7.1 Comparison of Basic Methods of NPL Excitation

As was noted in Sect. 1.2 of Chap. 1, the nuclear reactions that can be used for pumping gas NPLs in experiments with pulsed reactors are:

When reaction (7.1) is used, the laser medium is excited by protons and tritium ions. In this case, 3He plays the role of a buffer component of the laser mixture and is simultaneously a volume pumping source. Calculations of the specific energy deposition to the gas medium when the reaction (7.1) is used were carried out in the studies [1, 2]. The gas pressure and the transverse dimension of the laser cell were varied (it was assumed that the length of the cell greatly exceeded its transverse dimension). It was shown that for each pressure value there is an optimal transverse dimension of the cell. When the dimensions are less than optimal, the losses of reaction (7.1) products on the walls of the cell become great. When the dimensions are greater than optimal, the decrease of the neutron flux in the direction from the cell boundary to the depth of the gas volume starts to have an effect. Some results of calculations are provided in Figs. 7.1 and 7.2. It should be noted that the model [2] makes it possible to perform calculations for different neutron spectra when more precise deceleration principles of charged particles are used. The results of the calculations in studies [1, 2] for the case of a mono-energetic flux of thermal neutrons differ by 10-15 % (Fig. 7.1).

The gaseous compound 235UF6 can be used in the capacity of a volume pumping source along with 3He. Calculations of the energy deposition for the mixture Не — UF6 for different pressures and concentrations of UF6 are provided in

© Springer Science+Business Media New York 2015 S. P. Melnikov et al., Lasers with Nuclear Pumping, DOI 10.1007/978-3-319-08882-2_7

Fig. 7.2 Total absorbed energy Ei per unit of length of an infinite cylindrical tube depending on its radius r1 with a thermal neutron fluence of 1 cm-2 [1]. Numbers next to the curves indicate the 3He pressure in atmospheres

study [3]. However, the search for nuclear-pumped gas media based on UF6 has not yielded a positive result in experiments to date. The issue involved is attributed to the high quenching rates of excited atoms by UF6 molecules [4, 5].

Thin layers of materials containing the isotopes 10B or 235U (surface sources) are used to excite the active mixtures by means of the reactions (7.2) and (7.3).

However, in this case the efficiency of energy transfer to the gas mixture by the nuclear reaction products is limited to <50 % (for an ultra-thin layer) owing to the

isotropy of their recession. For uranium layers, when conditions are optimal, this efficiency is 10-20 %. To our knowledge, the first calculations of the energy deposition from the surface source according to the reaction of (7.2) were carried out in study [6].

From the energy standpoint, the use of 3He as the volume pumping source is as efficient as the use of thin uranium layers. Indeed, as an example let us examine two cylindrical cells of identical geometry. Let metallic 235U be applied to the internal surface of one of them with an optimal thickness <5u, the average fission fragment [7] in the uranium, that is, 5U « cell is filled with a laser mixture that does not contain 3He. Then the total energy transmitted to the gas by the fission fragment in a unit of time is

W = 2лr18ULcOfNUФE0 є, (7-4)

where E0 is the total kinetic energy of the fission fragment of the uranium nuclei; Lc is the length of the cell; NU is the density of the uranium nuclei in the active layer; r1 is the internal radius of the cell; є is the efficiency of energy transmission to the gas by fission fragment (ratio of the energy transmitted to the gas by fragments to the total kinetic energy of the fragments released in the uranium layer); cf is the cross section of uranium fission by the neutrons; and Ф is the neutron flux density.

Let the second cell not have a uranium coating, but be filled with a gas mixture whose basic component is 3He. The total energy released in the gas volume of this cell per unit of time is

WHe = ПГ^сСНє^єФЕнєЄНє, (7-5)

where NHe is the density of the 3He; EHe is the kinetic energy of the reaction (7.1) products; єНє is the efficiency of energy transmission by the products of reaction (7.1) to the gas; cHe is the cross section of the reaction. From Eqs. (7.4) and (7.5) we have

WHe_ r 1 cHe NHe EHe £He

W 2SU cf NU E0 є

To conduct a comparative assessment, we assume that the basic component of the gas mixture in the first cell is 4He and the gas pressure in both cells is «2 atm; the transverse dimension of the cell r1 ~ 1 cm. With such correlations between pressure (which at T0 = 300 K corresponds to NHe « 5 x 1019 cm~3) and transverse dimen­sion of the cell, the decrease of the neutron flux owing to the interaction with 3He is not great, and it can be ignored in estimates. On the other hand, the accepted correlation of the radius and pressure of a gas laser excited by fission fragment and not containing 3He is close to optimal [7]; at the same time, є « 0.16. The value of є№ for these parameters is in the limits of 0.7 < є№ < 1 and is determined by the influence of the cell walls on the energy deposition of the reaction products. Assuming for thermal neutrons cf = 582 x 10~24 cm2, cHe = 5,327 x 10~24 cm2,

and considering that NU = 4.8 x 1022 cm-3 (metallic uranium), E0 = 168 MeV, EHe = 0.76 MeV, from the last equality we find WHe/W ~0.5 r1eHe~0.5 r1 cm-1. Consequently, in both cases, the energy depositions can be comparable in amount. However a serious restriction for pumping the gas medium with reaction (7.1) is necessary to use component 3He in the capacity of the buffer component, greatly limiting the choice of gas mixtures for the laser media.

This limitation is eliminated when the reactions (7.2) and (7.3) are used. The total energy transferred to the gas per unit of time by products of the reaction (7.2) is

Wb = 2лrl8вLcaвNвФEaЄв■ (7.6)

Here Ea is the kinetic energy of the a-particles; NB is the density of the nuclei of 10B in the active layer; £B is the thickness of the boron layer; eB is the efficiency of energy transition to the gas by a-particles; aB is the cross section of the reaction (7.2). From expressions (7.4) and (7.6) we find:

W 8UeofNUE0

W в £b£b°bnbeb

An a-particle that appears as a result of a reaction (7.2) can travel from the boron layer into the gas mixture only if it was born at a distance from the coating-gas interface that is less than its stopping range in the coating (source) material. Therefore, the maximal effective thickness of the boron layer should not exceed the stopping range of an a-particle with an energy Ea = 2.38 MeV which is about £B « 0.6 x 10-4 cm with a density of boron nuclei of NB = 0.136 x 1024 cm-3. The maximal value of efficiency of the energy deposition, as already mentioned, cannot exceed 50 %, that is, eB < 0.5. Assuming laser cells with uranium or boron layers are fully identical to the above cell in regard to geometry and gas mixture compo­sition, then with allowance for the fact that for thermal neutrons, ffB « 3,840 x 10-24 cm2, we find W/WB > 5.6. The advantage of using uranium layers with their larger energy release is evident.

Because the absorption cross section for thermal neutrons by the isotopes 3He and 10B is quite large, the placement of laser cells with such isotopes in the core of the nuclear reactor can lead to a perceptible reduction in its core reactivity margin, and if the number of cells becomes too large, this may also bring the reactor to a subcritical state. But cells with 235U layers can simultaneously play the role of fuel elements in the reactor core, avoiding a reduction in criticality. Furthermore, if the configuration is optimal, an autonomous reactor-laser may be formed with an adequate super-criticality margin, using a core entirely assembled from such laser cells (channels).