EXTRACTION OF 10 MeV ACCELERATED ELECTRONS FROM A BETATRON USING A MAGNETIC SHUNT

L. S. SOKOLOV

(Presented by Prof. A. A. Vorob’ev, Doctor of Physical and Mathematical Sciences)

The simplest method for extracting an electron beam from a betatron is based on creating, in the accelerator’s controlling magnetic field, a field-free channel by means of a magnetic shunt [2]. The shunt is placed outside the equilibrium orbit, tangent to one of the circles that can become close to the equilibrium orbit under a certain change in the controlling field or in the acceleration conditions. Such a change is produced by means of a displacement winding fed by a pulsed current at the moment when the electron energy has reached the desired value. The electrons that enter the nonmagnetic channel move rectilinearly and emerge from it into a weak fringe field. A field-free channel may also be created by the opposing action of the field of pulsed currents—an impulse extractor [3;4].

Let us note that there are two other methods for extracting a beam from a betatron:

1. Focusing, by a magnetic lens, of the beam diverging during the displacement process [5].

2. Imparting a radial impulse to the electrons by means of an electric capacitor [1].

For comparison of the methods named, the concept of extraction efficiency has been introduced, as the ratio of the fraction of extracted electrons to the total number of electrons that have reached the end of acceleration (Table).

Table

In the present article the method of extraction using a magnetic shunt is considered.

Design of the Magnetic Shunt

Because the step between two successive electron trajectories during expansion of the orbit up to the last stable circumference is very small and lies in the range from \(1.6 \cdot 10^{-5}\) to \(2 \cdot 10^{-3}\) cm [6], and because the oscillations introduced by the magnetic shunt into the electron orbits are not exactly known, it would be risky to use iron of O-shaped cross section, which provides the most complete absence of field inside the channel. It is possible to use a C-shaped cross section of the iron (Fig. 1).

Fig. 1. Cross section of the magnetic shunt

It would have been desirable to take the channel height \(\Delta\) somewhat larger, in order to cover not only the height of the beam but also to facilitate vertical adjustment of the shunt; however, as \(\Delta\) is increased the boundary of field attenuation becomes less sharp. This may lead to the electrons being unable to enter the channel, since they will be thrown onto the wall of the vacuum chamber by the partially weakened field. Our measurements of the beam by the illumination of a KCl crystal give its height as 6 mm. In this case the edges limiting the height of the beam proved to be sharp. Skaggs et al. [2] adopted the value \(\Delta = 2\) mm.

In choosing the depth of the channel one cannot proceed only from the orbit step during its expansion, since the shunt perturbs the orbit long before it enters the channel, causing oscillations of the electrons.

The channel depth \(\varepsilon = 5\) mm adopted by Skaggs and his collaborators, as well as the height \(\Delta = 2\) mm, prove insufficient to accommodate the beam [2].

For preliminary experiments we adopted \(\Delta = 2.5\) mm and \(\varepsilon = 6\) mm; in doing so we used transformer steel E4AA, having a rectilinear portion of the magnetization curve up to an induction of 10–11 kG.

Let us find the thickness of the rear wall \(\delta\) and the lip \(\varepsilon\) of the shunt. Since the magnetic flux incident on the shunt must pass entirely through the rear wall of thickness \(\delta\), and the iron must not become saturated, one may write the inequality:

\[ \frac{K(\delta+\varepsilon)}{\delta} < \frac{B_H}{B_0}, \tag{1} \]

where

\[ \begin{aligned} B_H &\text{ is the induction at which the iron of the shunt begins to saturate,}\\ B_0 &\text{ is the amplitude of the magnetic-field induction at the place where the shunt is to be installed,} \\ &\text{practically equal to the amplitude of the induction on the orbit,}\\ K &\text{ is a coefficient allowing for the additional drawing-in of magnetic lines} \\ &\text{by the shunt from the space adjacent to the shunt.} \end{aligned} \]

The value of \(\delta\) was selected experimentally. Iron shunts with \(\Delta = 2.5\) mm, \(\varepsilon = 6\) mm, \(\alpha = 7\) mm, and various \(\delta\) were tested for saturation. In this case the emf from a coil placed inside the channel was fed to an oscillograph. The absence of saturation was determined by the absence of “humps” on the oscillogram. In this way it was found that the limiting thickness is \(\delta = 6\) mm. The corresponding induction values are:

\[ B_H = 10000\ \text{G} \quad \text{and} \quad B_0 = 2500\ \text{G}. \]

Now \(K\) can be determined from inequality (1), converting it into an equality.

In our case,

\[ \frac{K(6+6)}{6}=\frac{10000}{2500}\quad \text{and}\quad K=2. \]

The physical meaning of the coefficient \(K\) is easy to see. It characterizes the degree of perturbation of the magnetic field by the shunt. The coefficient \(K\) depends on the height of the shunt, on the thickness of the rear wall, on the magnetic permeability of the material, and on the operating regime of the shunt, and it can serve as an indicator of the suitability of the shunt for extraction, since too small a \(K\) is associated with a large residual field inside the channel, while too large a \(K\) characterizes an unacceptable boundary of field weakening. \(K\) can also be determined by measuring the induction with and without the shunt.

Let us now find the limiting height of the shunt. Since the magnetic flux incident on the visor must pass entirely through its cross section, we have, analogously to inequality (1),

\[ \frac{Kв}{\dfrac{a-\Delta}{2}} < \frac{B_{\mathrm{н}}}{B_0}. \tag{2} \]

For \(в=6\) mm; \(\dfrac{B_{\mathrm{н}}}{B_0}=4\); \(\Delta=2.5\) mm and \(K=2\).

We find \(a_{\text{limiting}}=8.5\) mm and the height of the visor

\[ \frac{a-\Delta}{2}=3\ \text{mm}. \]

The length of the shunt \(x\) is determined from the formula:

\[ x^2=r_1^2-r_2^2, \tag{3} \]

where \(r_1\) is the radius on which the exit end of the shunt is located when the shunt is placed tangentially to a circle of radius \(r_2\), with the entrance end located at the point of tangency.

For convenience in subsequent work with the extracted beam, it is desirable to extract the electrons into a field of half intensity.

In our betatron the circle where the field fall-off index \(n=1\) is located at radius \(r_2=160\) mm; the circle of half intensity is at radius \(r_1=190\) mm. Hence \(x=10\) cm.

Mutual arrangement of the shunt and the electron gun

It may be expected that the capture of electrons into acceleration will depend on the mutual arrangement of the shunt and the electron gun for a given radial position of the shunt. The following experiment was set up. A body made of laminated iron, C-shaped and similar to a magnetic shunt but of larger dimensions (\(a=15\) mm, \(в=10\) mm, \(б=10\) mm, \(\Delta=5\) mm), was placed tightly against the vacuum chamber at various azimuths.

The results of the experiment are shown in Fig. 2.

Subsequently, the effect of the shunt on the capture of electrons into acceleration was also investigated in two cases:

1. The extra-orbital injector was located behind the shunt at an azimuth of \(45^\circ\).

1. The off-orbit injector was placed behind the shunt at an azimuth of \(135^\circ\). It turned out that in the first case satisfactory radiation can also be obtained; however, the radial position of the injector is very critical with respect to adjustment for maximum output. In the second case the radiation output is stable, and the injector can be used without a selsyn.

Fig. 2. Experimental arrangement (б) and graph (а) showing the effect of the iron body on the capture of electrons into acceleration. The injector is located at an azimuth of \(0^\circ\). Acceleration of the electrons and motion of the iron body are carried out in the direction of increasing azimuth. The reading of the magnetic field on the equilibrium orbit is \(n = 0.6\). \(1.0\) is the radiation from the target without the iron body.

Experiments on the extraction of electrons with energies of 5 and 10 MeV

Experiments on extraction of the beam were carried out with the shunt shown in Fig. 3.

Fig. 3. Design of the magnetic shunt (б). The shunt is assembled from \(0.35\) mm plates (а), separated by baked BF-4 adhesive film.

When the shunt was moved along the radius, the radiation was measured with two ionization chambers. The experimental arrangement is given in Fig. 4, and the results of the experiment—in Fig. 5.

It is evident from Fig. 4 that ionization chamber 1 records the bremsstrahlung from electrons striking the shunt and the output absorber [[unclear: continuation cut off]].

while ionization chamber 2 records the electrons thrown by the shunt onto the wall of the vacuum chamber.

Fig. 4. Diagram of the experiment on electron extraction.
1 and 2 are ionization chambers.

Fig. 5. Radiation yield \((I)\), recorded by ionization chambers 1 and 2, as a function of the radial position of the shunt.
— — — radiation without switching on the displacement circuit,
——— readings of chambers 1 and 2 with displacement.

From the graphs in Fig. 5 the following conclusions can be drawn:

1. Automatic expansion of the orbit by the shunt does take place; however, as the oscillograms of the current from the photomultiplier show, this dumping occurs after the electrons have reached their maximum energy. These electrons are called uncontrolled.

2. The extraction efficiency of the shunt, estimated approximately as the ratio of the readings of ionization chamber 1 to the readings of ionization chamber 2 for electrons with controlled energy, increases as the shunt approaches the region of action of the focusing forces. The maximum efficiency occurs at a radius of 162 mm. For uncontrolled electrons this maximum is found at a radius of 170 mm.

1. Beginning at a radius of 170 mm and less, there is an overall drop in intensity, caused by the influence of the shunt on the process of capture of electrons into acceleration.

Thus, by moving the shunt toward the region of action of the focusing forces, although we gain in effectiveness, we lose in total intensity.

From this follow two obvious proposals for improving the action of the shunt.

1. The shunt should be placed, as far as possible, closer to the region of action of the focusing forces (in our case at a radius of 164 mm), and the field should be corrected at the moment of injection.

2. The shunt should be placed, as far as possible, farther from the equilibrium orbit, where it does not affect the capture process (in our case, at a radius of 172 mm), and the region of action of the focusing forces should be broadened at the moment of displacement.

When the first proposal is used, the shunt will differ little from a pulsed extractor in the complexity of the apparatus and its adjustment, but it will be inferior to it in extraction efficiency, since the extractor, unlike the shunt, introduces almost no oscillations into the orbit before it enters the channel free of the field.

When the second proposal is used, although the need for an additional circuit remains, it is no longer necessary to make electrical leads into the vacuum chamber, since the field increase of 300–400 Oe needed to broaden the region of action of the focusing forces up to the circumference on which the shunt is installed can be produced by means of currents flowing outside the vacuum chamber. Therefore the second proposal seems more acceptable.

With the aid of a magnetic shunt, a beam of electrons with an energy of 10 MeV was extracted. The magnitude of the current of the accelerated electrons at a distance of 5 cm from the window, measured with a Faraday cylinder, proved to be equal to \(1 \cdot 10^{-11}\) A.

Experiments were carried out on displacing 10 MeV electrons from the equilibrium orbit by means of a short displacing winding located beyond the orbit. It was found that, when displacement is produced by such a winding, the beam can be radially focused at the point of greatest outward displacement of the electrons from the equilibrium orbit. A luminous spot was obtained on the wall of the vacuum chamber.

The azimuthal extent of the winding was varied over wide limits. The best focusing is given by windings smaller than \(70^\circ\).

The perturbation of the betatron field by the winding is shown in Fig. 6.

Fig. 6. Decrease of the magnetic field with radius at the moment of displacement:
— without an additional winding,
— with the winding. \(H_0 = 2500\) Oe, \(\Delta H = 250\) Oe.
\((r_2 - r_1)\)—radial extent of the winding.

References

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

2. L. S. Skaggs, G. M. Almy, D. W. Kerst, L. H. Lanzl, Development of the Betatron for Electron Therapy. Radiology, 50, 197–173, 1948.

3. J. D. Lawson, H. T. Walford, J. H. Aram, Extraction of the Electron Beam from a 30-MeV Synchrotron. Nat., 166, 234, 1950.

4. R. S. Foote, B. Petree, A Pulsed Magnetic Extractor for Removing the Electron Beam from a Betatron, R. S. I., 25, 694–698, 1954.

5. S. L. Fawcett, E. C. Crittenden, Ejection of the Electron Beam from a Betatron. R. S. I., 21, 935, 1950.

6. J. D. Lawson, The Angular Distribution of Synchrotron Target Radiation: A Preliminary Experimental Study. Proc. Phys. Soc., 63 A, 653–661, 1950.