ON INDUCED ACTIVITY IN THE FLAW DETECTION OF THICK STEEL PRODUCTS USING BETATRON BREMSSTRAHLUNG

O. V. SOKOLOV

(Presented by the scientific seminar of the Research Institute of Electronic Introscopy)

In the flaw detection of steel structures using bremsstrahlung generated by a betatron, photonuclear reactions occur in the isotopes of the elements that make up steels. Taking photonuclear reactions into account is necessary in order to observe safety regulations.

It is seen from Table 1 that the radioactive isotopes arising as a result of photonuclear reactions emit mainly β-radiation. The exceptions are the isotopes Fe$^{53}$ and V$^{52}$, which are both β- and γ-emitters.

The magnitude of the induced activity is determined by the expression [5]

\[ a = N_{\gamma}\sigma n \left(1 - e^{-\frac{0.693\,t_1}{T_{1/2}}}\right) e^{-\frac{0.693\,t_2}{T_{1/2}}} \frac{\text{decays}}{\text{sec}}, \tag{1} \]

where \(a\) is the induced activity in decays/sec;
\(N_{\gamma}\) is the flux of γ-quanta;
\(\sigma\) is the reaction cross section;
\(n\) is the number of atoms of the irradiated substance;
\(t_1\) is the irradiation time;
\(t_2\) is the time after irradiation;
\(T_{1/2}\) is the half-life of the active isotope.

Since photonuclear reactions occur at a definite energy of γ-quanta, in order to calculate the induced activity it is necessary to know the spectral composition of the bremsstrahlung. A sufficiently accurate approximation to the real bremsstrahlung spectrum can be the spectrum described by the expressions obtained by Schiff [8].

When calculating the number of atoms of the irradiated substance, it is necessary to know the percentage content of the given element, as well as the area of the irradiated region and its thickness.

The area of the irradiated region is found from the known values of the focal distance \(r\) and the divergence angle of the bremsstrahlung beam \(\gamma\). The thickness of the irradiated material from which the escape of β-radiation arising as a result of photonuclear reactions is possible is determined by the value of the maximum range of β-particles in the given substance, which is determined by the formula

\[ R_x = R_{\mathrm{Al}_m}\, \frac{\left(\dfrac{Z}{A}\right)_{\mathrm{Al}}} {\left(\dfrac{Z}{A}\right)_x}, \tag{2} \]

Table 1

where \(R_{\mathrm{Al}\,m}\) is the maximum range in aluminum.

Depending on the energy, the maximum range of \(\beta\)-particles is found from the empirical formulas [9]:

\[ \begin{aligned} &\text{for } E_{\beta\max}=0.03\div 0.15\ \text{MeV}; \qquad R_{\mathrm{Al}\,m}=0.15E_{\beta\max}-0.0028\ \text{g/cm}^2;\\ &\text{for } E_{\beta\max}=0.15\div 0.8\ \text{MeV}; \qquad R_{\mathrm{Al}\,m}=0.407E_{\beta\max}^{1.38}\ \text{g/cm}^2;\\ &\text{for } E_{\beta\max}>0.8\ \text{MeV}; \qquad R_{\mathrm{Al}\,m}=0.542E_{\beta\max}-0.133\ \text{g/cm}^2; \end{aligned} \]

\(E_{\beta\max}\) is the maximum energy of the \(\beta\)-spectrum;

\[ \left(\frac{Z}{A}\right)_{\mathrm{Al}} \quad \text{and} \quad \left(\frac{Z}{A}\right)_x \]

are the ratios of atomic number to atomic weight for aluminum and for the given element.

All \(\beta\)-particles arising at depths greater than \(R_x\) will be absorbed in the material. The number of atoms of the \(i\)-th element of the irradiated substance is found from the expression

\[ R_i=\frac{N}{A_i}mp, \tag{4} \]

where \(N\) is Avogadro’s number;
\(A_i\) is the atomic weight of the element;

\(m\) is the mass of the irradiated region, \(m=R\times Sp_i\); \(S=4r^2\tan^2\dfrac{\gamma}{2}\),

if the beam has a square cross section;
\(P_i\) is the weight content of the element.

The dose at the surface of the given region, produced by \(\beta\)-radiation, is found from the formula [6]:

\[ D_\beta=0.5\cdot 1.6\cdot 10^{-8}E_{\beta\max}\tau, \tag{5} \]

where \(\tau\) is the specific activity, disintegrations/sec.

For \(\gamma\)-emitting isotopes, the dose rate near the surface of the product can be determined from the formula [10]

\[ P=\frac{2\pi\Gamma a_v}{\mu}\{1-\Phi(\mu d)\}, \tag{6} \]

where \(a_v\) is the activity per unit volume;
\(\Gamma\) is the gamma constant of the isotope;
\(\mu\) is the attenuation coefficient;
\(\Phi(\mu d)\) is King’s function.

As an example, a calculation of the induced activity was carried out for structural steel, the principal constituents of which are iron and carbon. In the calculation the following data were adopted: maximum energy in the bremsstrahlung spectrum of the betatron \(E_{\gamma\max}=32\) MeV; bremsstrahlung dose rate \(P=200\) rad/min·m; focal distance \(r=1.5\) m; half-angle of divergence of the bremsstrahlung beam is \(6^\circ\); irradiation time of the product \(t_i=30\) min; the thickness of the inspected product corresponding to this time is 300 mm.

The results of the calculations are summarized in Table 2.

It follows from Table 2 that, after irradiation of the product for 30 min, the holding time will be determined by the \(\gamma\)-radiation, and in order to obtain the maximum permissible dose (2.8 mR/hour) [7] it must be 33 min.

For experimental determination of the induced activity in structural steel, a betatron with a maximum bremsstrahlung energy \(E_{\beta\max}\) of 35 MeV was used. The dose rate at a distance of 1 m from the target was 230 rad/min. A specimen in the form of a disk 2 cm in diameter and 2 mm thick was placed at a distance of 2 m and irradiated for \(t_i=8\) min. The results of measurements of the total activity using a gas-discharge counter in a lead house are presented

Table 2

in Fig. 1. The efficiency of the counter with respect to $\gamma$-quanta was 0.4%, and the geometrical factor was 0.095. The number of $\gamma$-quanta emitted by the specimen immediately after irradiation was $3.14 \cdot 10^{6}$ quanta/cm$^{2}\cdot$sec; the activity per unit volume was $a_v = 0.067$ microcurie.

Fig. 1. Dependence of the counting rate from the irradiated specimen on the time after irradiation.

The dose rate from the specimen, determined by formula (6), was 0.139 R/h. Recalculation of the experimental data to the conditions used in the calculation gives a dose-rate value of 1.77 R/h.

The total measured activity for $\beta$-radiation was $1.15 \cdot 10^{6}$ disintegrations/sec. Recalculation of the experimental data to the calculated conditions gives a total activity for $\beta$-radiation of $a = 1.23 \cdot 10^{8}$ disintegrations/sec.

The discrepancies between the calculated and experimental values are explained by the difference in the maximum energies of the bremsstrahlung assumed and used in the experiment, by error in determining the counter efficiency, by uncertainties in determining the reaction cross sections and their thresholds, and also by the possible presence of impurities in the irradiated specimen.

The experimental data confirm the formation of a sufficiently high induced activity during flaw detection of steel products using betatron bremsstrahlung and the need to establish a holding time after irradiation in accordance with safety requirements. The holding time can be reduced to zero by shortening the time spent in the radiation field.

On the inner surface of the irradiated product, the magnitude of the induced activity will depend on the thickness of the irradiated structure. The calculations we have performed show that the dose rates both for $\gamma$-radiation and for $\beta$-radiation, for a steel thickness equal to 300 mm, will be below the maximum permissible values.

In flaw detection of products made of alloy steels, the total induced activity, according to Table 1, will increase.

References

1. Photonuclear Reactions. Collection of articles edited by R. L. Barinsky and U. Ya. Margulis. Moscow, Foreign Literature Publishing House, 1953.

2. W. Riezler. Introduction to Nuclear Physics. Moscow, Foreign Literature Publishing House, 1968.

3. Katz L., Johnus H., Backer R. G. Phys Rev 82, 271, 1951.

4. Sher R., Halpern I., Mann A. K. Phys Rev 84, 387, 1951.

5. N. N. Shumilovsky, L. V. Meltser. Radioisotope methods for automatic control of the composition of complex media. Moscow–Leningrad, “Energiya,” 1934.

6. Radiation Dosimetry. Edited by Hine and Brownell. Moscow, Foreign Literature Publishing House, 1932.

7. Instructions for Working with Radioactive Substances and Other Sources of Ionizing Radiation in Scientific Institutions. Moscow, Publishing House of the Academy of Sciences of the USSR, 1963.

8. O. V. Bogdankevich, F. A. Nikolaev. Working with a Beam of Bremsstrahlung Radiation. Moscow, Atomizdat, 1964.

9. E. I. Dolgirev, P. I. Maleev, V. V. Sidorenko. Detectors of Nuclear Radiation. Leningrad, Sudpromgiz, 1961.

10. S. N. Ardashnikov, S. M. Goldin et al. Protection from Radioactive Radiation. Moscow, Metallurgizdat, 1934.