SPATIAL DISTRIBUTION OF RADIATION FROM A 10 MeV BETATRON

V. A. MOSKALEV

(Presented by the scientific seminar of the Faculty of Physics and Technology)

Electrons accelerated in an induction accelerator, at the end of the operating cycle, are displaced from the equilibrium orbit and directed onto a metal plate called the target. In the material of the target the electrons undergo intense braking. Part of the energy of the electron beam is expended on ionization of the atoms of the target and on heating it; another part goes into the formation of electromagnetic oscillations of very short wavelength—superhard bremsstrahlung rays.

Since the intensity of bremsstrahlung is proportional to the square of the charge \(Z^2\) of the nucleus of an atom of the target material, targets are made of a heavy element—tungsten.

The spatial distribution of bremsstrahlung in thin targets was considered theoretically by Schiff [1], Lawson [2], and a number of other authors. They all give approximately identical results. At electron energies of several MeV, the radiation propagates predominantly in the direction coinciding with the direction of motion of the electron beam at the moment of its “fall” onto the target. The theory predicts symmetry of the radiation distribution with respect to the beam axis and an inverse proportionality between the angle of 50% intensity and the initial energy of the electrons.

The degree of directionality of the radiation is customarily characterized by the angle between the direction of the axis of the radiation beam and the direction in which the intensity of the beam of rays is 50% of the maximum. The vertex of this angle lies at the point of formation of the radiation, i.e., at the focal spot of the target. For simplicity and brevity, this angle will hereafter be called the “half-intensity angle” of the radiation.

Figure 1 shows theoretical graphs of the radiation distribution for different target thicknesses. From the graphs we see that these curves have sharply pronounced—

Fig. 1

maximum corresponding to the propagation of gamma radiation predominantly in the “forward” direction at sufficiently high energies of the accelerated electrons.

Spatial distribution of the hard radiation of the betatron

In the present work an experimental determination was made of the pattern of the spatial distribution of the radiation from a 10-MeV betatron. The measuring instruments used were a dosimeter with a thimble-type graphite ionization chamber, with a wall thickness from 3 to 33 mm and a working volume of 1 cm³, made by us in the laboratory of the Tomsk Polytechnic Institute, and a standard instrument of the USD-6 type with an aluminum ionization chamber of volume 1000 cm³. The latter chamber served for continuous monitoring of the radiation output. The thimble chamber was placed at a distance of 1 m from the radiation source and could move smoothly along a circumference whose center lay at the location of the target. The procedure for moving the indicator chamber and all measurements were carried out from the control room with the aid of special devices. The arrangement of the experiment is shown in Fig. 2, and the results

Fig. 2. Experimental arrangement. 1. Control ionization chamber. 2. Selsyn actuator for moving the thimble ionization chamber. 3, 4—the outline of the betatron electromagnet.

of the measurements are presented as the graph in Fig. 3 (1). It is seen from the graph that the radiation of the 10-MeV betatron has a very sharply expressed intensity maximum. The direction of maximum intensity coincides with the direction of motion of the beam of accelerated electrons at the moment of its collision with the tungsten target. Upon deviation from the beam axis, the radiation intensity decreases sharply and reaches half the maximum value at an angular deviation of 10° to the left and 14.5° to the right. The subsequent course of the radiation-distribution curve is due to absorption of the quanta and their scattering in the various structural parts of the accelerator.

and therefore has an indeterminate shape. In the absence of such details the radiation will evidently vary smoothly from a maximum value to some minimum (dashed line, Fig. 3).

Fig. 3

Figure 4 presents the distribution of radiation in the main beam. Curve 2 is constructed from calculated data, and curve 1 from experimental data. The fairly good agreement of the theoretical and experimental graphs confirms the correctness of Lawson’s theory for the distribution of radiation from a thin betatron target. The existing deviation of the experimental curve from the theoretical one in the right-hand part of the graph is explained as follows. In the theoretical treatment of the problem it is assumed that the beam “falls” onto the center of a thin plate of strictly uniform thickness. In reality, under the action of the displacement pulse, the electron beam approaches the target along a spiral path with a very small pitch (of the order of \((5 \div 2)\cdot 10^{-5}\) cm). Therefore the electrons experience braking only at the outer edge of the target.

Fig. 4

For a sufficiently thick target this causes the appearance of an asymmetry in the radiation distribution, since the electrons deflected after the first collisions toward the edge of the target leave the target after traveling a shorter path in the target material than the electrons deflected

in the opposite direction. Thus, less radiation will arise on one side than on the other. This means that asymmetry in the angular distribution of the radiation of betatron- and synchrotron-type accelerators must always occur. The results of some authors who worked with accelerators at higher energies confirm this proposition [3].

The distribution of the radiation intensity in the vertical plane proved to be symmetrical; the “half-intensity angle” is \(17^\circ\), which agrees well with the value predicted by theory.

Presence of a Second Maximum in the Spatial Distribution of Betatron Radiation

In the course of investigating the spatial distribution of betatron radiation in 1950, we discovered the presence of a second radiation maximum, displaced relative to the main beam by \(15\)—\(20^\circ\), Fig. 3(2). This radiation is observed only in measurements with a thin-walled ionization chamber. The energy of the radiation here does not exceed \(1\) MeV and is completely absorbed by a material thickness of \(1.65\ \mathrm{g/cm^2}\). This soft radiation propagates around the betatron as a broad fan with a blunt, poorly defined peak.

The presence of a large amount of soft radiation, the direction of whose maximum does not coincide with the direction of the maximum of the hard radiation, was observed for five betatrons and is evidently characteristic of all betatrons of similar design.

Many experiments were carried out to determine the nature of the second radiation maximum, and it seems possible to us to explain the occurrence of intense soft radiation as follows.

The range of electrons with energy \(10\) MeV in tungsten is about \(2\)—\(3\) mm. The thickness of the target practically used in our betatron is \(0.2\)—\(0.4\) mm. Consequently, accelerated electrons, upon striking the target, have the possibility of “penetrating” it through and through, losing in the process a considerable part of their kinetic energy. Such electrons will be sharply turned by the magnetic field toward the center of the system and will “fall” onto the inner wall of the accelerating chamber. The most probable azimuth at which the electrons that have passed through the target will strike the wall of the accelerating chamber can be roughly determined from the equation relating the period of radial oscillations \(T_{\mathrm{osc}}\) of the electron to the period of revolution \(T_{\mathrm{rev}}\) of the electron in the equilibrium orbit [5]:

\[ T_{\mathrm{osc}} = T_{\mathrm{rev}}\left(\sqrt{1 - n}\right)^{-1}, \]

where \(n = 0.75\) is the exponent in the law of decrease of the magnetic induction.

It follows from the equation that the electron makes one complete oscillation in two revolutions around the center of the system. Consequently, electrons that have passed through the target may strike the wall of the accelerating chamber after making one revolution along the orbit, i.e., at an azimuth close to the azimuth of the position of the electron gun. In this case, upon braking in the material of the chamber walls and in the silver layer covering the chamber from the inside, the electrons will give rise to abundant soft radiation, coinciding with or deviating somewhat from the direction of propagation of the main, hard beam.

Consideration of the motion of electrons with different velocities (having different values of the constant \(C\)) [6] shows that the electrons must “fall” onto the inner wall of the chamber the sooner, the lower their velocity (electrons with lower velocity oscillate in potential wells with a lower inner barrier than electrons with higher

with a velocity) [7]. Thus, the greater the energy loss of an electron during braking in the target, the earlier the collision of the electrons with the chamber wall will occur, which will cause the maxima of the “hard” and “soft” beams of rays to approach one another. These considerations are confirmed by the experiment described below.

To study the nature of the spatial distribution of hard and soft radiations and the mutual position of their maxima as a function of the thickness and configuration of the target, a mechanism was designed and built that permitted several targets to be changed and adjusted without breaking the vacuum during operation of the betatron [3]. The mechanism was installed at the azimuth opposite to the azimuth of the gun location, and measurements were made of the spatial distribution of radiation from targets of various thicknesses.

Figure 5 a, b, c presents the results of measurements of the distribution of radiation from three tungsten targets of different thickness and configuration, showing a second (right-hand in the figure) maximum in the distribution

Fig. 5 a

Fig. 5 b

of the radiation, shifted from the main, hard beam by 10–15° toward the center of the system. It is interesting that for all three targets, having a th—

for targets of thickness 0.1 mm and 0.5 mm of cylindrical shape, a picture of the spatial distribution of the radiation was obtained with two clearly expressed maxima. The position of the left-hand maximum coincides with the direction of the tangent to the orbit at the point where the target is located. The second maximum for targets of thickness 0.5 mm is displaced relative to the first by 25°. For a target of thickness 0.1 mm this angle is 35°.

Fig. 5 c

The increase in the angle between the maxima when the thickness of the target is decreased confirms the correctness of the statement made concerning the origin of the second maximum in the spatial distribution of the radiation. With a smaller target thickness, the electrons that have passed through it can lose a smaller fraction of their kinetic energy than in the case of a thicker target.

Possessing greater kinetic energy, the electrons will approach the inner wall of the chamber along a less steep spiral and will strike the wall later (i.e., at a larger azimuth) than electrons that have passed through a thicker target and have lost a comparatively large fraction of their kinetic energy. This will cause the maximum of the soft radiation to shift toward larger angles.

LITERATURE

1. L. J. Schiff. Phys. Rev. 70, 87, 1946.

2. J. D. Lawson. The angular distribution of synchrotron target radiation. Proc. Phys. Soc. A 63, 563, 1950.

3. Moskalev V. A. Development and Investigation of a Betatron for Medical and Biological Research. Dissertation. Moscow, 1953.

4. D. J. Lees, L. H. Mettale. Measurement of polar diagram of synchrotron target radiation. Proc. Phys. Soc. A 63, 681, 1950.

5. Ternetskii Ya. P. On the stability of electron motion in the induction accelerator, betatron. Journ. of Phys. USSR, 9, 3, 1945.

6. Rodimov B. N. On the mechanism of electron capture into acceleration in a betatron. Izvestiya TPI, vol. 87, 1957.

7. Rechini J. A., and Cherry W. H. Journ. Frank. Inst. 243, 501–525, 345–391, 1947.