EXTRACTION OF AN ELECTRON BEAM FROM THE BETATRON CHAMBER

L. S. Sokolov

(Presented by Professor, Doctor A. A. Vorob’ev)

The principal problem in extracting accelerated electrons from a betatron is to remove the electrons from the strong magnetic field in which they rotate during acceleration, in the form of a narrow beam and with the least possible losses.

Until now this has been accomplished by means of an extraction device located near the outer edge of the acceleration zone.

In the present article we report the experimental realization of the extraction of an electron beam with an energy of 10 MeV from a betatron. The proposed method of extracting electrons from a betatron does not include an extraction device located inside the vacuum chamber of the betatron.

It may be regarded, in essence, as a limiting case of displacement of the equilibrium orbit of the electrons from its initial positions. In the literature known to us this method has not been described, and it has been carried out by us for the first time.

For extracting the 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 a 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 a circumference where the magnetic-field fall-off index \(n = 1\). On the rear side of the injector there is a tungsten target. Extraction 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 pumping out the vacuum chamber. A view of the vacuum chamber installed in the betatron is shown in Fig. 2. In the foreground is the extraction window; on the left is the injector; on the right is the mechanism for moving the target installed in branch pipe 5 (Fig. 1).

For convenience in carrying out the experiments, the displacement windings are made in the form of 24 coils with four turns in each coil, which are fastened to two thin textolite disks (0.5 mm thick) (Fig. 3). One of the disks is placed below, the other above the vacuum chamber. 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, producing different angles \(\Theta_1\) and different azimuthal positions of the winding in the interpole space of the betatron. There is also a winding (ten turns) on the central inserts (“galettes”) and

special winding (Fig. 4), making it possible to vary the magnitude of the intensity of the betatron magnetic field with radius.

The first experiments were carried out with a displacing winding of extent \(\Theta_1 = 135^\circ\), arranged as shown in Fig. 5. The pulsed current flowing through the displacing winding produces, by its magnetic field, a weakening of the controlling magnetic field of the betatron.

Fig. 2. Installation of the vacuum chamber in the betatron.

The electron orbit is displaced outward, in the direction of branch pipe 5 (Figs. 5 and 1), until the electrons are freed from the influence of the focusing forces toward the orbit.

No less than \(1/3\) of the beam enters the extraction window and, through copper foil, emerges from the vacuum chamber. The extraction efficiency 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 electrostatic capacitor, achieved by Goward [2] without the use of scattering foil.

Fig. 3. Windings for displacing the equilibrium orbit.

Figure 6 presents photographs of the electron beam taken perpendicular to the beam axis directly at the extraction window (upper photograph) and at a distance of \(10\) cm from it (lower photograph). Horiz—

The total size of the beam as the electrons emerge from the window is 6 cm and is equal to the horizontal size of the extraction window. Using a thimble ionization chamber of the “Pion” type, we measured the distribution of ionization over the horizontal cross section of the beam. This distribution is shown in Fig. 6 above the photograph of the beam. The table gives the numerical values of the ionization intensity.

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 cross section of the beam is considerably larger. Compared with the dimensions of the beam immediately 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 beam dimensions is due to scattering of the electrons as they pass through the copper foil and through the air.

To determine the trajectory of the released beam inside the vacuum chamber, the following experiment was performed. An ionization chamber of

Fig. 4. Special biasing winding.

200 cm\(^3\) was placed at the point where the maximum ionization is produced (point 1 in Fig. 5). A tungsten target, installed in branch pipe 3 (Fig. 1), was gradually advanced into the vacuum chamber. For each position of the target, the radiation registered by the 200 cm\(^3\) chamber was noted (Fig. 7). As the target is advanced into the vacuum chamber, the radiation at first does not change. This means that the electrons leave the vacuum chamber without touching 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, there is a sharp decrease in the radiation intensity: the target intercepts the outgoing electron beam. The interval of displacement of the target corresponding to complete blocking of the electrons’ 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 picture the general extraction scheme (Fig. 5), from which it is not difficult to determine the mean angle \(\varphi_{cp}\) of emergence of the beam outward and the divergence angle \(\psi\) 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 \(32\ \text{cm}\): \(\varphi_{cp} \simeq 9^\circ,\ \psi \simeq 10^\circ\).

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

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

In accordance with the results obtained, it is advisable to introduce the concept of external and internal electron losses; here the electrons constituting the inner part of the emerging beam and not entering the extraction window because of collisions with the walls of the vacuum chamber determine the internal losses, while the electrons traveling 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. 5).

Fig. 5. General scheme for extracting an electron beam with energy of \(10\ \text{MeV}\) from a betatron.
\(1\) and \(2\)—ionization chambers.

Fig. 6. Images of the beam.

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

In the linear approximation [3]:

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

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

where \(n\) is the index of the decrease of the betatron magnetic field with radius; \(m\) is the harmonic order of the forced oscillations \((m=1,2,3,\ldots)\).

When \(\Theta_1\) changes, \(\varepsilon_0\) and \(\varepsilon_m\) change in accordance with formulas (1). For example, when \(\Theta_1=\pi\), the first harmonic has a maximum value, while the second harmonic is absent. When \(\Theta_1=\frac{\pi}{2},\ \frac{3}{2}\pi\), the second harmonic has a maximum positive or negative value.

…whereas the first harmonic is considerably smaller than its maximum value (at \(\Theta_1=\pi\)), etc.

The question arises of how the efficiency of extracting electrons from the accelerator chamber will change when the azimuthal extent of the winding \(\Theta_1\) is varied.

The experiment was carried out as follows.

The displacing winding and the ionization chamber 1, which recorded the intensity of the accelerated-electron beam emerging from the vacuum chamber, were installed as shown in Fig. 5.

Without changing the azimuthal position of the middle of the displacing winding, we varied the azimuthal extent of the winding \(\Theta_1\). In all, five 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 results of the experiment are shown in Fig. 8, from which it follows that changing the azimuthal extent of the displacing winding within the limits 90—

Fig. 7. Change in the ionization intensity at point 1 when the radial coordinate of target 3 is varied (Fig. 1).

Fig. 8. Influence of the azimuthal extent of the displacing winding \(\Theta_1\) on the extraction efficiency \(J\).

270° and the corresponding change in the relative magnitude of the components of the forced motion do not lead to a change in the extraction efficiency. At \(\Theta_1=270^\circ\) the electron extraction 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 \(\varphi_{\mathrm{cp}}\) of the electron beam’s outward exit and the angle \(\psi\) of beam divergence inside the vacuum chamber also remain unchanged.

The experiment shows that, before the electrons are released from the influence of the focusing forces, a regime of forced oscillations arises which does not depend on the azimuthal extent of the displacing winding. It follows that whatever combinations of displacing windings we might 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 extracting electrons from the accelerator cannot be changed.

The azimuthal extent of the displacing winding \(\Theta_1\) may be chosen such that the minimum reactive energy is required for the complete removal of the accelerated electrons from the working zone of the betatron [4].

Let us turn again to Fig. 5. Take \(\Theta_1=90^\circ\) and assume that the middle 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 this 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. 9, 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, with an extent of \(90^\circ\). From Fig. 9 it is evident that, in order to obtain the maximum extraction efficiency, it is necessary to choose the optimum 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. A sketch of a winding by means of which one can change the law of perturbation of the betatron magnetic field along the radius is shown in Fig. 10, and its general appearance in Fig. 4.

Fig. 9. Influence of the azimuthal position of the displacing winding relative to the extraction window on the extraction efficiency.

Fig. 10. Sketch of the displacing winding.

With series connection of windings 1, 2, and 3 (Fig. 10) a sector winding is obtained. With connection of windings 2 and 3 (with winding 1 disconnected) a beyond-orbit winding is obtained, while by connecting windings 1 and 2 (with winding 3 disconnected) an intra-orbit displacing winding is obtained. The sector and beyond-orbit windings act identically, and the sector winding has already been considered by us. Let us study the intra-orbit winding in the process 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-orbit 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 operates synchronously with the main displacement circuit and delivers a current pulse of adjustable amplitude and width equal to the width of the main displacement pulse. By gradually increasing the amplitude of the additional current pulse (in winding 3), one can at a certain moment produce an action on the electrons equivalent to the action of a sector winding.

Fig. 11. Change in the efficiency of extraction of electrons \(J\) from the chamber as a function of the change in current amplitude \(I\).

1 — in winding 3 (Fig. 10); 2 — in the central winding; 3 — the same with increasing current; 4 — in windings 1, 2, and 3.

It is interesting to trace the change in the efficiency of extraction of electrons from the chamber when the current amplitude in winding 3 (Fig. 10) is varied, as shown by curve 1 (Fig. 11). Dependence 1 (Fig. 11) has a complicated character and does not lend itself to complete explanation. Let us compare it with dependence 4 (Fig. 11), which characterizes the change in the efficiency of ex—

…of electrons when the amplitude of the displacement current in the sector winding is varied. 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 increase the efficiency of extracting electrons from the chamber by a factor of 1.15. Such an increase in extraction efficiency cannot be regarded as acceptable; therefore it is necessary to seek new ways of acting on the process by which electrons are freed from the influence of the focusing forces.

The displacement winding can be made in the form of an ordinary sector winding with a radial dimension equal to the radial dimension of the inter-pole space of the betatron.

It is known that the action of a displacement winding placed on the central inserts (cheeks)\(^1\) 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 circle (the outer unstable orbit). By using such a winding together with a sector displacement winding, one can achieve limitation of the oscillations and simultaneous displacement of the point of electron release into the vacuum chamber.

We carried out the combined synchronous action of two displacement windings on the electron beam. The use of two displacement windings, supplied from separate pulse circuits, led to very good results.

In Fig. 11, dependence 2 characterizes the change in the efficiency of extracting electrons from the chamber when the amplitude of the current in the central winding is varied. In this case a current of unchanged amplitude flows in the sector winding. In comparison with the value of the extraction efficiency attained when a single sector winding is used, the extraction efficiency with the combined use of sector and central displacement windings increases by a factor of 1.5.

Practically, the increase in extraction efficiency is due mainly to a decrease in the external losses, whose change with increasing current in the central winding is characterized by dependence 3 (Fig. 11).

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

From the technical point of view, the problem of increasing the orbit-displacement velocity encounters a number of difficulties. This problem was solved at TPI by the diploma student T. Bizenkov under the supervision of Candidate of Technical Sciences V. M. Razin. The improved pulse circuit for displacement does not differ in principle from the former displacement circuit [5], except for the replacement of the I-100/1000 ignitron by a ball discharger. However, by increasing the voltage \(u\) to which the capacitance \(C\) is charged, and by decreasing the parasitic inductances, it proved possible to raise the orbit-displacement velocity to \(30\ \mathrm{mm}/\mu\mathrm{sec}\).

The parameters of the new displacement circuit are \(C = 0.5\ \mu\mathrm{F}\); \(w = 1\); \(\Omega = 0.8 \cdot 10^6\ \dfrac{1}{\mathrm{sec}}\).

For displacement of the orbit, the limiting values possible in our circuit were used,

\[ u = 5\ \mathrm{kV}\quad \text{and}\quad I = 1000\ \mathrm{A}. \]

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

It is interesting to note that, when the synchronous action of the sector and central windings is used in the case where, under the action of the sector—

\(^1\) In what follows we shall call it the central winding.

the orbit is displaced at a rate of \(30\ \mathrm{mm}/\mu\mathrm{s}\), we nevertheless obtain a further 1.5-fold increase in the extraction efficiency.

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

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

The shape of the beam cross section remains unchanged. It is shown in Fig. 6.

Of all the 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 particle beam.

The author expresses his gratitude to Professor, Doctor of Technical Sciences A. A. Vorob'ev for proposing the topic and for supervising the research work, and also to Candidates of Technical Sciences V. A. Moskalev and V. M. Razin for their comprehensive technical assistance in the work, numerous consultations, and advice.

References

1. Skaggs L. S. et al., Development of the Betatron for Electron Therapy, Radiology, 50, 167—173, 1948.

2. Gund K., Paul W., Experiments with a 6-MeV Betatron, Nucleonics, 7, 36—46, 1950.

3. Goward F. K., Effect of Azimuthal Inhomogeneities in the Magnetic Field of a Betatron, Proc. Phys. Soc., 61, 234, 1948.

4. Goward F. K., Pain J., Optimum Disturbing Field for Synchrotron Beam Ejection, Nat., 159, 639, 1947.

5. Sokolov L. S., Investigation of the Electron Beam inside the Vacuum Chamber of a Betatron, Izv. TPI, vol. 94.