SCINTILLATION METHOD FOR FLAW DETECTION WITH A MONOENERGETIC ELECTRON BEAM

B. A. Kononov, V. V. Evstigneev, V. M. Zykov

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

In [1] it was shown that, in the thickness range of \(2 \div 3\ \mathrm{g/cm^2}\), quality control of products is expediently carried out using a monoenergetic beam of fast electrons. The use of a monoenergetic electron beam is most expedient for the inspection of layered products, when a layer of light material shielded by layers of heavy material is being inspected. In a certain range of ratios of the mass thicknesses of the heavy and light layers, inspection by X-radiation is impossible because of the strong attenuation of the bremsstrahlung beam in the layer of heavy material. In [1] an analysis is given of the attainable sensitivity of inspection by a monoenergetic electron beam on the basis of the experimentally obtained distribution of the absorbed beam energy in materials of different chemical composition, and it is shown that, for inspection, it is most expedient to use the linear portion of the absorbed-energy distribution. The present work gives an approximate analysis of the sensitivity of the scintillation method of inspection with a monoenergetic electron beam and presents experimental results of a sensitivity study.

The sensitivity of the scintillation method of flaw detection with an electron beam is most simply estimated under the assumption that the detector material (scintillator and light guide), in effective atomic number, differs little from the material of the product being inspected, and that the probing electron beam is narrow in comparison with the radius of the detector located behind the product being inspected, \(r_0\ 0.5R_\mathrm{e}\), where \(R_\mathrm{e}\) is the extrapolated range of electrons in the material of the product being inspected. In this case, to estimate the sensitivity one can use the known data on the energy dissipation of a monoenergetic electron beam in a semi-infinite homogeneous absorber. Depending on the size of the sensitive region of the scintillation detector \(x_c\) in the direction of transmission, the initial energy of the electron beam \(E_0\), and the mass thickness of the product being inspected \(x\), the detector readings will be proportional to the energy of the electron beam \(D(x)\) absorbed at depth \(x\) in the material of the product, or to the total energy of the electron beam \(I(x)\) beyond the product being inspected. The energy of the electron beam absorbed in the sensitive volume of the detector, in the case where \(x_c \ge R_{\mathrm{res}}\), where \(R_{\mathrm{res}}\) is the residual range of the electrons in the scintillator material, as a function of the thickness of the product being inspected \(x\), can be represented in the form

\[ I(x)=\overline{E}(x)\cdot \eta(x), \tag{1} \]

where

\(E(x)\) is the mean energy of the electrons behind the inspected article,

\(\eta(x)\) is the attenuation of the electron flux in the beam by the inspected article. In formula (1), the quantity \(I(x)\) is normalized to one electron incident on the inspected article. The mean energy of electrons with initial energy \(E_0\) behind a layer of material of thickness \(x\) can, with sufficient approximation, be written in the form

\[ \overline{E}(x)=E_0\left(1-\frac{x}{R_{\mathrm{e}}}\right). \tag{2} \]

Substituting the value \(\overline{E}(x)\) into expression (1), we have

\[ I(x)=E_0\left(1-\frac{x}{R_{\mathrm{e}}}\right)\eta(x). \tag{3} \]

Here \(R_{\mathrm{e}}\) is the extrapolated range of electrons with initial energy \(E_0\) in the material of the inspected article, expressed in \(\mathrm{g}/\mathrm{cm}^2\). The energy absorbed at depth \(x\) can be found from the formula

\[ D(x)=\frac{dI(x)}{dx} = E_0\left[ \frac{d\eta}{dx}\left(1-\frac{x}{R_{\mathrm{e}}}\right) - \frac{\eta}{R_{\mathrm{e}}} \right]. \tag{4} \]

For the attenuation of the number of electrons \(\eta(x)\) of a monoenergetic electron beam by barriers of different chemical composition at different initial energies, there exist a number of empirical formulas based on experimental studies and Monte Carlo calculations [2, 3, 4].

To obtain an expression for \(D(x)\) on its rectilinear segment \((x=0.6\div0.9\,R_{\mathrm{e}})\), it should be taken into account that the extrapolated ranges determined from the rectilinear portions of \(\eta(x)\) and \(D(x)\) practically coincide. The value of the derivative \(d\eta/dx\) on the linear portion of \(\eta(x)\) can be expressed through \(R_{\mathrm{e}}\)

\[ \frac{d\eta(x)}{dx} = -\frac{\eta(x)}{R_{\mathrm{e}}}\, \frac{1}{1-\dfrac{x}{R_{\mathrm{e}}}} . \tag{5} \]

Hence, for the linear part of \(D(x)\) we have

\[ D(x)=-2\frac{E_0}{R_{\mathrm{e}}}\eta(x), \tag{6} \]

where the “minus” sign indicates that the energy of the electron beam decreases.

From expressions (3) and (6) one can estimate the sensitivity of the scintillation method of flaw detection with fast electrons in cases where \(x_c \ll R_{\mathrm{ost}}\) and \(x_c \gg R_{\mathrm{ost}}\). For the case \(x_c \ll R_{\mathrm{ost}}\), differentiating expression (6) with respect to \(x\) and passing to finite increments, we obtain, taking (5) into account,

\[ \frac{\Delta D}{D} = \frac{1}{1-\dfrac{x}{R_{\mathrm{e}}}}\, \frac{\Delta x}{x}, \tag{7} \]

where \(\dfrac{\Delta D}{D}\equiv \delta D\) is the relative change in absorbed energy caused by the relative change in the thickness of the inspected article \(\dfrac{\Delta x}{x}\equiv\delta x\). The minimum detectable relative change in the thickness of the inspected article is equal to

\[ \delta x_{\min} = \xi\left(1-\frac{x}{R_{\mathrm{e}}}\right)\delta D_{\mathrm{n}}, \tag{8} \]

where

\(\delta D_{\mathrm{p}}\) is the threshold sensitivity of the flaw detector, equal to the relative change in the output signal due to the combined action of all destabilizing factors,

\(\xi = 3\) is the reliability coefficient,

\(x = (0.6 \div 0.9) R_{\mathrm{e}}\) varies within the limits of the linear portion \(D(x)\).

For the case of a scintillator with complete absorption \((x_c \geq R_{\mathrm{res}})\), the inspection sensitivity, taking into account the expression for \(dI/dx\) in the form (6), is equal to:

\[ \delta x_{\min} = \xi \frac{R_{\mathrm{e}}}{2x} \left( 1 - \frac{x}{R_{\mathrm{e}}} \right) \delta I_{\mathrm{p}}, \tag{9} \]

where \(\delta I_{\mathrm{p}}\) is the threshold sensitivity of the flaw detector for the case under consideration. From a comparison of the inspection sensitivity in the case where \(x_c \ll R_{\mathrm{res}}\), and in the case where \(x_c \geq R_{\mathrm{res}}\), it follows that a scintillator with complete absorption of electrons provides a sensitivity greater by a factor of

\[ \frac{2x}{R_{\mathrm{e}}}. \]

In practice, the electron beam is accompanied by bremsstrahlung, which is generated in the structural elements of the monoenergetic-electron source, in the collimating device, and in the article being inspected. The bremsstrahlung accompanying the electron beam is recorded by the detector as background, which undergoes fluctuations associated with fluctuations in the intensity of the electron beam; this leads to a decrease in inspection sensitivity. The sensitivity of a single-channel flaw-detector scheme, taking background into account, is

\[ \delta x'_{\min} = \xi \frac{2x}{R_{\mathrm{e}}} \left( 1 - \frac{x}{R_{\mathrm{e}}} \right) (1 + N) \delta I'_{\mathrm{p}}, \]

where

\(N\) is the ratio of the component of the detector signal caused by the constant component of the background to the component of the detector signal caused by the electrons that have passed through the inspected article,

\(\delta I'_{\mathrm{p}}\) includes fluctuations of the detector signal due to the background.

Since in practice the main contribution to bremsstrahlung is made by the bremsstrahlung generated in the structural elements of the monoenergetic-electron source, the contribution of bremsstrahlung to the detector signal can be reduced by applying focusing of the electron beam at the entrance to the collimating device and by using additional shielding of the detector unit from scattered bremsstrahlung.

The efficiency of recording bremsstrahlung by a scintillation detector increases with increasing scintillator dimensions. Therefore, in order to reduce the contribution of bremsstrahlung to the detector signal, the initial energy of the electron beam \(E_0\) must be chosen so that the thickness of the article is closer to the extrapolated range of the electrons \(R_{\mathrm{e}}\). In doing so, it must be taken into account that, as the value of \(R_{\mathrm{e}}\) approaches the size of the article, the statistical error of measurement and the error due to fluctuations of the initial electron energy \(E_0\) increase.

When a scintillation detector is used, the instability of the output signal of the recording device consists of the instability due to fluctuations of the initial energy of the electron beam, instability of the intensity of the electron source, instability of the spatial position of the electron beam, the statistical error of measurement due to the statistical nature of the interaction of electrons with matter, and instability of the detector gain coefficient, to which the main contribution is made by the instability of the coeffici-

…of the photomultiplier gain and the instability of the bremsstrahlung background. Instabilities of the output signal caused by instability of the initial energy, instability of the electron-source intensity, and the bremsstrahlung background can be reduced severalfold by using a differential measurement circuit, owing to the deterministic character of these instabilities. The expression for the inspection sensitivity in the form of (9) also remains valid for the case in which a differential measurement circuit is used, if \(\delta I_n\) is understood as the ratio of the fluctuations at the output of the differential circuit to the signal magnitude at the input of the differential circuit. The inspection sensitivity calculated from formula (9) is presented in Fig. 1 for the case \(\delta I_n = 0.02\). From the nature of the dependence it is clear that \(\delta x_{\min}\) decreases as \(x \to R_{\mathrm{e}}\). Since, in calculating the sensitivity, no account was taken of the increase in \(\delta I_n\) as \(x \to R_{\mathrm{e}}\) due to the increasing contribution of the background, statistical error, and the influence of the instability of the energy \(E_0\), in the real case, as \(x \to R_{\mathrm{e}}\), the sensitivity increases up to a certain limit determined by the combined instability due to the factors indicated.

Fig. 1. Dependence of the minimum detectable change in thickness on the ratio of the product thickness \(x\) to the extrapolated electron range \(R_{\mathrm{e}}\) at \(\delta I_n = 0.02\)

Since the change in the characteristics of the electron beam when the thickness of the absorber, expressed in \(\mathrm{g/cm^2}\), is varied depends only weakly on the effective atomic number of the absorber material, then in the case of inspection of layered materials, when the inspected layer of material with a small atomic number is shielded by a material with a large atomic number, the inspection sensitivity will practically be determined by the relative nonuniformity of the thickness of the high-\(Z\) layer, \(\delta x_{\mathrm{t}}\),

\[ \delta x_{\min} = k \xi \delta x_{\mathrm{t}}, \tag{11} \]

where

\(k\) is the ratio of the mass thickness of the layer with large atomic number to the mass thickness of the layer with small atomic number,

\(\xi\) is the reliability coefficient.

The inspection sensitivity for a low-\(Z\) material shielded by layers of high-\(Z\) material can be substantially increased if, into the signal at the output of the scintillation flaw detector, one introduces a correction for the change in the thickness of the high-\(Z\) layers by measuring them with one of the known inspection methods, for example, the electromagnetic method.

An experimental investigation of the sensitivity of the scintillation method of inspection by fast electrons was carried out using a practically monoenergetic electron beam with an energy of \(3 \div 6\ \mathrm{MeV}\) and a differential measurement circuit on specimens with a mass thickness of \(1.5 \div 2\ \mathrm{g/cm^2}\). An inspection sensitivity of \(0.3\%\) of the total mass thickness of the inspected specimen was obtained for transverse dimensions of defect simulators equal to the diameter of the probing electron beam and a linear inspection speed of \(0.25\ \mathrm{m/min}\).

In the case of layered specimens, the validity of expression (11) for the sensitivity of inspection has been experimentally confirmed.

In conclusion, it should be noted that the formulas given above for estimating the sensitivity of the scintillation method of inspection using a beam of monoenergetic electrons are also applicable to the case of semiconductor electron detectors.

REFERENCES

1. B. A. Kononov, K. A. Dergobuzov, Yu. M. Stepanov, “Defektoskopiya,” No. 4, p. 77, 1968.
2. B. N. Subba Rao, Nucl. Instrum. and Methods, 44, 155, 1966.
3. B. W. Mar, Nucl. Science and Engin., 24, No. 2, 193, 1966.
4. D. Harder, G. Posehet, Phys. Letters, 24B, No. 10, 510, 1967.