Extraction of an Electron Beam from the Betatron Chamber

L. S. Sokolov

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

This article reports the experimental realization of the extraction of a beam of electrons with an energy of 10 MeV from a betatron. The proposed method for extracting electrons from a betatron does not involve the presence of an extraction device located inside the vacuum chamber of the betatron. In essence, it may be regarded as the limiting case of displacement of the equilibrium orbit of the electrons from its initial positions. This method has not been described in the literature known to us, and we have implemented it for the first time.

For extracting an electron beam from the betatron we used a ceramic vacuum chamber, manufactured according to our drawing at the Leningrad Porcelain Factory named after M. V. Lomonosov (Fig. 1).

Fig. 1. Sketch of the vacuum chamber for extracting electrons with an energy of 15 MeV from a betatron.

An injector is placed in branch pipe 1. It is located in the plane of the equilibrium orbit on the circumference where the fall-off index of the magnetic field [[unclear: text continues off page]].

$n=1$. On the rear side of the injector there is a tungsten target. The exit window 2 is closed with copper foil 0.2 mm thick, which is soldered to a brass flange. Separate tungsten targets are placed in branch pipes 3 and 5. Branch pipe 4 was used for evacuating the vacuum chamber.

For convenience in carrying out the experiments, the displacement windings were made in the form of 24 coils, 4 turns in each coil, which are fastened to two thin (0.5 mm thick) textolite disks (Fig. 2). One of the disks is placed under the vacuum chamber, the other above it. Each pair of opposite coils forms a displacement winding of azimuthal extent $\Theta_1 = 30^\circ$. The individual displacement windings can be connected in series in any combinations, giving different angles $\Theta_1$ and different azimuthal positions of the winding in the interpole space of the betatron. There is also a winding (10 turns) on the central inserts (galettes) and a special winding (Fig. 3), making it possible to change the magnitude of the perturbation of the betatron magnetic field in radius.

Fig. 2. Windings for displacing the equilibrium orbit.

Fig. 3. Special displacement winding.

The first experiments were carried out with a displacement winding of extent $\Theta_1 = 135^\circ$, arranged as shown in Fig. 4. The pulsed current flowing through the displacement winding produces, by its magnetic field, a weakening of the guiding magnetic field of the betatron. The electron orbit is displaced outward, in the direction of branch pipe 5 (Figs. 4 and 1), until the electrons are freed from the influence of the focusing forces toward the orbit. At least $1/5$ of the beam enters the exit window and, through the copper foil, leaves the vacuum chamber. The extraction efficiency obtained is twice as high as the efficiency achieved by Skaggs [1] in extracting electrons with a magnetic shunt, and is almost equal to the efficiency of electron extraction by means of an electric capacitor, achieved by Gund [2] without the use of scattering foil.

Fig. 4. General scheme for extraction of an electron beam with an energy of 10 MeV from the betatron.
1 and 2—ionization chambers.

In Fig. 5 are shown photographs of the electron beam, taken perpendicular to the beam axis directly at the exit window (upper photograph) and at a distance of 10 cm from it (lower photograph). The horizontal size of the beam at the exit of the electrons from the window is 6 cm and is equal to the horizontal size of the exit window. With the aid of a thimble ionization chamber of the “Pion” type, we measured the ionization distribution over the horizontal cross section of the beam. This distribution is shown in Fig. 5 above the photographs of the beam. The numerical values of the ionization intensity are given in the table.

Fig. 5. Photographs of the beam.

Table

The electron density is distributed nonuniformly over the horizontal cross section of the beam. There is a maximum in the electron density.

At a distance of 10 cm from the window the beam cross section is considerably larger. In comparison with the dimensions of the beam directly at the chamber window, the radial size of the beam at a distance of 10 cm from the window increases by a factor of 1.5, and the height of the beam by a factor of 5. The increase in the dimensions of the beam is due to the scattering of the electrons as they pass through the copper foil and in air.

To determine the trajectory of the extracted beam inside the vacuum chamber, the following experiment was carried out. An ionization chamber of volume 200 cm³ was placed at the location where maximum ionization is produced (point 1 in Fig. 4). A tungsten target mounted in branch pipe 3 (Fig. 1) was gradually moved into the vacuum chamber. For each position of the target, the radiation recorded by the 200 cm³ chamber was noted (Fig. 6). As the target was moved into the vacuum chamber, the radiation

at first does not change. This means that the electrons leave the vacuum chamber without striking the target. Then the intensity increases somewhat (by 5%). The increase in intensity is due to the fact that some of the electrons are scattered at the edge of the target. Their angle of emergence outward increases. Finally, a sharp decrease in the radiation intensity occurs. The target intercepts the emerging electron beam. The interval of displacement of the target corresponding to complete blocking of the electron exit by the target may be taken as equal to the radial size of the beam at the azimuth of the target.

Now we can represent the general extraction scheme (Fig. 4), from which it is not difficult to determine the mean angle \(\varphi_{\mathrm{av}}\) of emergence of the beam outward and the angle \(\psi\) of divergence of the beam inside the vacuum chamber, if the distance along the beam axis from target 3 (Fig. 1) to the foil of window 2 (Fig. 1) is 32 cm,

\[ \varphi_{\mathrm{av}} \simeq 9^\circ,\qquad \psi \simeq 10^\circ . \]

The divergence of the beam in air is approximately \(17^\circ\) horizontally.

Fig. 6. Change in the ionization intensity at point 1 (Fig. 4) with change of the radial coordinate of target 3 (Fig. 1).

The magnitude of the current of accelerated electrons, measured by a Faraday cylinder at a distance of 3 cm from the extraction window, is \(2\cdot 10^{-10}\) A. The extraction efficiency is not less than 22%.

In accordance with the results obtained, it is expedient to introduce the concept of external and internal losses of electrons; in this case, the electrons constituting the inner part of the emerging beam and failing to enter the extraction window because of collisions with the walls of the vacuum chamber determine the internal losses, while the electrons lost outside the axis of the emerging beam determine the external losses. We measured the relative magnitude of the external losses by means of ionization chamber 2 (Fig. 4).

Work on increasing the extraction efficiency should expediently begin with a study of the effects on the processes of orbit displacement and release of electrons from the influence of the focusing forces when changing the dimensions, shape, and position of the displacing winding. Let us determine the significance of the components of the forced motion of electrons under the action of inhomogeneities in the betatron control magnetic field. The relative magnitude \(\varepsilon_m\) of the components of the forced motion depends on the order of the harmonic \(m\) and on the azimuthal extent \(\Theta_1\) of the inhomogeneity in the betatron control magnetic field.

In the linear approximation [3]

\[ \varepsilon_0=\frac{\Theta_1}{2(n-1)}, \]

\[ \varepsilon_m= \frac{2\sin \dfrac{m\Theta_1}{2}} {\pi(m^2+n-1)} . \tag{1} \]

When \(\Theta_1\) is changed, \(\varepsilon_0\) and \(\varepsilon_m\) change in accordance with formulas (1). For example, when \(\Theta_1=\pi\), the first harmonic has its maximum value, while the second harmonic is absent. When \(\Theta_1=\dfrac{\pi}{2},\ \dfrac{3}{2}\pi\), the second harmonic has maximum positive or negative values, while the first harmonic is considerably smaller than its maximum value (at \(\Theta_1=\pi\)), etc.

The question arises: how will the efficiency of extraction of electrons from the accelerator chamber change when the azimuthal extent of the winding \(\Theta_1\) is changed?

The experiment was carried out as follows.

The displacing winding and ionization chamber 1, which recorded the intensity of the beam of accelerated electrons emerging from the vacuum chamber, were installed as shown in Fig. 4.

Fig. 7. Effect of the azimuthal extent of the displacing winding \(\Theta_1\) on the extraction efficiency \((J)\).

Without changing the azimuthal position of the midpoint of the displacing winding, we varied the azimuthal extent of the winding \(\Theta_1\). In all, 5 windings were tested: \(\Theta_1=90,\ 150,\ 210,\ 270,\ 330^\circ\). For each winding the intensity of the electron beam emerging from the chamber was measured. The result of the experiment is the graph in Fig. 7, from which it follows that changing the azimuthal extent of the displacing winding within the limits \(90\div270^\circ\) and the corresponding change in the relative magnitude of the components of the forced motion does not lead to a change in the extraction efficiency. At \(\Theta_1=270^\circ\) the electron output ceases, since the first harmonic of the forced oscillations is greatly reduced and the displacement of the orbit becomes symmetric.

When \(\Theta_1\) is changed, the mean angle \(\varphi_{\text{av}}\) of emergence of the electron beam outward and the angle \(\psi\) of divergence of the beam inside the vacuum chamber also remain unchanged.

The experiment shows that, before the electrons are freed from the influence of the focusing forces, there arises such a regime of forced oscillations that does not depend on the azimuthal extent of the displacing winding. It follows that, whatever combinations of displacing windings we may create, provided only that the relative magnitude \(\varepsilon_1\) of the first harmonic of the forced oscillations does not become smaller than some critical value, the efficiency of extraction of electrons from the accelerator cannot be changed.

The azimuthal extent of the displacing winding may be chosen such that the minimum reactive energy is required for complete removal of the accelerated electrons from the working zone of the betatron [4].

Let us return again to Fig. 4. Take \(\Theta_1=90^\circ\) and suppose that the midpoint of the displacing winding is located at an azimuth equal to zero.

How will the efficiency of extracting accelerated electrons from the vacuum chamber change if the same displacing winding is placed in different azimuthal positions relative to the extraction window?

The answer to this question is given by the graph in Fig. 8, which represents the dependence of the intensity of the electron beam emerging from the chamber on the azimuthal position of the midpoint of the displacing winding of length \(90^\circ\). It is seen from Fig. 8 that, in order to obtain the maximum extraction efficiency, it is necessary to select the optimal position of the displacing winding relative to the extraction window of the chamber.

Let us consider a series of experiments with a change in the shape of the displacing winding.

With a series connection of windings 1, 2, and 3 (Fig. 3), we obtain a sector winding. When windings 2 and 3 are connected (with winding 1 disconnected), we obtain an extra-orbital winding; and when windings 1 and 2 are connected (with winding 3 disconnected), an intra-orbital displacing winding is obtained. The sector and extra-orbital windings act in the same way, and we have already considered the sector winding. Let us investigate the intra-orbital winding in the course of its transformation into a sector winding.

The process of transforming one winding into another may be represented as follows. Let windings 1 and 2 be connected in series and form an intra-orbital displacing winding. Under the action of such a winding, the intensity of the electron beam emerging from the chamber is approximately \(2/3\) of the intensity obtained using the sector displacing winding. Let us connect winding 3 to an additional pulsed circuit, which acts synchronously with the main displacement circuit and produces a current pulse with adjustable amplitude and duration equal to the duration of the main displacing pulse. By gradually increasing the amplitude of the additional current pulse (in winding 3), it is possible, at a certain instant of time, to exert on the electrons an action equivalent to the action of a sector winding.

Fig. 8. Influence of the azimuthal position of the displacing winding relative to the extraction window on the extraction efficiency.

It is interesting to trace the change in the efficiency of extraction of electrons from the chamber when the current amplitude in winding 3 is varied (curve 1 in Fig. 9). Dependence 1 has a complex character and does not lend itself to complete explanation. Let us compare it with dependence 4 (Fig. 9), which characterizes the change in the efficiency of electron extraction when the amplitude of the displacing current in the sector winding is changed. By changing the shape of the winding, leading to a change in the magnitude of the perturbing magnetic field along the radius, it is possible to achieve an increase in the efficiency of extraction of electrons from the chamber by a factor of 1.15. Such an increase in efficiency

Fig. 9. Change in the efficiency of extraction of electrons from the chamber \((J)\) as a function of the change in current amplitude \((I)\): 1—in winding 3 (Fig. 3), 2—in the central winding, 3—change in external losses of electrons, 4—in windings 1, 2, and 3.

cannot be regarded as acceptable; therefore it is necessary to seek new ways of influencing the process of releasing electrons from the action of the focusing forces.

The displacing winding may be made in the form of an ordinary sector winding with a radial dimension equal to the radial dimension of the interpolar space of the betatron.

It is known that the action of a displacing winding placed on the central inserts (“galettes”)¹ leads not only to an increase in the radius of the equilibrium orbit, but also to a simultaneous decrease in the radius of the release circumference (the outer unstable orbit). By using such a winding together with a sector displacing winding, one can achieve limitation of the oscillations and simultaneous displacement of the point of electron release into the vacuum chamber.

We have carried out the joint synchronous action of two displacing windings on the electron beam. The use of two displacing windings fed from separate pulse circuits led to very good results.

In Fig. 9, curve 2 characterizes the change in the efficiency of extracting electrons from the chamber when the current amplitude in the central winding is varied. In this case a current of unchanged amplitude flows in the sector winding. In comparison with the extraction efficiency attained when a single sector winding is used, the extraction efficiency with the combined use of sector and central displacing windings increases by a factor of 1.5.

In practice, the increase in extraction efficiency is due chiefly to a reduction of external losses, the change of which with increasing current in the central winding is characterized by curve 3 (Fig. 9).

The experiments described above were carried out at displacement velocities of the equilibrium orbit of \(1 \div 3\ \mathrm{mm}/\mu\mathrm{sec}\). In order to increase the orbit-displacement velocity, it is necessary to increase the rate of rise with time of the displacing magnetic field.

From the technical standpoint, the problem of increasing the orbit-displacement velocity involves a number of difficulties. This problem was solved at the Tomsk Polytechnic Institute by the diploma student Bizenkov under the supervision of Candidate of Technical Sciences V. M. Razin. The orbit-displacement velocity was brought up to \(30\ \mathrm{mm}/\mu\mathrm{sec}\).

Increasing the displacement velocity of the electron orbit from 2 to \(30\ \mathrm{mm}/\mu\mathrm{sec}\) leads to a doubling of the efficiency of extracting accelerated electrons from the vacuum chamber, owing to a reduction in the internal losses of electrons.

Applying the synchronous action of the sector and central windings in the case where, under the action of the sector winding, the orbit is displaced at a velocity of \(30\ \mathrm{mm}/\mu\mathrm{sec}\), we nevertheless obtain a further increase in extraction efficiency by a factor of 1.5.

As a result, we achieved an increase in the extraction efficiency to 75%.

The maximum value of the current of accelerated electrons, measured by a Faraday cylinder at a distance of \(3\ \mathrm{cm}\) from the extraction window, is equal to \(6 \cdot 10^{-10}\ \mathrm{A}\).

The shape of the transverse cross section of the beam remains unchanged. It is shown in Fig. 5.

Of all methods known to us for extracting a beam of charged particles from cyclic accelerators, the proposed method is the most effective and the simplest. Its drawback is the unsatisfactory focusing of the emerging beam of particles.

¹ Hereafter we shall call it the central winding.

References

1. L. S. Skaggs, G. M. Almy, D. W. Kerst, L. H. Lanzl. Radiology, 50, 167–173, 1948.
2. K. Gund, W. Paul. Nucleonics, 7, 36–46, 1950.
3. F. K. Goward. Proc. Phys. Soc., 61B, 284, 1948.
4. F. K. Goward, J. Dain. Nature, 159, 636, 1947.