On the Study of the Distribution of Fast Electrons Stopped in Matter
Abstract Generated abstract
This paper describes the design and testing of a vacuum detector for measuring the depth distribution of fast electrons stopped in matter, a quantity relevant to estimating low-energy electron spectra and radiation damage. The method uses a movable collecting electrode and backscatterer arrangement, with attention to operating pressure, electrode thickness, secondary-electron effects, beam geometry, and current measurement sensitivity. Measurements for aluminum and copper at initial electron energies of 3.2, 4.9, and 8.1 MeV show distributions with maxima whose positions depend on energy and atomic number, and provide relative half-width values for each material and energy. The authors note that the steep rear slope of the aluminum distributions may allow more accurate determination of monochromatic electron-beam energy than conventional transmission curves.
Full Text
ON THE STUDY OF THE DISTRIBUTION OF FAST ELECTRONS STOPPED IN MATTER
K. A. Dergobuzov, O. B. Evdokimov, B. A. Kononov
(Presented by the scientific seminar of the Faculty of Physics and Engineering)
The character of radiation damage in substances is determined by the electron spectrum, the low-energy part of which can be estimated from the distribution of stopped electrons. The form and the relative half-width of the distribution provide information on the influence of multiple scattering and fluctuations of energy losses on the passage of electrons through thick layers of substances.
This article reports the design and testing of an instrument for recording the distribution of electrons stopped in matter, \(I(x)\), from a betatron with initial energy from 2 to 15 MeV. Results of measurements in aluminum and copper are presented.
Design of the Detector and Its Characteristics
The distribution of electrons stopped in matter was measured by moving a thin plate of the material under study—the collecting electrode 1 of the detector (Fig. 1)—through the depth of the substance under study by increasing the thickness of the absorber in front of it. Behind the collecting
Fig. 1. Design of a detector of stopped electrons
A backscatterer made of the material under study, with a thickness greater than the maximum range of the source electrons, is installed behind the collecting electrode; this makes it possible to compare the measurement results with calculations for a semi-infinite absorber.
To avoid the influence of ionization [1] on the instrument readings, the air is pumped out of its volume.
To determine the optimal operating pressure, the dependence of the instrument readings on the pressure inside it was measured; it is shown in Fig. 2. The curve was obtained for an electron energy of 7.9 MeV and an aluminum absorber thickness of 10 mm in front of the detector. The operating region
Fig. 2. Dependence of the instrument readings on the air pressure inside it at the maximum of the distribution for an electron energy
begins at a pressure of \(10^{-2}\) mm Hg; the observed reversal of the sign of the measured current indicates that, at atmospheric pressure, the instrument operates in the mode of a capacitor ionization chamber.
The accuracy with which the distribution of stopped electrons is obtained also depends on the thickness of the collecting electrode. In order to determine the optimal electrode thickness, a study was carried out of its effect on the accuracy of recording the distribution. It turned out that an electrode thickness of \(2.5\%\)–\(5\%\) of the mean total electron range provides the required accuracy. In this case, on the one hand, the measured current has an acceptable magnitude, while on the other hand the distributions are recorded
Fig. 3. Experimental distributions of stopped electrons in aluminum at initial energies of 3.2, 4.9, and 8.1 MeV.
Fig. 4. Experimental distributions of stopped electrons in copper at initial energies of 3.2, 4.9, and 8.1 MeV.
with a small error due to the finite thickness of the electrode \(d\). The error does not exceed the following value:
\[ \delta < \left| \frac{(x_1+d)^n-\dfrac{n}{2}x_1^{\,n-1}d+\dfrac{n(n-1)}{3}x_1^{\,n-2}d^2}{(x_1+d/2)^n} - 1 \right|, \]
where \(n\) is the order of the polynomial by which the distribution can be approximated within the thickness of the collecting electrode. The readings of the instrument, divided by the electrode thickness, were referred to the depth in the material corresponding to the midpoint of the electrode thickness.
To study the influence of secondary electrons with energies up to 10 keV, grids were installed between the collecting electrode (1), the flange (4), and the backscatterer (2) (not shown in Fig. 1), to which a voltage from 0 to 10 kV was applied through the lead-in (5). The upper limit is determined by the fact that the predominant number of secondary electrons have energies within 10 keV in the investigated range of initial energies [2].
The lower boundary of the investigated energy range, 2 MeV, is determined by the thickness of the front flange (400 \(\mu\)m Al), and the upper one by the lateral spread of the electron beam in the material. The beam passes through a collimator 15 mm in diameter; at larger dimensions, a noticeable number of electrons scattered in the absorber misses the collecting electrode, which is especially significant for materials of low density. A further reduction of the collimator diameter is impractical because of the small magnitude of the measured currents.
The current of the collecting electrode is measured by the dc amplifier of a “Cactus” micro-rentgenometer, with compensation of the measured current, so that the amplifier operates as a null instrument. This makes it possible to eliminate error due to nonlinearity of the amplifier and mismatch of its scales. The use of a vacuum fluoroplastic insulator made it possible to measure reliably currents down to \(10^{-12}\) A.
Experimental results and their discussion
The distribution \(l(x)\) of stopped electrons is obtained by increasing the absorber thickness in front of the detector and measuring the current from the collecting electrode at a given thickness. Measurements were carried out in aluminum and copper at energies 3.2, 4.9, and 8.1 MeV; the results are presented in Figs. 3 and 4. All curves have maxima that shift toward smaller thicknesses when the energy and the atomic number of the material decrease, even if the thickness is expressed in units of the mean actual range of the source electrons.
To characterize the curve \(l(x)\), it is reasonable to introduce the relative half-width: the ratio of the width of the distribution at half-height to the mean actual range. The half-width values for Al at energies 3.2, 4.9, and 8.1 MeV are respectively 0.61, 0.59, and 0.57; and for copper at energies 3.2, 4.9, and 8.1 MeV they are respectively 0.63, 0.52, and 0.55.
It is necessary to note the following practically important circumstance. The steepness of the falling part of the curves in aluminum (the rear front) is significantly greater than that of electron transmission curves, which makes it possible to expect that the distributions may serve as a basis for determining the energy of a monochromatic beam with greater accuracy than from transmission curves.
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