STUDY OF THE DEPTH DISTRIBUTION OF ABSORBED ENERGY OF HIGH-ENERGY BREMSSTRAHLUNG IN COPPER

V. A. VOROB'EV, A. V. PUSHKIN

A study has been carried out of the distribution of absorbed energy in copper, aluminum, graphite, and lead. The distribution curves of absorbed energy in all the materials have the same form; in the present work, therefore, only the results for the depth distribution of absorbed energy in copper are presented.

The source of high-energy bremsstrahlung is the synchrotron of the Tomsk Polytechnic Institute at 1.5 GeV. A collimated bremsstrahlung beam, purified of electrons, was incident on the absorber block. With a collimator of diameter \(10 \div 30\) mm and an air distance from the target of 12 m, the bremsstrahlung beam is approximately parallel. A study of the beam cross section before the absorber by the photometric method showed that the radiation field is uniform when the beam is collimated to a diameter of 30 mm.

The study of the depth distribution of absorbed energy (DDAE) was carried out by the photographic method [1, 2, 3, 6]. A set was assembled from absorber blocks 200 mm in diameter or from plates measuring \(100 \times 100\) mm. The total set reached a thickness of up to 200 mm for copper. At various depths of the absorber, paper cassettes with X-ray film were installed. The exposed films were processed simultaneously. This procedure made it possible to increase the accuracy of the measurements, since errors associated with instability in the operation of the accelerator and with the conditions of film processing were eliminated. The main errors remaining with the chosen method are due to changes in the sensitivity of the X-ray film over the area of the sheet and from sheet to sheet for one and the same type of film, and do not exceed 4%.

The total error of the method, taking into account the deviation of the characteristic curve from a linear dependence on the selected interval and the accuracy of photometry on the microphotometer, does not exceed \(7 \div 8\%\).

The study of the DDAE in copper was carried out using X-ray films of types RT-1, RT-2, and RM-1 at various exposure doses. In the experiments the bremsstrahlung energy was varied from 250 MeV to 1000 MeV.

The DDAE curves in copper for four values of the bremsstrahlung energy along the beam axis are shown in Fig. 1. They are similar to the curves of the depth distribution of absorbed energy for bremsstrahlung energies of several tens of MeV [2, 4, 7, 8].

At absorber depth \(t \to 0\), the value of the absorbed energy is not equal to 0 and depends on the bremsstrahlung energy. For copper it varies—

varies from 0.04 to 0.09 of the dose at the maximum of the DDAE curve when the energy changes from 1000 MeV to 250 MeV. As the bremsstrahlung energy increases, the position of the maximum of absorbed energy shifts

Fig. 1. Depth distribution of absorbed energy in copper along the beam axis at various bremsstrahlung energies

into the depth from the front wall of the absorber. Thus, for bremsstrahlung energies of 250, 500, 750, and 1000 MeV, the maximum of absorbed energy is located at depths of 20; 23.7; 25; and 26.3 mm. The values of \(t_{\max}\) for energies of 250 and 500 MeV agree well with the results obtained in [5] for a bremsstrahlung energy of 330 MeV. Using the data obtained on the position of the maximum of absorbed energy and data obtained by other authors, for example [4], one can construct the dependence on bremsstrahlung energy in the interval from several MeV to 1000 MeV. Such a dependence was constructed by us. Its form is similar to the analogous dependence given in [2].

The rate of decrease of the absorbed-energy value after the maximum depends on the magnitude of the bremsstrahlung energy. As the bremsstrahlung energy increases, it increases, which is probably due to the increase of the linear attenuation coefficient in copper with increasing bremsstrahlung energy within the indicated limits.

Comparison of the DDAE curves obtained in our work by the photomethod with the DDAE curves obtained by the ionization method using extrapolation chambers [4, 5] shows that the falloff of the latter occurs more slowly. This difference is due to the measurement technique and is also observed at low bremsstrahlung energies [3]. In measurements with an extrapolation chamber, the mean value over the whole area is measured, whereas with the photomethod measurements are made at a point. This should be especially pronounced for small collimator dimensions.

...when the relative magnitude of energy “leakage” from the beam projection is large.

Figure 2 shows curves of the radial distribution of absorbed energy over the beam cross section in copper, in relative units, at various absorber depths for bremsstrahlung energy of 1000 MeV and a collimator diameter of 10 mm. The absorbed energy on the beam axis is taken as 100%. As can be seen, with increasing absorber depth the uniformity of the absorbed-energy distribution over the beam projection deteriorates, and the relative magnitude of energy “leakage” increases.

Vertical axis: absorbed energy, relative units.
Horizontal axis: \(R\), mm.

Fig. 2. Distribution of absorbed energy over the beam cross section in copper at various absorber depths: curve 1—5 mm; 2—10 mm; 3—30 mm; 4—50 mm.

A similar dependence in the distribution of absorbed energy over the beam cross section is observed at other values of bremsstrahlung energy. A further increase in absorber depth (more than 50 mm for copper) is accompanied by convergence of the curves of the radial distribution of absorbed energy. At depths of 100–120 mm they merge into one.

We believe that the TDAE curves obtained by the photographic method satisfactorily reflect the true picture and do so more accurately than those obtained by the ionization method using an extrapolation chamber.

The authors express their deep gratitude to Professor Doctor Aleksandr Akimovich Vorob'ev for suggesting the topic and supervising the research.

References

1. E. Charlton and H. Bread. Amer. J. Roentgenol., 60, No. 2, 158 (1948).
2. B. M. Isaev, M. I. Shal'nov. Atomic Energy, 6, issue 1, 57 (1959).

1. V. A. Balitskii, E. A. Vainer, V. S. Grammatikati, A. M. Litvitskii, I. R. Merkushev, A. A. Nelyubov. Dosimetry of Large Doses. Proceedings of the Second Coordination Meeting on Dosimetry of Large Doses. Tashkent, “FAN” Publishing House, 1966.

2. S. P. Kruglov. ZhTF, XXXI, no. 9, 1092 (1961).

3. W. Blocker, R. M. Kenney, W. K. H. Panofsky. Phys. Rev., 79, 419, 1950.

4. V. A. Vorob’ev. Dissertation, Tomsk, TPI, 1965.

5. V. A. Vorob’ev, V. N. Rudenko. Izv. TPI, 140, 90 (1965).

6. V. A. Vorob’ev, V. N. Rudenko. Izv. Vyssh. Uchebn. Zaved. SSSR, Fizika, 2, 174 (1965).