In study [48], it is proposed that cell wall heating be carried out at the same time as laser pumping in order to diminish, or totally eliminate, a passive zone. The simplest means for putting this process into effect is to inject 235U nuclei into the
cell walls: during the irradiation of a laser of this type by a neutron flux, cell body heating due to the nuclear fission of the uranium injected into its walls occurs synchronously with the escape of fragments from uranium-containing layer into the gas.

It is convenient to examine the synchronous heating process based on the example of a cylindrical laser cell with an active uranium layer that is directly deposited to its inner wall surface. Let us assume that the concentration of uranium nuclei in the cell wall material is such that, over the course of a neutron flux rise time that exceeds the typical temperature equalization time of the gas in the cell, tt, determined by means of correlation (8.33), there is no noticeable flow of thermal energy from the gas to the wall and vice versa. Thus, the correlation that defines the optimum concentration of uranium nuclei in the wall directly follows from gas, uranium layer, and wall temperature equality requirements at any given time during irradiation, as well as from the absence of a heat flow from the gas to the wall:

(8.37)

2

_____________ CvP0rU_____________

CvP0rU + CUPu(r2 — rUl) + CwPw(r2 — r) where Cu, cw are the specific heat capacities of the uranium-containing layer and the cell wall material; rU, r1 are the internal and external uranium layer radius values; r2 is the external radius of the tube wall; £w is the fraction of energy that the fission fragments transfer to the gas from all the energy released in the cell, including the energy released within the wall; and pU, pw are the uranium-containing layer and cell wall density density values.

In fact, when the above conditional requirements are present

(cUVUpU E CwVwpw)(T T0) (1 £w)Ew,

CvP0V(T — T0) = £wEw,

£wEw — £Eu .

Here, Ew is the total energy released in the uranium layer and the cell wall; EU is the energy released in the uranium layer; and V, VU, Vw are the volumes of the gas, the uranium layer, and the tube wall, respectively. Taking into account the fact that energy release in the wall and the uranium layer is proportional to the concentration of uranium nuclei therein, it is not difficult to derive correlation (8.37) from the latter three equations.

In order to verify the effect of the uranium, series of calculations were performed that involved different uranium concentration values, Nw, in the wall for different neutron flux rise times, starting with т — 4 ms or higher. These calculations revealed that at Nw — Nw0, the passive zone completely disappears at any of the neutron flux rise times studied. The temperature profiles for several successive moments in time

at Nw = Nw0 = 4.95 x 1021 cm—3 are designated by the broken line in Fig. 8.13. The calculated dependences of the radial coordinate of the active region’s outer bound­ary and the fraction of fission fragment energy absorbed in this region, Qg(tA)Qg (r1), upon the total energy absorbed in the gas, as well as of the refractive index gradient in this region upon the Nw concentration value at D0 = 0.5 a neutron flux rise time of t = 0.04 s, are presented in Fig. 8.16.

The calculations demonstrated that, despite a positive effect, the synchronous wall heating process has a specific drawback: over a time frame of t < 0.1 s (see Fig. 8.13), the cell wall and the gas are heated by more than ДT = 1,000 °K, which limits opportunities for using the process.

We note that injecting uranium nuclei into the cell wall material is virtually equivalent to simply increasing the uranium mass in the uranium layer by a value that equals its mass in the wall. In Fig. 8.13, Nowк5 x 1021 cm—3, which at r1 = 1 cm and in the presence of a wall thickness of Sw = 1 mm, is equivalent to increasing the thickness of a metallic uranium layer by ~40 times. In the presence of such an increase, the energy that the fragments carry into the gas (D1 is increased from 0.5 to 20), which is proportional to D1e(D1) (see Chap. 7, Sect. 7.3), increases by 7 %. The energy (1 — e) that the fragments do not carry into the gas is released directly onto the inner surface of the cell wall; thus, just as when uranium is placed in the wall material, energy release therein is more homogeneous. In the example under consideration, the wall is made from zirconium, the thermal diffusivity of which is aw к 0.12 cm2/s; the typical temperature equalization time for a wall thickness of 8w = 1 mm comes to tw ~ S2w /aw ~0.1 s, which is an order larger than the neutron pulse rise time. Therefore, when all the necessary uranium is concentrated in the active uranium-containing layer, the cell wall’s inner surface will be heated quite a bit more intensely than during uranium blending, which will lead to a decrease in the permissible fluence values and accordingly in irradiation time. However, it follows from the foregoing that in order to achieve the desired effect over fairly short rise time of т < tw when concentrating all the uranium in the active layer, its total quantity may be smaller than during its blending. It cannot be ruled out that under specific conditions, the version when all the uranium is concentrated in the uranium-containing layer may prove to be preferable. The question of the optimum placement location and the total quantity of the additional uranium must be separately considered in each given case based on actual structural solutions and the requirements imposed on laser characteristics.