Method of Measuring the Efficiency of the Conversion of Nuclear Energy into Optical Energy

Amethod ofmeasuring the efficiency of converting nuclear energy into optical energywas developed based on correlations between intensities of the research line and the nitrogen second positive system in anAr-N 2 mixture. In addition, the values of the coefficient of the conversion of nuclear energy into radiation at the lines of a Hg triplet in mixtures of HA-Hg and Kr-Hg were determined. The values measured correspond to a selectiveness of pumping of 7S 1 that was close to 1 (δ = 0.8 ± 0.2).


Introduction
The study of optical (laser and spontaneous) radiation of nuclear-excited plasmas is of interest for the development of a method to extract energy from nuclear reactors and to control and adjust nuclear reactors' parameters [1][2][3].The essential parameters in the process of studying nuclear-excited plasma radiation are the values of the power of the nuclear reaction products deposited into gas and the efficiency of the conversion of nuclear energy into optical energy ().The power of nuclear reaction products deposited into gas can be calculated for a specific geometry of the irradiating area or measured based on the gas overpressure after the pumping pulse [3].The measurement of the parameter  is more complex, as one must measure the absolute intensity of the optical radiation from the area under consideration [4][5][6].
This paper focuses on developing a method for measuring the coefficients for converting nuclear energy into optical energy; our method involves radiation intensity comparisons in the mixture under study, where the radiation intensity was measured in a well-studied mixture.The studies were carried out with Polonium-210  particle excitations.

Experimental Setup
The parameter  (the ratio of the optical power at the defined wavelength or molecular band to the power deposited into the gas) was determined by comparing the measured radiation intensities in the studied mixture with the intensity of the b 3 ^u-j 3 ^g nitrogen band in an Ar + N 2 mixture.The gas pressure was selected such that the maximal range of  particles with energies of 5 MeV was similar for all the mixtures and the pumping power was comparable.A cylinder of diameter 25 mm and length 70 mm, carrying on its surface 18 sources containing 210 Po, was installed in a stainless steel chamber (Figure 1).The maximal range of  particles with energies of 5 MeV in Ar, Kr, and Xe under normal conditions is 37, 28, and 20 mm, respectively [7].The activity of the  sources was 9.6 GBq, which corresponds to an average energy deposition  of approximately 10 −4 W⋅cm −3 in 1.5 atm of Ar.Before we set up the sources, the chamber was heated and degassed under vacuum with a pressure of approximately 10 −3 Pa.After the chamber was set up, the  sources were pumped down without heating for 2-3 weeks until the receipt of well-reproduced (up to 3-7% of intensity for various gases) luminescence spectra was verified.The gas pressure was measured by a standard mano-vacuum meter and VDG-1 To SPM-2 To gas system vacuum meter, and the spent gases' purities were as follows: 99.992% for Ar and 99.999% for both Kr and Xe.The emission spectrum was analysed by a SPM-2 monochromator with a quartz prism and FEU-106 photomultiplier operating in the photon counting mode.The emission spectra were recorded under the maximal width of the monochromator slit; the forms of all the studied lines were similar to a triangle.In this case, the maximal value of the signal from the photomultiplier was proportional to the integral spectral intensity of the lines.

Efficiency of the Ar + N 2 Mixture's Luminescence
The efficiency of the Ar + N 2 mixture's luminescence was determined by calculation.A scheme of kinetic processes similar to the one described in [8] was used.The lifetime of Ar's metastable levels is approximately 50 s [9], and the radiation transferred from 3 `1 and 1 `1 into a normal state under atmospheric pressure was fully trapped.Therefore, all 4 levels of 3 `and 1 `, as well as one level of Ar * , were considered.Table 1 presents the processes relevant to the calculations and the proper rate coefficients.
).The number of photons emitted in this transition is determined by the following formula: where the Einstein coefficients  0, are presented in [10] and the density of nitrogen molecules on the C 3 ^u,V  =0 level was calculated by considering processes 1-23.Moreover, the direct nitrogen excitation was insignificant, as our measurements show that the intensity of the nitrogen second positive system in N 2 (100 Torr) is approximately 140 times less than that in the Ar (1140 Torr) + N 2 (100 Torr) mixture.The intensity of the transitions from V  = 1 in the Ar + N 2 mixture was approximately 15 times less than the intensity of the transitions from V  = 0.The coefficient of the conversion of nuclear energy into optical energy can be determined by comparing the measured transition intensity (  ) of the nitrogen molecules at the wavelength   and the studied transition intensity (  ) at the wavelength   .A simple formula can be derived in the case of radioisotope pumping when processes 4, 22, and 23 can be ignored: where  21 is the transition energy with wavelength   ,  * ≈ 20.6 eV is the energy consumed by the formation of one Ar * atom in processes 1-5, and () is the relative spectral sensitivity of the setup.To reduce the effect of the determination error of () on the accuracy of the definition of , N 2 molecular transitions closer to the wavelength of   were selected.The radiation intensity dependence measured in line 337.1 nm on the partial pressure of N 2 in an Ar + N 2 mixture is satisfactorily correlated with the dependence of  on the N 2 pressure within the range of 3-100 Torr (Figure 2).

Efficiency of the Luminescence of Gas Mixtures with Hg
In the mixtures of Xe or Kr with Hg, the 7 3 S 1 level of the Hg atom is effectively populated by pumping with a rigid ionizer [11].The main part of the energy (>98%) within 200-830 nm is emitted at triplet and resonance Hg lines (Figure 3).Because the harmful impurities that can result from radiation-chemical reactions are not accumulated in this mixture, it can be used as a scintillator for a nuclearexcited source of light.Thus, the values of the coefficient of the nuclear energy conversion into optical energy in these mixtures have great significance.The step of populating the 7 3 S 1 level occurs in the processes of dissociative recombinations of molecular ions (Hg 2 + , XeHg + , and KrHg + ) with electrons [11].Here, we describe the more essential processes in Xe + Hg plasma (where V is the third particle): He 2 + + Hg → Hg + + 2Xe Hg + + Xe + M → HgXe + + M HgXe + + Hg → Hg 2 + + Xe Hg 2 + + e → Hg (7 3 S 1 ; 7 3 P) + Hg (8) The 7 3 S 1 level is populated either in process (8) or by cascade transitions from the 7 3 `0,1,2 levels.
In the recombination mechanism of the 7 3 S level, populating the dependence of the emission intensity of this level on Hg vapour's density is determined by the following formula [18]: where  ∞ is the intensity under a high density of Hg atoms;  is the rate constant of charge exchanges of Xe 2 + (Kr 2 + , KrXe + ) ions at Hg atoms [19]; and the  coefficient of electron-ion recombinations is assumed to be identical for basic molecular ions (≈10 −6 cm 3 s −1 ).
By the above method, the ratio of the optical radiation's power to the power deposited into the gas () was determined for Hg triplet lines in mixtures of He + Hg and Kr + Hg.In terms of laser creation, the value of the 7 3 S 1 level pumping

Table 1 :
Rate constants of processes in an Ar-N 2 mixture.