r) is the specific power depo­sition at a point, r, in the presence of a homogeneous unperturbed gas density distribution, p0. For an infinitely expanded planar geometry that is characterized by dependence upon a single y coordinate alone, this equality is strict due to the absence of edge effects [61].

For the gas velocities at which inequality (9.97) holds true, the temperature increment of a particular gas particle of unit mass after it has traversed a distance of x, according to the approximations used, equals

Because the gas pressure differential in the channel is small, (ДP/P) << 1, then pursuant to the ideal gas state equation, p(x, y) = T0p0/T(x, y). Thus,

The surface power density of the fission fragments from the uranium layers into the gas can be expressed by way of the specific power deposition of the gas averaged over the transverse cross-section, qs = pfd. Thus, condition (9.97), in the presence of which correlation (9.98), used to derive Eq. (9.152), holds true, is equivalent to the condition (fxCpU0T0) << 1. Therefore, expanding (9.152) into a series and selecting the first-order terms, we obtain

With a plane-parallel uranium layer arrangement, the specific power deposition in a unit mass of gas in the coordinate system shown in Fig. 9.1, ignoring the edge effects, is determined by the equations [61]

1 R

f (y) = — E0qR-I(Y); P0 R0

— G 20 + Y + D1 , (9.154)

where Y = y/R0; R0, R1 are the average range of a fission fragment in the gas and in the uranium layer material, respectively; D0 = d/R0 is the normalized gas channel width; and D1 = 8R1 is the normalized uranium layer thickness, while the G function is determined by the correlation

G(£)= 2(1 — + 2^ln^). (9.155)

Following the appropriate transformations and the expansion of the addends containing the logarithms into a series for the small parameter 2YD0, with an accuracy up to terms of the second-order of smallness for central regions located near the channel’s plane of symmetry, we obtain

where

From the heat balance condition in the stationary circulation mode

X

0

in the approximation qS(x) = const for overheating averaged throughout the chan­nel’s cross-section, we get

ДT = T(b) — T0 = qsb. (9.157)

cpp0du0

We will express the surface power density of the fission fragments from the uranium layers into the gas, qS, in terms of the total energy of the uranium nuclear fission fragments, E0, the intensity of uranium fissions per unit volume, q, uranium layer thickness, £u, and energy deposition efficiency, є (the share of fission frag­ment energy transmitted to the gas):

qs = 2E0qSu£. (9.158)

Determining the refractive index based on its unperturbed value at the inlet, n00,

n(x, y) = 1 + (П00 — 1)p(X;y),

P0

then from Eqs. (9.153), (9.154), and (9.156) with allowance for the relationship of Eqs. (9.157) and (9.158) between q and ДT at x = b, we obtain Eq. (9.151), in which

The dimensionless у parameter determined by formula (8.40) was introduced in ref. [56] (see Chap. 8.5). Under a given spatial distribution of specific sources, it increases with an increase in energy deposition. The value of this parameter at which the infringement of the stability condition m < 1 begins is called the critical value. The ycr parameter reaches its highest values in the case of a cavity made up of

planar mirrors (with radii of curvature of r1 = r2 = 1), as well as a cavity with codirectional mirrors of identical curvature (r1 = —r2). In the case of other mirror curvature combinations, the ycr value does not exceed 1.5. The dependence of ycr upon the relative length of the clearance between a mirror and the active volume boundary, L1/La, calculated using the technique described in ref. [56], is presented in Fig. 9.31 for several radius of curvature values, r1, of one of the mirrors. It was assumed that L1 = L2, while the radius of curvature of the second mirror was Г 2 = 1.

If it is assumed that the stability condition should not be infringed in the x = const planes within the gas regions of x > b, where energy deposition reaches the maximum value, then from the requirement у < ycr, as well as Eqs. (8.40) and (9.159), we obtain

__ < n0(D0 + 2Р1)^0еГ0yKp < 4(n00 — 1)LA

During medium overheating, _T < 104 K (n0 — 1) << 1; therefore, in Eq. (9.160), n0 can be replaced with unity. Thus, according to the criterion under consideration, permissible gas overheating through values of D0, D1, R0, e, and La is determined by gas mixture density, the geometric dimensions of the active gas volume, and uranium layer thickness, while through ycr, it is determined by resonator mirror curvature and the distances from the mirrors to the active volume.

The L1 and L2 distance values are selected in such a way that the uranium nuclear fission fragments do not reach the cavity mirrors. In actual designs, they usually

come to L1 = L2 « 10 cm; thus, at LA ~ 1 m, it can be roughly assumed for estimates that ycr < 1.5. For the laser channel of the LM-4 apparatus (d = 2 cm, 5U = 2.7 x 10~4 cm, and LA = 1 m) during the pumping of a gas mixture, the basic component of which is helium (P0 = 2 atm) at T0 = 300 K, an estimate using formula (9.160) yields AT < 1,900 K, while for an argon-based mixture at P0 = 0.5 atm and T0 = 300 K, AT < 860 K. According to Eq. (9.160), a twofold increase in active length, LA, while the other parameters remain unchanged, as exemplified by an argon-based mixture, will result in the stability limitation becoming more rigorous (AT < 230 K.)

Initial studies of nuclear pumping concentrated on molecular gas lasers such as CO2 because early theoretical predictions indicated lasing with low pump (neutron flux) thresholds of ~1010 n/cm2 s [6, 7]. Indeed, experiments at the University of Illinois initiated during this period showed an enhanced output from an electrically excited CO2 laser with nuclear pumping superimposed [11]. Experiments at the Sandia National Laboratories also demonstrated reactor-ionized electrical excitation of the CO2 laser [6]. However, it was later found that lasing in CO2 was prevented by dissociation of the molecule during irradiation. Thus, other NPLs were sought.

In their search for a NPL, Sandia workers led by David McArthur obtained, in early 1974, a small-signal gain and lasing in CO gas cooled to 77 °K [7]. This provided the first clear observation of lasing in the United States with pure fission — fragment excitation. Preliminary systems studies were then performed to study NPL scaling to large sizes and large powers with a source configuration that retained existing pulsed reactor technology [8, 18]. An early attempt at scaling of the cooled CO laser used a “folded path laser” apparatus, which lased at a power ~100 W.

Lasing was subsequently observed in rare gas mixtures and in CO gas mixtures at room temperature.

Shortly thereafter, a University of Florida team lead by Richard Schneider obtained pumping in a noble gas laser (He-Xe at 3.51 qm) in collaborative experi­ments at the Los Alamos Scientific Laboratory [19]. Subsequently, much was learned about the physics of nuclear pumping of noble gas NPLs through a series of studies by the NASA-Langley Research Center group led by Frank Hohl and Russell Deyoung (supported via Karl Heinz Thom in NASA headquarters). This work involved lasers with wavelengths generally in the near infrared. The NASA studies used a fast-burst reactor at the Army Aberdeen Test Laboratory and the 3He (n, p)3H reaction for pumping. Specifically, lasing was achieved in 3He-Ar (1.27, 1.79 qm), 3He-Xe (2.026 qm), 3He-Kr (2.19, 2.52 qm), and 3He-Cl (1.58 qm) using thermal neutron pulses of 200 ps full width and approximately 1016 n/cm2 s [20]. These systems lased on atomic transitions where inversion occurred by collisional radiative recombination of the noble gas atomic ions. A record peak laser power of 3.7 W was achieved from a relatively small 3He-Ar (1 % Ar) (1.79 qm) NPL at a total pressure of 4 atm. However, further increases in laser power were prevented by the small fraction of neutrons interacting with either 3He or coated walls in the cell. Thus, a new laser geometry was devised to intercept more of the reactor neutrons. The laser volume was expanded to 40 x 30 x 3 cm by use of internal mirrors to create a “zigzag” type optical path through the excited 3He-Ar media as shown in Fig. 13.1.

Aiianrenl user

GoWo’ Aluminum
Plane Mirror

Neutral Density Filler

brevister ^ngle Window

Dielectric Output Mirror

-A) Array Detector

Fig. 13.1 Nuclear pumped multiple pass box laser [21]

An output of 1.1 kW was achieved with a 3He-Ar mixture at 2,300 Torr total pressure (0.74 % Ar) at 4.3 x 1016 thermal n/cm2 s [21]. This system demonstrated the ability to scale the NPL power with increased laser gas volume. During this period, much progress was made in the theoretical interpretation of the pumping mechanism with stress on the secondary electron energy distributions created by the nuclear reaction products. Studies at the University of Illinois [22—24] employed both Monte Carlo and analytic solutions for a variety of gases, including the possible superposition of a weak electric field. This work is discussed in more detail in the theory section later in this chapter. Intensive numerical studies were also done at North Carolina State University [25]. These results defined the source term for reaction rate calculations. Next, attention turned to kinetic calculations for both noble gases [20] and excimers [26].

Another important pumping reaction considered at NASA Langley is the 235UF6(n, ff)FF reaction, yielding 160 MeV of kinetic energy via the two highly charged fission fragments (FF5). The importance of this reaction is the possibility of using a gaseous core reactor to combine the reactor and laser as one integral system. With this in mind, experiments were done in the U. S. Army Aberdeen Test Center Fast Burst Reactor to excite a mixture of 235UF6-Ar-Xe (600 Torr). This produced lasing at 2.65 qm in Xe [27]. UF6 gas is an effective laser quencher; thus, only small amounts could be added. A uranium coating, deposited from the UF6 condensing on the internal laser cavity wall also produced fission fragments that excited the gas. Some results from this experiment are shown in Fig. 13.2.

With 3 Torr of UF6 in Ar-Xe, 38 % of the energy deposited came from gaseous UF6 and the remainder from the a 235U coating formed on the cavity wall by UF6

decomposition. In summary, both 3He and 235UF6 have been effective for pumping noble gas lasers. This coating reaction does not scale with volume as desired. Hence, if an ultra-compact fission core laser is desired, additional research is needed to find efficient systems for using UF6 to achieve volumetric reactions.

One alternate approach that could avoid the quenching limits on the UF6 concentration uses an aerosol of fissile microspheres in a fluorescer gas, making it an attractive approach to a higher-power nuclear-pumped flashlamp [28]. Thus work at the University of Missouri addressed an aerosol reactor concept called Aerosol Reactor Energy Conversion System (ARECS), illustrated in Fig. 13.3. The key component is a nuclear-driven flashlamp. Flashlamps do not require a long photon mean free path as do lasers. Thus, a media with relatively poor optical transport properties can be used to provide “pump” photons for lasers.

The ARECS fuel consists of fissile microspheres mixed with a fluorescer gas as an aerosol. The transport efficiency of the radiation from the nuclear fuel to the fluorescer medium strongly depends on the micropellet size distribution and the uniformity of pellet density. For example, as the radius of the micropellets increases, the transport efficiency decreases. While there have not been any experi­mental observations of a fissioning aerosol at high temperatures and flow, some key points are clear. A relatively high particle density with sizes averaging 2-10 qm in radius at temperatures of around 1,000 °K is required. Other experience with aerosols suggests that these conditions are achievable.

The fluorescer medium must channel the energy absorbed from the nuclear radiation to an excited state (versus gas heating). Irradiation of rare gas and rare gas halide mixtures can efficiently generate excimer fluorescence at relatively short wavelengths; thus, these gases are prime candidates for the fluorescer.

Several options are possible for coupling the light out of the fluorescer. One is to cause lasing directly in it. The other is to transport the light out via a “non­concentrating” cell geometry such as in Fig. 13.3 (light concentrating geometries are also possible). The coupling efficiency of a non-concentrating geometry can range from 30 to 80 % (the more complicated concentrating geometry could achieve even higher efficiencies).

The ARECS concept is potentially attractive for several applications including: photolytic lasers, photo-chemical production, and photoelectric or photo­
electrochemical generation of electricity. These processes can be achieved at both high efficiency and high temperature. Consequently, they can serve as topping cycles for an even more efficient, integrated energy conversion system. To illustrate the potential performance, Boody and Prelas considered a photolytic laser system [29]. Such lasers are relatively efficient energy conversion systems, primarily due to resonance transitions. Boody and Prelas estimated an overall system efficiency of 0.03 using a photolytically pumped XeF* laser. This result compares well with other high power laser alternatives which have predicted system efficiencies in the 0.005-0.05 range.

The first successful experiment to pump lasers with nuclear radiation occurred on May 12, 1972 at VNIIEF using a He-Xe mixture, but VNIIEF researchers were not able to publish their first article about NPLs until 1979 [5]. This article contained the results of later experiments, while information about first experiments was briefly presented later in a survey paper [7].

In the first series of experiments, the pulsed water reactor VIR-2 [2, 33], which was used for research from 1971 through 1978, was used as the neutron source. In 1979, the modified reactor VIR-2 M [2, 33], with a strengthened reactor core and minor changes in the parameters of the reactor pulse, was placed in operation. A solution of uranium salt (UO2SO4) in ordinary water served as the fuel in these reactors.

The arrangement of the VIR-2 and VIR-2 M reactors in the building is shown in Fig. 2.5. The reactor is located in the two-hall building having a concrete wall thickness of 2-6 m. The reactor core vessel (height 2 m; diameter roughly 0.7 m; wall thickness 65 mm) was enclosed in a concrete block measuring 4 x 4 x 3.5 m, which was the biological shielding. The bottom of the vessel is at the level of the lower hall’s ceiling, and can be closed by a protective shutter. The following experimental channels are used to locate the following exposed objects:

(a) A central channel with an internal diameter of 142 mm.

(b) A hemispherical cavity with an internal diameter of 300 mm.

(c) Side channels with a diameter of 100 mm abutting the side surface of the reactor core vessel.

(d) A cavity close to the surface of the reactor core with a cross-section of 560 x 620 mm2.

(e) A lower reactor hall with a height of 2.5 m.

Figure 2.6 shows a diagram of the first experiments. The vertically arranged laser cell was irradiated in the side channel of the VIR-2 reactor. The average fluence of the thermal neutrons along the length of the cell was 1.3 x 1013 cm~2 with a reactor pulse duration of around 4 ms.

An aluminum tube was placed inside the cylindrical body of the cell with an internal diameter of 27 mm and a length of 100 cm. A layer of 235U3O8 was deposited on the tube’s surface with a thickness equivalent to around 2-3 mg/cm2

of metallic 235U. To increase the flux of the thermal neutrons, the cell was enclosed by a polyethylene moderator with a wall thickness of 30 mm. The laser cavity was formed by mirrors with a silver coating: a spherical 100 % reflectivity mirror with a radius of curvature of 10 m and a flat output coupler on quartz or BaF2 substrate.

Fig. 2.7 Oscillogram of a reactor pulse (upper trace) and laser radiation pulse (lower trace) for He-Xe mixture at a pressure of

1 atm. Division value is

2 ms

The laser radiation is extracted from the cell through a coupling hole with a diameter of 1-2 mm in the flat mirror. The distance between the mirrors is 120 cm.

The measurement devices were kept away from the irradiation zone at a distance of around 10 m from the laser cell. In the searching experiments, a FEU-28 photomultiplier was used to register radiation in the range of 400-1,100 nm, while a liquid nitrogen-cooled Ge:Au photoresistor was used to register IR radiation (2-11 qm). After detection of laser radiation, an IEK-1 calorimeter was used to measure the energy of the laser pulse.

Initially, the active medium used was a He-Xe mixture (10:1) at pressures of 0.08-1 atm. An oscillogram of one of the first experiments at a mixture pressure of 1 atm is shown in Fig. 2.7. The laser wavelength, determined approximately using light filters was ~3 qm. The power of the laser radiation in the mode optimal for pressure and composition was 25 W with an efficiency of ql ~ 0.5 % with respect to the energy absorbed in the mixture.

In the next series of experiments on the pulse reactor TIBR-1 M (1974-1976), uranium layers more resistant to mechanical loads were used, and the laser cell was arranged horizontally, which made it possible to eliminate the uranium-dust con­tamination of the lower spherical mirror that had been observed in prior experiments.

The core of the TIBR-1 M reactor includes a ZrH19 moderator layer, which in comparison with other fast neutron reactors, leads to a reduction in dynamic loads on the fuel elements of the reactor core and to an increase in the duration of the reactor pulse to ~500 qs [2]. The diameter of the uranium-molybdenum alloy reactor core is around 30 cm.

The cylindrical laser cell, enclosed by a polyethylene moderator with a layer of 235U3O8 around 9 mg/cm2 thick deposited to the internal surface, was arranged close to the surface of the reactor core (see Fig. 2.8). In order to reduce the effect of thermal neutrons emerging from the moderator, on the reactor core the laser cell was surrounded by screens made of cadmium and boron carbide.

A diagram of the experiment is shown in Fig. 2.9. The measuring equipment (except for the IEK-1 calorimeter) was placed on the other side of the biological shielding in a neighboring room. To register the laser radiation, along with the IEK-1 calorimeter, Ge:Au photoresistors and DKPs surface-barrier silicon diodes were used [49]. The length of the uranium layer in the cell was 57 cm, with a diameter of 2.7 cm. The cell was irradiated with a pulsed flux of thermal neutrons with a half-height pulse duration of around 0.8 ms and an average fluence along the length of the uranium layer of 4.2 x 1013 cm~2, which made it possible at a helium pressure of 2 atm to obtain a specific power deposition at the pulse maximum of q = 600 W/cm3. In the experiments, binary mixtures of rare gases were studied: He-Ne (Ar, Kr, Xe), Ne-Ar(Kr, Xe), Ar-Kr(Xe), and Kr-Xe. The total pressure of the mixtures was equal to one atmosphere, and the partial ratio of components ranged from 200:1 to 200:30. Lasing was obtained with use of the mixtures He-Ar(Kr, Xe) and Ar-Kr(Xe) in a range of 2-10 ^m, and the mixtures He-Ar and Kr-Xe in a range of 0.2-1.2 ^m (see Fig. 2.10).

In this series of experiments [5, 50], the most intensive laser transitions were found for ArI (X = 1,15; 2.40 ^m), KrI (X = 2.52 ^m), XeI (X = 2.6 ^m), and thus the existence of the family of NPLs operating on IR transitions of atoms of rare gases was obtained. For the NPLs that were studied in greatest detail, based on mixtures He-Xe (X = 2.6 ^m) and He-Ar (X = 1.15 ^m), laser powers of 2,000 W and 250 W were found for Ці = 0.8 and 0.1 %, respectively.

Interest in the study of luminescence characteristics of mixtures of rare gases with molecular gases is related primarily to the search for new lasing transmissions for NPLs and to the study of the influence of molecular impurities on the parameters of known NPLs. The most significant studies in this area are shown in Table 4.13.

In studies [92, 93], apart from the luminescence spectra of mixtures (Ar)-N2, the time dependencies of luminescence and populating efficiencies of the states N2(C3nu), N2+(B2Xm+) were also determined.

Numerical investigations of the dynamics of the development of inhomogeneities during NPL excitation by pulsed neutron fluxes from a TIBR reactor [21] with a duration (at half the exciting pulse height) of t1/2 = 0.8 ms were among the first performed. During experiments [4] on this reactor, the aluminum cylindrical cell employed had an inside diameter of 2.7 cm and an effective length of 57 cm. A 235U oxide-protoxide layer with a thickness of 9 mg/cm2 was applied to the cell’s inner surface. The cell wall thickness was 2 mm, while the distance between the cavity mirrors equaled 1 m, and the average thermal neutron fluence per pulse over the cell’s effective length was 4.2 x 1013 cm~2. Curve 1 in Fig. 8.1 represents the time dependence of the thermal neutron flux density. Figure 8.2а reflects the results of computerized numerical calculations of the time evolution of the gas density distribution in a cell filled with an He-Xe mixture (a component ratio of 200:1) in the presence of an initial pressure of P0 = 1 atm and an initial temperature of T0 = 300° К [4]. These calculations demonstrate that the spatial distribution of temperature is inversely proportional to density distribution, while the pressure at any given moment in time is virtually uniform throughout the cell’s cross-section. This behavior is expected, because the typical distribution time scale for the perturbation in the cell, тр ~ r1 /us (us is sound velocity in the gas, and r1 is the cell’s inside radius), is significantly shorter than exciting pulse duration.

The results of numerical investigations [22, 23] revealed that the gas volume is divided into two parts. The equation dp(r, t)/dr = 0 defines the rA(t) interface. In the active region, 0 < r < rA(t), the gas density gradient, and consequently the refractive index gradient, are negative. At rA(t) < r < r1 (the passive zone), the gradient is positive and far exceeds the absolute value of the gradient in the active region. A passive zone originates where heat removal to the cell wall plays a leading role,

because the heat capacity per unit volume appreciably exceeds the gas unit volume heat capacity. At I = r1 — rA << r1, the time dependence of this zone’s transverse dimension is well described by the correlation [22, 23]

i ~ fat;

where a represents gas thermal diffusivity. When long-duration pulses are present, the passive zone involves the entire gas volume over a time frame of t ~0.1s.

The results of similar calculations for a gas mixture of the same composition during excitation by a pulse with a duration of t1/2 « 1 s, a fluence of 4 x 1014 cm-2, and a close-to-rectangular shape (see Curve 2, Fig. 8.1) are presented in Fig. 8.2b. The passive zone encompasses the entire gas volume in a few tenths of a millisecond.

Stationary Mode. Under stationary conditions, heat removal through the outer surface of a sealed cell must be arranged. Heat removal of this type can be realized by means of a gaseous or liquid heat-transfer agent washing over the outer surfaces of systems with internal heat release. As is generally known, a liquid heat-transfer agent is more efficient than a gas, so it is preferred.

Unlike the pulsed alternatives described above, a precise analytical solution to the problem of gas temperature and density distribution exists for the stationary mode. Under the conditions being examined, the temperature distribution along the cylindrical cell’s tube wall is defined by the expression

where kw is the thermal conductivity coefficient of the tube material; qw is the thermal flux density at the interface of the tube and the gas filling it; r2 is the radius of the tube’s inner surface that the heat-transfer agent washes over; Tw (r) is the tube wall temperature at a point with a coordinate of r; T, is the temperature of the external heat-transfer agent; and a, is the coefficient of heat transfer from the tube’s outer surface to the heat-transfer agent. We derive equation (8.4) by means of solving a thermal conductivity equation for a geometry with cylindrical symmetry

1 3 ( dTw _ dTw awr dr r dr dt ’

and with boundary and initial conditions of the type

(8.6)

where aw is the thermal diffusivity of the tube material.

System (8.5) and (8.6) describes the temperature space-time distribution in a cylindrical layer, r1 < r < r2, on the outer surface of which, with a coordinate of r = r2, convective heat exchange occurs. On the layer’s inner surface, at r = r1, a thermal flux of qw(t) is specified.

When the aw and kw coefficients are constant, the solution to (8.5) and (8.6) takes the form:

T / (0)exp{awX„ (t — 0) }d0 — Tw0exp{ — awX„t}}.

(8.7)

The eigenvalues of Xn are roots of the equation

kwVK{N1 (v^nr 1)J1 (ffiAnr2) — J1 (v^nr 1)N1 (лДйr2)} = a/jN Xnr^/0 Kr2) — J1 ^nr^N0 ХпГ2 ,

while the eigenfunctions that correspond to them are given by

Фп(г) = N^/k^r^j — *(0^).

Here Jv, Nv are the (first-order) Bessel and v-order Neumann functions. It is not difficult to see that in the stationary case, i. e., at dqw/dt = dT//dt = 0 and t! 1, and the solution to (8.7) takes on the simple form of (8.4).

In the stationary mode, the equation for heat balance in the gas on a surface with a coordinate of r in the presence of problem cylindrical symmetry is written as

where, as before, F is specific power deposition of gas; kg is the thermal conduc­tivity coefficient of the gas, which is very slightly dependent upon density for rare gases [24]. However, its dependence upon temperature is communicated with the same degree of accuracy as during the polynomial representation by the equation [24, 25]

kg(T) = kg0(T/Tk0f. (8.9)

The fragments transfer a portion of the uranium nucleus fission energy released in the uranium layer to the gas, while a portion (1 — e) remains in the layer itself.

Due to this layer’s low thickness (5U~ 1-10 ^m), the layer can simply be regarded as a surface heat source with a surface power density of SU when solving a thermal conductivity problem. In this case, the following boundary conditions must be satisfied at the gas and cell wall interface when r = r1:

Source surface power density equals (see the designations in Chap. 7, Sect. 7.1)

Su = (1 — e)NUOf Ф5цЄ0.

The balance of the energy released in a cylindrical gas volume of unit length and a radius of r1 is written as

Integrating equation (8.8) with allowance for equation (8.9) and using the conditions of (8.10)-(8.12), we obtain

Tw(r) = T, + —- — ^ln — , r1 < r < r2.

1 — Є —,r2 kw r2,

The heat transfer coefficient, a,, can be determined using the formula [26, 27]

Nu = 0,023Re0,8 x Pr04 (8.15)

through a Nusselt number of Nu = — ,de /k,, a Prandtl number of Pr = v, /a,, and a Reynolds number of Re = ude /v,, where de is the equivalent diameter of the heat — transfer agent channel, k, is the thermal conductivity coefficient of the heat-transfer agent, u is its velocity, and v, is the heat-transfer agent’s kinematic viscosity.

Using the expressions obtained, the temperature spatial distribution was calcu­lated in a gas mixture of the same composition as in the previous section at three liquid heat-transfer agent circulation velocities. Water at a temperature of T, = 323 K was selected as the heat-transfer agent. The equivalent diameter of the
heat-transfer agent channel was de = 2 cm. Gas density spatial distributions were determined based on the temperature fields found using a state equation. All the calculations were performed for a thermal neutron flux density of Ф = 4 x 1014 cm-2 s-1. The calculation results (Fig. 8.2c) demonstrate that the density and refractive index gradients are positive in the entire gas volume in the stationary mode.

Evaluation of Optical Characteristics. Reducing of radiation angular divergence and bringing it down to the diffraction limit insofar as possible is one of the most urgent problems in laser physics. Its solution is linked to the problem of the electromagnetic field distribution within a cavity. This field depends on the type of cavity used, the design and type of the laser itself, and the optical quality of the active medium filling the cavity (determined by refractive index spatial distribution, as well as this medium’s gain and absorption factors). In the general case, wave optics techniques should be used to calculate the characteristics of a cavity filled with an active medium. However, the solution of a wave equation is difficult for a wide range of cavity configurations involving an inhomogeneous medium [28, 29]. Still, a number of important characteristics, especially when high Fresnel number values, Nf = a^fkLf (ar is the transverse dimension of the cavity Lf is the distance between its mirrors, and X is the radiation wavelength) are present, can also be determined using ray optics techniques [28—30]. For example, a formula in a paraxial approximation is derived in [31] for estimating the laser beam divergence with an inhomogeneous transverse refractive index distribution of laser medium

& « 2v/2An, (8.16)

Here An is the refractive index variation in the transverse direction within the confines of the lasing zone. This procedure provides quit good agreement with experiments [31, 32].

Moreover, for optical systems that can be represented in the form of a series of mirrors and elements equivalent to thin lenses, or for systems with a quadratic transverse refractive index dependence, and for combinations of these systems (see study [30] for an example), it has been shown that a ray approximation is in full agreement with the results provided by a Gaussian beam wave optics approxima­tion. Gaussian beams play a significant role in laser optics: at Nf >> 1, they quite accurately describe the radiation field of a broad range of lasers with a stable cavity.

An important advantage of ray optics is visualization and the possibility of the comparatively simple qualitative and quantitative interpretations of the results obtained. In a geometric optics approximation, the equation that defines the shape of light rays takes the form [30, 33]:
(8.17)

where n is the refractive index; q is the length of the ray arc from a certain fixed point to a point that is characterized by the radius vector, “r(q); and, q = dr /dq is a unit vector that is tangential to the ray trajectory; it determines the direction of light beam propagation, i. e., it coincides with the normal to the electromagnetic wave front.

Here, it is appropriate to note a peculiarity. Let us assume that ez is the unit vector in the direction of the optical axis, z. For the variation of the scalar product of ez x n q along the light ray, we have

The right-hand part of an equation based on (8.17) can be rewritten in the form of ez • Vn. If Vn is perpendicular to the z axis everywhere, then from the latter equation we get ez x nq = const; i. e., the scalar product of ez x nq remains unchanged along the ray. Hence it follows that

where n0 is the refractive index at the point where the beam enters the gas volume under consideration; &0 is the angle between the z axis and the direction of the incoming ray and & is the angle between the tangent to the beam at this point and the z axis.

Let us suppose that a medium’s refractive index spatial distribution has a cylindrical or planar symmetry, and is only dependent on a coordinate perpendic­ular to the axis (or plane) of symmetry. Assume that in the region where the refractive index gradient is negative, a light ray passes parallel to the axis (or plane) of symmetry at a certain point at a distance of r0 from it, i. e., at this point, cos&0 = 1. In this instance, whatever trajectory a ray traces as a result of the

effect of the refractive index gradient, n ^ r ^, may not be less than n0 = n (r0), since cos& < 1 always, ray distance from the axis (or plane) of symmetry must not exceed Г0.

If the laser beam divergence with a gas density distribution that is only depen­dent upon a single transverse coordinate, as is the case in [31], is estimated as double the value of the maximum angle by which a ray intersecting an active lasing region can be deviated during propagation, formula (8.16) for estimating this divergence then follows from equation (8.18) in the & << 1 and n — 1 << 1 approximations.

In the paraxial approximation, & << 1, equation (8.17) for a cylindrically sym­metric system with a transverse refractive index dependence takes the form [30]:

d2r 1 dn

dz2 n dr

If a parabolic dependence approximates refractive index distribution

OV) ;

which quite accurately communicates the real refractive index distribution in the bulk of an NPL’s gas volume [2, 34—36], then from (8.19) at n — 1 << 1 and in the presence of the boundary conditions

we have [30]

Hence, in particular, it follows that the rays in a cavity formed by planar mirrors and filled with the inhomogeneous medium under consideration oscillate around the optical axis with a period of z0 = 2пД/an1.

Similarly, if the refractive index can be approximated by the dependence

n(r) = n„( 1 + Opr2) ;

in the same approximations from equation (8.19), we have

&0

r = r0ch(v«n2z) + —f=s

an2

In the case of irradiation by a pulse with a duration of t1/2 = 0.8 ms at a moment in time of t = 2.2 ms (Curve 4, Fig. 8.2а) in an active region of r < rA, then according to the well-known dependence n — 1 = pCn (Cn is the constant for a gas
of this type), the gas refractive index distribution can be approximated by a parabola with a coefficient of an1« 2.4 x 10~6 cm~2, which yields z0 ~ 40 m for the ray oscillation period. The displacement of a beam with initial parameters of $o = 0, z = 0, and r0 = 1 cm after transmission the active section of a cell with a length of Lc = 57 cm equals Дr ~ 10~6 cm. In the passive region, r > rA, so a rough approximation yields an2 « 0.77 x 10~4 cm~2. Given this an2 value, following a single pass with a distance of Lc = 57 cm along the cell axis, rays with initial parameters of &0 = 0, z = 0, and r0 > 1.2 cm reach its wall. Furthermore, following several cavity passes, almost all rays with parameters of &0 called = 0, z = 0, and r0 > rA reach the cell wall; therefore, the passive zone may also be a “dead zone.” The divergence of output laser beam from an active region, r < rA, estimated using formula (8.16), comes to & ~3 x 10~3 rad.

For the quasistatic irradiation mode, starting at t« 0.1 s, and for the stationary mode (Fig. 8.2b, c), the refractive index spatial distribution at r > 0.6 cm can be roughly approximated by a parabola with a coefficient of an2 > 0.5 x 10~4 cm~2. At this an2 value, a light ray that has initial parameters of &0 = 0, z = 0, and r0 > 0.6 cm is displaced toward the cell wall (r1 = 1.35 cm), traversing a distance of z < 2 m, which almost corresponds to a single round trip of a cavity with planar mirrors.

Thus, in sealed gas lasers with fission fragment pumping in the stationary excitation mode, conditions created in the bulk of the gas volume that are not favorable for lasing. The same thing also occurs in a quasi-stationary excitation mode, starting at a time of t~10-1 s. Under these conditions, lasing can only originate in the region adjacent to the cell axis.

In pulsed excitation modes with a duration of t1/2 < 10~2 s, the refractive index gradients in the bulk of the gas volume are negative and small, which provides the conditions needed to achieve lasing.

Comparison with Experiments. Already the results of the initial numerical and theoretical investigations of the inhomogeneities originating in NPLs have attracted much attention. Experiments using the interference procedure were carried out in 1982 to study inhomogeneities. The results of these investigations were later published in the unclassified press [2]. In the wake of these experiments, calcula­tions [23] were performed that modeled them with the maximum possible approx­imation of actual conditions using the procedure described at the start of this chapter. The set of gases, their initial pressure and temperature values, and the irradiation intensity time dependence embedded in the calculations fully duplicated the corresponding experimental characteristics.

The conditions under which the experiments [2] were performed, and the parameters of the cell with a cylindrical uranium layer that was used, are presented in Sect. 7.4 of Chap. 7. The longitudinal cross-section of a cell with the plane in which the axis of symmetry is situated along with the relative distribution of the thermal neutron flux is presented in Fig. 8.3. The full internal volume of the cell (excluding the space occupied by the aluminum cylindrical substrate) was 561 cm3. The volume of the cell’s active section (i. e., the internal volume of the substrate tube, bound by its end faces) equaled 351 cm3. We will call the difference in these

two volumes (i. e., the space between the windows in the cell’s outer body and the end faces of the aluminum substrate, as well as the gap between this substrate and the cell’s inner cylindrical surface), the “buffer” volume.

During the calculations, all physical parameters, including the distribution of specific energy sources in the gas and the uranium layer, were assumed to be dependent on a single coordinate, r, alone. The approach used corresponds to a one-dimensional calculation of the processes in a certain equivalent cell with an inside radius, r1, and active volume equal to the inside radius and full volume of the real cell. An uranium layer of the same thickness and composition as those of the real cell stretches over the entire length of the equivalent cell, which equals the ratio of the real cell’s full volume to the cross-sectional area of the active volume’s gas column. Here, it is assumed that the thermal neutron flux distribution is not dependent on the coordinates but equals the average flux value over the length of the equivalent cell. This value is normalized in such a way that the total fissions occurring in the real and equivalent cells were the same.

When using an approach of this type no allowance is made for the possibility of the longitudinal motion of the gas and its partial seepage into the buffer volume. Also, certain density and temperature distributions averaged over the length of the cell are obtained as a result of the calculations. However, it should be remembered that over the course of experiments [2] aimed at investigating changes in density distributions along a cell’s cross-section, an interference procedure was used. During this measurement the variation in the optical path of an He-Ne laser probing beam over the entire length of a cell, also including the end buffer volumes, is recorded. Experimental results obtained in this manner only make it possible to approximately evaluate the gas density changes averaged over the entire length of a cell [2]. Of course, it is impossible to regard a density distribution “averaged” along a beam’s optical path in this manner as fully equivalent to the distribution obtained
during calculations. Nevertheless, a comparison of the results of such calculations with a similar experiment permits a judgment to be made concerning the accuracy of the concepts advanced for the physics of the origination and development of optical inhomogeneities.

It was shown in Chap. 7 that uranium-containing layer inhomogeneities can lead to a decrease in the efficiency of fission fragment energy deposition into a gas. A series of photographs of the transverse sections of the layers used in the experiments (similar to the photos in Fig. 7.10) reveal that the thickness deviations in these layers from the average value are 50-70 %, while the shape of the inhomogeneities is reminiscent of something halfway between rectangular and sinusoidal protuberances. As analysis demonstrates (see Chap. 7, Sect. 7.7), such fluctuations necessarily lead to a 5-18 % decrease in energy deposition efficiency. During the calculations, an average value of 11 % was selected for this decrease, i. e., Є = 0.89є, where є is the energy deposition efficiency for an ideal uranium layer. This correction factor was taken into account in the subsequent calculation of specific energy depositions.

Over the course of the experiments [2], changes were recorded in the pressure, ДP(t) = P(t) — P0 (P0 is the initial gas pressure in the cell), and the optical path of the He-Ne probing laser beam. The density changes of the media under investiga­tion were recalculated using optical measurement data, which are unequivocally related to the changes in the optical path.

The dependences of pressure variation within the cell upon time and density spatial distribution at different moments in time obtained from the calculations are in good agreement with the experimental results. Some calculated (the solid lines) and experimental (the broken lines) dependences of pressure, ДР(0, and relative density distribution, x(r, t) = p(r, f)p0, over the radius of a cell, as well as changes in relative density at the cell axis over time, are shown in Figs. 8.4, 8.5, 8.6, and 8.7. In addition, the shape of the neutron pulse is presented in Fig. 8.4.

ДP, atm; Ф, r. u.

The characteristics obtained experimentally and as a result of calculations are presented in Table 8.1 (F(1)/F(0) is the ratio of the specific energy deposition into the gas at a distance of r = 1 cm from the cell axis to its value at r = 0; APmax is the maximum value of the pressure increase within the cell; and x(0, t) is the relative density value at the cell axis at a moment in time of t = 10 ms.) With the exception of two calculations involving argon at pressures of P0 = 0.25 and 0.5 atm, wherein the deviation in calculated relative density from the experimental value reached 20 %, this deviation was less than 2.5 % in all of the remaining calculations. The fact that the calculated relative density, x(0, t), consistently exceeds the experimen­tal value stands out. This is probably explained by the fact that no allowance was made in the calculations for the gas seepage into the buffer volume during the course of irradiation. However, the overrun is not large and does not lead to noticeable differences in the density profile’s spatial distribution.

An estimate of the effect of gas fraction seepage into the buffer volume can be obtained from quite simple considerations. It was noted in Sect. 7.4 of Chap. 7

that the pressure within a cell over the course of irradiation by a pulsed neutron flux with a duration of t1/2 > 3 ms can, as a first approximation, be assumed to be homogeneous at any irradiation pulse moment, and that gas density redistribution can be regarded as having an equilibrium nature. In this instance, the gas density distribution averaged over the cross-section along the z coordinate, which coincides with the cell’s optical axis, can be presented in the form

where T(z, t) is the effective average (for the cell cross-section) temperature value, determined by the equation

at which time formula (8.20) holds true.

From the condition of gas mass constancy within a cell, we obtain

In this case it is noted that energy release distribution along the z axis is symmetrical relative to the geometric center of the cell. Thus,

For simplicity’s sake, we assume that the T(z, t) dependence takes the form

where LA is the length of the real cell’s active volume. Such a dependence must approximately correspond to the real temperature distribution, as can be concluded from the type of thermal neutron flux distribution (see Fig. 8.3). Placing the distribution from (8.23) into (8.22), we obtain

From (8.23) and (8.24) for the relative variation of average density, we have

^ ^ — 1 =—(L — La) ^ . (8.25)

p0 p0 L — La 1 — TB

The temperature determined using formula (8.21) can be used as the tempera­ture, TA(t), for estimates. In this instance, the T(r, t) dependence is taken from a calculation using the procedure described above.

For the approximate determination of the gas temperature in the buffer volume, it can be assumed that its compression over the course of gas expansion from the active volume occurs adiabatically, i. e.,

/—1

T«(t) = To( £)’

where P0, T0 are the initial pressure and temperature values in the cell. Such an approach is equivalent to ignoring heat removal on the cell wall within the buffer volume. In approximate calculations, this is warranted by the fact that, even in the active volume, ~30 % of the energy absorbed in the gas is carried away by means of similar heat removal. However, the temperature gradients in the buffer volume must be smaller than in the active volume, and accordingly, smaller than the share of energy carried off by means of heat transfer.

The results of a ApA/p0 calculation for all the gas pressures that were studied in the experiments [2] are presented in Table 8.2. The moment in time tm in the table corresponds to the irradiation pulse peak, while the moment in time tc corresponds to the pulse termination.

The calculated and experimental results revealed that for the rare-gas NPLs the lower density difference values, and consequently the lower refractive index values take plact for gases with a lower atomic numbers. The difference values decrease as the initial pressure drops. The experiments confirmed that a narrow region with a large positive density gradient originates near a substrate with a uranium-containing layer. This region grows over time. A comparison of the calculated and experimen­tal results makes it possible to reach a conclusion concerning the applicability of the proposed calculation model to the investigation of the optical properties of NPLs.

The experimental data [2] were later examined in study [37]. The calculations described above [23] were performed in accordance with a full gasdynamic pro­gram that quite correctly reflected heat transfer processes but made no allowance for gas seepage into the buffer volumes. A simplified analytical model was devel­oped in [37] within which an attempt was made to take gas seepage into account while simultaneously introducing a correction factor for heat exchange between the gas and the cell’s metal wall. The authors [37] proposed that viscosity and thermal conductivity are absent in the main part of the cell (not adjacent to the wall), that the gas is ideal, and that the gas pressure is homogeneous at any given moment of time. The thickness of the heat exchange zone adjacent to the wall, which is called the “passive” or “dead” zone, was taken to equal I = fat. Using the latter equation, the heat flux in the active and buffer parts of the cell wall was found, and then the correction factor for the calculated pressure was determined, which consists of the last addend in equation (7.20). The transverse specific energy deposition profile was
assumed to be constant in Lagrangian coordinates. In the longitudinal direction within the active part of the cell, the specific energy deposition was regarded at homogeneous, while in the buffer part, it was considered to equal zero.

A comparison of calculation results [37] and experimental data [2] revealed that a somewhat better agreement was achieved between the calculated and experimen­tal values in five of the six cases examined. Here, the maximum discrepancy between the calculation results from studies [23] and [37] is exhibited during exciting pulse termination. As far as density, the greatest discrepancy in these results (~5 %) is observed for neon. In the remaining cases, these discrepancies are 0.3-2.7 %. All these figures are perceptibly lower than the estimated value of the effect of neglecting gas seepage into the buffer volumes cited in Table 8.2.

In conclusion, the numerical and theoretical investigations of other authors concerning the development of transverse optical inhomogeneities should be mentioned [18, 38—40]. The authors [18, 38, 39] completely ignore heat exchange. Furthermore, in [39], the specific energy deposition profile, tied to Eulerian coordi­nates, is assumed to be constant over the entire duration of the excitation pulse. In studies [18, 38], above profile is tied to Lagrangian coordinates, which more properly corresponds with the physics of the processes occurring. In study [40], the depen­dence of the specific energy deposition profile upon variable density is precisely defined; however, simplified gasdynamic equations are used.

The most progress in searching for active media for NPLs, studying their charac­teristics, and developing various nuclear-laser devices was achieved when high — pressure gas media were used. However, there have been repeated attempts in Russia and the United States to pump different condensed media with nuclear radiation and carry out feasibility studies on developing powerful nuclear-laser devices based on these media. The active material in solid-state and liquid lasers is a dielectric in a condensed phase. As compared to gases, it is possible to create a higher density of active particles in condensed media, and, as consequence, to obtain more specific output energy of laser radiation.

When uranium, for example, is introduced into a condensed media it is possible to achieve essentially uniform excitation of the active volume at close to 100 % deposition efficiency (due to a small path length for charged nuclear particles in a condensed medium). Therefore in the initial stage of NPL investigations at the end of the 1960s and the beginning of the 1970s, when known gas lasers operated only at low pressures, the emphasis was on condensed media. At that time, these studies were carried out at VNIIEF [1—3] in Russia and in the laboratories of the North American Rockwell Corporation, General Atomics, etc. in the United States (see the literature cited in publications [4—6]). Later, other laboratories became involved in the investigation of condensed-media NPLs. A significant number of studies were fulfilled at FEI [Physics and Power Engineering Institute] (Russia) and the University of Missouri-Columbia (USA).

Two pumping alternatives were considered for excitation of condensed-media NPLs: immediate (direct) pumping using nuclear radiation when nuclear reactions occur inside the laser medium; and pumping with help of optical radiation from intermediate devices—nuclear-optical transformers or convertors (nuclear-excited plasma and solid-state or liquid scintillation media). In the first case, the pumping region and the region where population inversion is created coincide, in the second, they are spatially separated.

© Springer Science+Business Media New York 2015 S. P. Melnikov et al., Lasers with Nuclear Pumping, DOI 10.1007/978-3-319-08882-2_11

The spectra of rare-gas atoms have a number of intensive lines belonging to the transitions (n + 1)p-(n + 1)s (where n = 5, 4, 3, 2 for Xe, Kr, Ar, and Ne, respec­tively), which end in metastable states (n + 1)s. The efficiency of populating the upper levels (n +1)p in a recombination-nonequilibrium plasma is very high [80,

81] , so these transitions are promising in the search for lasing. However, in order to obtain lasing on the transitions (n + 1)p-(n + 1)s in cw mode, a high depopulating rate of (n + 1)s-levels is necessary. This can be ensured by two methods: through collisional “quenching” by atoms of the buffer gas (as, for example, in a nuclear — pumped laser at the line of 1.15 qm of the Ar atom [8, 16]), and using additional “quenching” impurities.

The difficulty in choosing the impurity is related first of all to the fact that it must not substantially influence the population of the upper level. This scheme was implemented in a neon NPL operating on transitions 3p-3s of the Ne atom in the lines 585.3-; 703.2- and 724.5-nm [2, 32, 33, 82—91]. Apart from nuclear radiation, electron [92—96] and ion [97] beams were used to pump the neon laser; when electron beams were used, lasing was also observed at the 626.7-; 633.4-; 659.9- and 743.9-nm lines [95]. The quenching impurities in the case of NPLs were М = Ar, Kr, Xe, H2, and with electron beam pumping, NF3 also. Quenching of the lower 3p-levels occurs through the Penning reaction: Ne*(3p) + M! M+ + Ne + e. A diagram of the Ne atom levels with laser transitions is provided in Fig. 3.3.

A neon laser was first pumped with nuclear radiation at VNIIEF in 1985, immediately after the first reports [92, 93] about successful pumping of this laser with an electron beam. These results were published in the public press in 1995 [2,

82] . The basic results of researching NPLs operating on 3p-3s transitions of the Ne atom, obtained in various laboratories, are shown in Table 3.8.

In lasers using binary mixtures Ne-M (M = Ar, Kr, Xe), lasing was observed at two lines—703.2 and 724.5 nm—while with a change in the concentration of the quenching impurity of M, there was restructuring of the lasing spectrum [82­84]. By way of illustration, Fig. 3.4 shows data for the mixture Ne-Kr. The ranges of impurity M pressure at which simultaneous lasing was observed at two lines are diverse. Thus, in the mixture Ne-Ar, simultaneous lasing occurs at PAr«28- 55 Torr, in the mixture Ne-Kr—PKr« 30-50 Torr, while for the mixture Ne-Xe

о

о

cp

О

ON

W

this pressure range is very narrow (close to РХе ~ 28 Torr). Similar results were also obtained in the mixtures He-Ne-Kr (Ar) [89].

The use of hydrogen as the quenching impurity is expedient only when there are sufficiently high specific power depositions (q > 1 kW/cm3) because of competition of the processes of depopulation of 3s-levels of the Ne atom and charge-transfer of the molecular ions Ne2+ on molecules of H2 [83, 85]. Therefore, the report [88] about obtaining lasing at the 585.3-nm line in NPLs using the mixture He-Ne-H2 for q ~ 100 W/cm3 is doubtful.

The ці ~ 0.1 % obtained in experiments for neon NPLs is much lower than in the case of NPLs operating on IR transitions of rare gas atoms, although in experiments by FIAN associates with electron beams for an He-Ne-Kr laser (A = 585.3 nm), ці = 1.6 % [94] was noted. As was shown by the results of theoretical analysis [98], the maximal efficiency of a neon laser at the 585.3-nm line cannot exceed 0.5 %, therefore the high efficiency cited in study [94] is evidently explained by an error in determining the energy deposition. In later studies by FIAN associates, values of ці = 0.1-0.2 % are cited for the neon laser at the 585.3-, 703.2-, and 724.5-nm lines.

By 1980, a report [99] was published stating that lasing had been obtained at transition 5s'[1/2]1°-3p'[3/2]2 of the Ne atom Ne (A = 632.8 nm) while the mixture 3He-Ne was excited by nuclear reaction products 3He(n, p)3H. According to the authors of [99], the laser efficiency was around 0.03 %, and the laser threshold was achieved at a very low thermal-neutron flux density of ФгА = 2 x 1011 cm~2 s_1. The results of these experiments are doubtful, and are the subject of discussion in references [100, 101]. The simple evaluations cited in study [100] show that under the conditions of [99], it is not possible to obtain lasing even in the maximal case, when all power deposited to the active medium is transferred without losses to populate the 5s'[1/2]1°-level and this level is not “quenched” in collisions with atoms. In later experimental investigations, it is noted that attempts at obtaining lasing at the 632.8-nm line with excitation of the mixture He-Ne using an ion beam [102] and radiation of a stationary nuclear reactor [103] yielded negative results. Numerous investigations [60, 103—107] of the luminescence spectra of the mixture He-Ne, excited by various types of nuclear radiation, showed the absence of a

632.8-nm line. The data cited allow us to conclude that the information [99] about creating a low-threshold NPL at the 632.8-nm line was erroneous.

In conclusion, let us examine the possibility of creating NPLs operating on the transitions (n + 1)p-(n + 1)s of other rare gas atoms: Xe, Kr, and Ar. Such explor­atory experiments were carried out at VNIIEF on the LUNA-2M setup in a range of 700-1,000 nm for those transitions (n + 1)p-(n +1)s of Ar, Kr, and Xe atoms at which maximal values of luminescence efficiency were obtained [81]. Studies were performed on Ar, Kr, and Xe, and the mixtures He-Ar (Kr, Xe) and Ar-Xe at pressures of up to 2 atm. For quenching of the lower (n +1)s states, impurities of the molecular gases CO, H2, N2, and NF3 were used, as well as Kr and Xe at partial pressures of 8-60 Torr. The numerous experiments did not yield a positive result, which possibly may be explained by the insufficient rate of quenching of the lower laser levels and/or the essential reduction in the populations of upper laser levels in the presence of impurities. The absence of lasing can be provoked by the fact that the experiments were conducted at low specific power depositions (q < 50 W/cm3), so that the small-signal gain could be deficient for achieving the lasing threshold. It is helpful to conduct such research experiments at higher specific power deposi­tions, for example using beams of fast electrons. This is confirmed by the successful experiments [108] in pumping of a laser using the mixture Ar-NF3 (transition 4p-4s of an Ar atom, X = 750.4 nm) by an electron beam.

The mechanism of a laser operating on the transition 7p2P3/2-7s2S1/2 of the Hg+ ion (A = 615.0 nm) was considered in studies [4, 106, 122]. Populating of the upper laser level 7p2P3/2 occurs as a result of the charge-transfer process He+ + Hg! (Hg+)* + He. For low concentrations of Hg atoms, populating of the level 7p2P3/2 can also occur by means of the Penning process with the participation of excited mercury atoms: He* + Hg* ! (Hg+)* + He + e [122]. The basic quenching channels of the upper laser level are the Penning reaction on its own atom (Hg+)* + Hg! Hg+ + Hg+ + e and collisions with electrons [4, 106]. Calculations in [4, 106] show that at the 615.0-nm line, even in optimal modes, the energy laser characteristics are not great (see Table 5.10).

Significantly higher output energy parameters were obtained for NPLs operating on the transition 73S1- 63P20 of the Hg atom Hg (A = 546.1 nm) when the mixture He-Xe-Hg-H2 was used (see Chap. 3, Sect. 3.3). The lasing mechanism and the possibility of pumping this laser with nuclear radiation were examined in the studies [122, 123] before lasing was obtained in experiments with the EBR-L pulsed reactor [116].

The most detailed kinetic models of the mercury laser at the 546.1-nm line are presented in studies [88, 124, 125]. The main populating channel of level 73S1 is dissociative recombination Hg. j~ + e! Hg * (73S1) + Hg, and the populating effi­ciency of level 73S1 by means of this process may reach 80 % [123,124]. Formation of Hg2 ions occurs in a sequence of processes: Xe^ + Hg! Hg+ + 2Xe, Hg+ + Xe + M! XeHg+ + M, XeHg+ + Hg! Hg^ + Xe (Xe is the buffer gas, M is a third particle). The presence of helium in the active medium leads to a reduction in the electron temperature and an increase in the rate of dissociative recombination of Hg2 molecular ions with electrons. The use of an additional admixture (in this case Н2) for selective quenching of the lower levels 63P20 is a specific feature of this laser. We note that even before the appearance of the first lasers, the experiments of [14] were carried out on quenching of the levels 63P0012 of the Hg atom during collisions with H2 molecules, in which amplification was obtained at all lines of the mercury triplet: 546.1, 435.8, and 404.7 nm.

The lasing mechanisms of NPLs based on metal vapors, in which the necessary concentration of vapors (~ 1 Torr) was created by means of thermal evaporation of metals inside the laser cell, were examined above. A number of studies by MIFI associates (see [126, 127], for example), examine a different lasing mechanism, based on the formation of excited ions or atoms directly as a result of bombarding the metallic layer with charged particles. In the opinion of the authors [126, 127], this “atomization” mechanism of laser operation, which does not require a buffer gas, and forms excited particles directly in the upper laser states, makes it possible to increase laser efficiency by a factor of five to seven. To confirm this hypothesis, studies [126, 127] cite data that was obtained in experiments with the VIR-2 M pulsed reactor at irradiation by a neutron flux of two laser cells that have thin cadmium layers deposited to the walls and are filled with 3Не at a pressure of

1.1 atm. As the authors of [126, 127] state, the output laser power at the 441.6-nm line was < 3 mW, with anomalously low temperatures of laser cells of 460 and 510 °K. At such temperatures, the concentration of cadmium vapors due to thermal evaporation was very low, <2 x 10~4 Torr.

Based on a very limited number of experiments, one cannot draw an unequivocal conclusion regarding the presence of lasing effect in studies [126, 127], because signals from the photodetectors were too low and scarcely exceeded the level of electrical and radiation noise. If one assumes that lasing did indeed occur, then as the calculations in [128] show, the results of this experiment can be entirely explained based on the traditional kinetic model, if one allows for the effect of atomization of the cadmium layer by products of the nuclear reaction 3He(n, p)3H and subsequent injection of atomized cadmium atoms into the active medium.

The most important parameter that characterizes a gas flow is the Reynolds number

(9.1)

where d is the typical transverse dimension of the channel; U is the velocity of the gas flow averaged over the channel cross-section; and v is the kinematic viscosity.

© Springer Science+Business Media New York 2015 S. P. Melnikov et al., Lasers with Nuclear Pumping, DOI 10.1007/978-3-319-08882-2_9

At Reynolds numbers, Re, lower than the critical value, Rec, a flow is laminar. At Re > Rec, the laminar mode makes the transition to the turbulent mode. Under normal conditions for a flow in a round tube, Rec«2,300. For channels with another transverse cross-section shape, it is close to this same value [2, 3].

During a laminar gas flow in a cylindrical channel, the pressure differential along its length, bL, comes to [4]

др = 8UpA,

r1

while for a channel formed by two parallel planes, the distance between which equals d,

др = (9.2)

During a turbulent flow in a channel with any transverse profile, the pressure differential along the channel’s length is determined by the expression [5—7]

_ 2 b

др = tpU2-L, (9.3)

2de

where £ is the resistance coefficient. The channel’s equivalent diameter, de, is expressed by way of the area of the channel’s transverse cross-section, Sc, and the total perimeter, nc, of the channel surface that the gas washes over,

de = 4Sc/nc-

The resistance coefficient can be determined based on the Blasius law [6, 7]

£ = 0,3164Re~°,25.

Other formulas also exist for determining the £ parameter [3-5], but they all yield a similar result. An estimate based on formula (9.2) for U ~ 10 m/s and bL ~ 1 m yields др < 3 x 10 4 atm. From a similar estimate based on formula (9.3) for U~100 m/s, we get ДР < 0.03 atm. In both cases, the ДP parameter value is negligible as compared to the optimum pressure value of P ~ 1 atm used in NPLs. Consequently, the gas pressure in a laser channel can be roughly regarded as homogeneous.

In this case, the heat balance equation for a laser channel with a stationary gas flow that operates in the steady-state mode takes the forms:

qcScbi = P0U0Sccp(Tb — 7q),

where cp is the specific heat capacity of the gas at a constant pressure; qc is the specific power deposition averaged over the volume; T0, Tb are the gas temperatures
at the laser channel inlet and outlet; U0 is the gas velocity at the channel inlet; and p0 is the gas density at the channel inlet. Thus,

qA

p0cp(Tb — T0)

Because the operating length of the laser channels is bL > 1 m, then at a specific power deposition of q > 10 W/cm3, gas circulation along a channel already requires the use of high gas velocities (U0 ~ 100 m/s) in order to prevent conspicuous active medium overheating (for example, by AT = Tb — T0 < 100°K). In the presence of a channel transverse dimension of d ~ 1 cm, these velocities correspond to Re > 104. These Re values markedly exceed the Rec value at which a laminar flow mode makes the transition to a turbulent mode. Because bL >> d and Re >> Rec, a well — developed turbulent flow is then established in the bulk of the cell volume, which can adversely affect the optical quality of the active medium as a whole.

The investigations performed at VNIIEF on different types of NOCs and the neodymium lasers excited by them permit consideration of a series of schemes for pulsed reactor lasers (RLs) using neodymium active elements with laser radi­ation energy <10 MJ and intended for studies of some problems of inertial confinement fusion [41, 42].

One of the variants is a modular design. The modules are placed in the reactor matrix, which contains nuclear fuel, reactor control units, a neutron moderator and reflector, etc. Inside the module, which has an 80-cm diameter, are about 100 neo­dymium rods 45 mm in diameter and 1,200-cm long (Fig. 11.13a). The space between the rods, which are arranged as a hexagonal grate with 80 mm steps, is filled with a UF6-Xe (4:1) mixture at 2 atm.

The laser rods are pumped with the optical radiation of the plasma (temperature <104 K), which forms under the impact of neutron pulses ~3 ms duration with a fluence of ~3 x 1014 cm~2. The total energy of the laser radiation of a single module is about 400 kJ at ~2.5 % efficiency for conversion of the released nuclear energy into laser radiation.

Fig. 11.13 A schematic of a laser module with uranium hexafluoride (a) and uranium layers (b) [42]:

(1) laser elements; (2) filters that absorb UV-emission; (3) NOC; (4) NOC body with a uranium layer; (5) the module body

Fig. 11.14 Schematic of a pulsed RL [42]: (1) laser module; (2) “start-up” reactor; (3) peripheral reactor module — multiplicator; (4) neutron moderator; (5) reactor body

Another possible variant in the module design uses uranium fission fragments that escape from the uranium layers to excite the xenon plasma (Fig. 11.13b). The uranium layers are deposited to the internal surface of the NOC body (hexagonal in cross-section), which is filled with xenon at ~1 atm. There are 60-70 laser elements at the same module dimensions, and the energy of the laser radiation is no more than 250 kJ. If this variant of the module design is used, the efficiency will be approximately ten times lower due to the lower transmission efficiency of the fission fragment energy to the gas medium. This requires an increase in the total energy release in the module.

It should be noted that the modules considered have a significant neutron multiplication factor, and, as follows, contribute to the total reactivity of the reactor system. This allows loading of additional nuclear fuel into the reactor to decrease.

A RL based on these modules with an output laser energy of ~10 MJ can be proposed, for example, in an 18 module design with the modules placed in six channels and three tiers (Fig. 11.14) [42]. In the central part, there is a “start-up” reactor with control units. All of the device elements are placed in a matrix-neutron moderator and comprise a single nuclear-physical system. The pulse duration of the nuclear fission and laser radiation in the free-running mode may be 1-10 ms. The typical liner dimensions of such a facility are 3 m; the total mass is no more than 100 t.