Investigation of scattered radiation from a betatron bremsstrahlung beam with maximum energies of 15 and 25 MeV after absorbers
Abstract Generated abstract
This paper examines scattered radiation and buildup factors for betatron bremsstrahlung beams with maximum energies of 15 and 25 MeV after passage through copper absorbers, motivated by applications in betatron flaw detection. The authors combine calculations by the method of successive collisions, with an approximate treatment of multiply scattered quanta, and an experimental method using a scintillation detector to infer integral radiation characteristics without constructing the detector crystal sensitivity matrix. The calculations indicate that, over the investigated thickness range, the buildup factor increases monotonically and can be approximated by monoenergetic sources of selected effective energies, reducing computational effort. Measurements with a NaI(Tl) detector and differential registration circuit are reported to agree reasonably with calculation, with deviations at larger thickness attributed to the approximate treatment of scattering.
Full Text
STUDY OF THE SCATTERED RADIATION OF A BETATRON BREMSSTRAHLUNG BEAM WITH MAXIMUM ENERGIES OF 15 AND 25 MeV BEHIND ABSORBERS
V. A. VOROB’EV, Yu. O. GAVKALOV, A. V. POKROVSKII
(Presented by the scientific seminar of the Laboratory of Dielectrics and Semiconductors)
The possibility is discussed of experimentally determining the buildup factor for a bremsstrahlung beam with a scintillation detector without constructing the sensitivity matrix of the crystal. Results of theoretical calculation and experiment are given. The study was carried out for problems of betatron defectoscopy.
The increasing role of betatrons in nondestructive methods for inspecting thick products, and the wide use of beams of high-energy bremsstrahlung in physics and medicine, make it necessary to conduct a comprehensive study of the transfer of energy of a flux of bremsstrahlung quanta through layers of various materials.
As a result of interaction with matter, the energy of a flux of electromagnetic-radiation quanta decreases owing to absorption or scattering. The determination of the quantitative and qualitative characteristics of scattered radiation is the most laborious and complex problem in theoretical and experimental solution.
As in the case of a monoenergetic point or plane source collimated in the direction \(x\), the attenuation of a narrow beam of a complex spectrum may be represented by Lambert’s law of attenuation
\[ J_{\mathrm{n.b.}}^{(x)} = J_0 e^{-\mu(E_{\mathrm{eff}})\,x}, \tag{1} \]
where \(J_{\mathrm{n.b.}}^{(x)}\) is the radiation intensity at absorber depth \(x\), \(J_0\) is the radiation intensity of the working beam of the betatron, and \(\mu(E_{\mathrm{eff}})\) is the attenuation coefficient of the complex spectrum, where \(E_{\mathrm{eff}}\) is defined as the energy of a monoenergetic flux of electromagnetic-radiation quanta whose attenuation in an absorber of thickness \(x\) is equivalent to the attenuation of the radiation intensity of the complex spectrum.
Similarly, to estimate the response of a detector to a complex spectrum, one may introduce the concept of the effective sensitivity of the detector, which is determined by the energy of a monoenergetic flux of electromagnetic-radiation quanta producing in the detector a signal of the same amplitude. For a betatron spectrum the effective energy \(E_{\mathrm{eff}}\) does not remain constant as the absorber thickness changes.
The radiation intensity behind an absorber in the case of a broad beam is conveniently represented for calculations by expression (1), with the introduction of a coefficient that takes into account the contribution of scattered radiation
\[ J_{\text{broad}}^{(x)} = B_{(x)} J_0 e^{-\mu(E_{\mathrm{eff}})x}, \tag{2} \]
where the coefficient \(B_x\) is customarily called the buildup factor [4]. Being an integral characteristic of scattered radiation, the buildup factor is determined by the ratio of the total intensity of quanta of electromagnetic radiation to the intensity of primary quanta at absorber depth \(x\). The buildup factor depends on the spectral composition of the betatron radiation, on the thickness, and on the physicochemical properties of the absorber.
Fig. 1. Experimental arrangement.
\(1\) — betatron, \(2\) — bremsstrahlung beam,
\(3\) — movable increment of the specimen, \(4\) — specimen,
\(5\) — detector shielding block.
To develop a method for experimental determination of the buildup factor, the flux and energy of singly and doubly scattered quanta of a complex spectrum in copper were calculated by the method of successive collisions for barrier geometry. Multiply scattered quanta of electromagnetic radiation were taken into account by the method proposed in [2].
The results of the calculation are presented in Fig. 2. It turned out that, over the thicknesses investigated, the buildup factor for a complex spectrum is a monotonically increasing function of thickness. This circumstance makes it possible, over separate thickness intervals, to identify with a high degree of accuracy the buildup factor for the corresponding selected energy with the buildup factor for the spectrum and thereby to reduce considerably the amount of computational work. Thus, the buildup factor of the spectrum \(E_{\max}=25\) MeV over the interval up to 300 mm of copper agrees, with an accuracy of \(\pm 4\%\), with the buildup factor of a monoenergetic source of 9 MeV; the buildup factor of the spectrum \(E_{\max}=15\) MeV agrees with the buildup factor of a monoenergetic source of 5.5 MeV. For these sources, the contribution of the energy fluxes of triply scattered quanta to the flux of quanta that have passed without interaction is, respectively, 7% and 15% at a copper thickness of 20 cm. Thus, the method of successive collisions proves rational for estimating the intensity of bremsstrahlung radiation behind an absorber up to 30–40 cm of copper, since, with calculation up to doubly scattered quanta, it is the least labor-intensive. At the same time, an error of 20–30% in estimating the energy contribution of multiply scattered quanta will not introduce a large error into the determined total energy flux.
Experimental investigations with a bremsstrahlung beam present considerable difficulty and laboriousness. The known methods of integral measurement of a broad beam are laborious, or the results are varia-
... cannot be interpreted with sufficient justification because of the complex nature of the change in the spectral composition of the scattered radiation as the absorber thickness increases.
The objective of the present work is to develop an economical and not labor-intensive method for obtaining integral characteristics of the radiation behind an absorber as applied to a scintillation detector. These characteristics are necessary for developing the theoretical foundations and determining ways to improve the methods of betatron flaw detection.
The prerequisite for developing the method is the circumstance that the response of a scintillator to a change in the radiation intensity over a certain absorber thickness \(\Delta x\) considerably exceeds the response to a change in the quality of the radiation spectrum. The possibility of realizing this phenomenon is determined by the parameters achieved in betatron flaw detectors [1].
Fig. 2. Buildup factor of bremsstrahlung as a function of absorber thickness.
1 — calculated for a spectrum with maximum energy \(E_{\max}=15\) MeV; 2 — calculated for monoenergetic radiation of 5.5 MeV; 3 — calculated for a bremsstrahlung spectrum with maximum energy \(E_{\max}=25\) MeV.
The flaw detectors developed by the Scientific Research Institute of EI TPI have the capability of recording a change in the energy flux of radiation when the absorber thickness is increased or decreased by 1% [1].
In the proposed method, the measured quantities are the radiation intensity behind an absorber of thickness \(x\) and the radiation intensity behind an absorber of thickness \(x+\Delta x\). The mathematical processing of the recorded quantities is as follows.
Differentiating expression (2), we obtain
\[ dJ_{(x)}= \frac{\partial B_{(x)}}{\partial x} J_0 e^{-\mu(E_{\mathrm{eff}})x}\,dx - B_{(x)}J_0 \frac{\partial \mu(E_{\mathrm{eff}})}{\partial E_{\mathrm{eff}}} \frac{\partial E_{\mathrm{eff}}}{\partial x} x e^{-\mu(E_{\mathrm{eff}})x}\,dx - \]
\[ - B_{(x)}\mu(E_{\mathrm{eff}})\cdot e^{-\mu(E_{\mathrm{eff}})x}\,dx \tag{3} \]
For a finite increment \(\Delta x\), one can write
\[ \frac{\Delta J_{(x)}}{J_{(x)}\Delta x} = \frac{1}{B}\frac{\partial B_{(x)}}{\partial x} + \left[ -\frac{\partial \mu}{\partial E_{\mathrm{eff}}}\frac{\partial E_{\mathrm{eff}}}{\partial x}\,x - \mu(E_{\mathrm{eff}}) \right]. \tag{4} \]
The left-hand side of the equation is the measured quantity; the expression in brackets is equal to the measured quantity \(-\dfrac{\Delta I}{I\Delta x}\) for a narrow beam and is found by extrapolation to a “zero” collimator area from successive measurements with a decreasing diameter of the collimator aperture.
Since the calculations carried out show that, over the range of thicknesses studied, the functions \(B(x)\) and \(\mu^{E_{\mathrm{eff}}}\) are smooth, the buildup factor can be found with high accuracy by numerical solution of the equation [4].
A number of works, for example [3], show good agreement between experiment and calculation using the Schiff spectrum; therefore, for determining the buildup factor \(B(x)\), calculated values of the function \(\mu^x\) may be used.
The error in finding the buildup factor will be determined by the accuracy of the method and of the measurements.
The accuracy of the method is determined by the degree of change in the quality of the radiation spectrum over the thickness \(\Delta x\) and by the sensitivity function of the detector. The attenuation of the photon flux of electromagnetic radiation by the NaJ(Tl) crystal used in the experiment was measured. A relative change in attenuation of not more than 0.5% was obtained for a 1% change in the copper thickness in the thickness interval 5–20 cm. Since the quality of the spectrum is not constant as the thickness changes, the conversion coefficient from attenuation energy to light pulse also changes. An estimate from the shift of the maximum of the calculated spectrum behind a copper thickness of 50–200 mm for \(E_{\max}=30\) MeV showed that in this case the effective sensitivity of the crystal changes by no more than a factor of 2.
It may be assumed that the accuracy of the method, obtained from an analysis of the change in relative attenuation for a layer \(\Delta x=1\%\) and of the effective sensitivity of the detector, is no worse than one percent.
The experiment was performed on the 5–30 betatron of the Scientific Research Institute of Electrical Instruments, TPI. To carry out the experiment, a differential registration circuit was developed [1]. A NaJ(Tl) crystal \(40\times 50\) and an FEU-12 were selected as the detector.
Copper plates of area \(100\ \text{cm}^2\) and thickness 50 mm were studied, with collimators having apertures of 5, 8, 12, 16, 20, 30, and with the crystal placed directly adjacent to the absorber. To approximate the theoretical model, a betatron collimator with an aperture diameter of 4 mm was installed. The front plane of the detector was at a distance of 1.9 m from the betatron target.
The basic experimental arrangement is shown in Fig. 1.
The measurement error
\[ \frac{\Delta U}{U} \sim \frac{\Delta I}{I} \]
is due to the accuracy of the method, the random process in the detector, the electrical circuits of the registration system, the measuring instrument, and the error in setting the collimator on the beam axis.
The calculated error for the parameters of the constructed registration circuit, with the betatron operating in the mode \(5\text{--}20\ \text{r/min}\cdot\text{m}\), does not exceed the accuracy of the method.
Owing to the use of the differential circuit and deep integration before the final amplifier of the measuring channel, it is possible
to maintain the high accuracy of the method when the betatron intensity is unstable by 10–15%. However, a considerable error is introduced by inaccurate alignment of the collimators and detector along the beam axis. To reduce this error, the beam axis was determined by the radiographic method for three points.
The results obtained are shown in Fig. 2. The 10% deviation of the experimental points at a thickness of 20 cm from the calculated ones is explained by the fact that the latter were calculated by an approximate method.
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