ELECTROSTATIC EXTRACTION OF ELECTRONS FROM A BETATRON

Part I

STUDY OF CERTAIN CHARACTERISTICS OF A BEAM OF ACCELERATED ELECTRONS IN A BETATRON CHAMBER

B. A. Kononov

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

An electron beam with an energy of 5–25 MeV for research in physics, biology, and medicine can be obtained from an induction accelerator—a betatron. Several methods have been proposed for extracting electrons from a betatron [1–10], the description and analysis of which were made by us earlier [11]. At the Tomsk Polytechnic Institute the extraction of electrons from a 15 MeV betatron has been carried out by several methods [12]. The technique of extracting electrons by the electrostatic method has already been described in sufficient detail [13]. In the present article we wish to dwell on some preliminary experiments on extracting an electron beam from a betatron, which determined the design of the entire extraction device.

In solving the problem of extracting electrons from the betatron chamber it is necessary to know the following characteristics of the beam of electrons moving in the vacuum chamber of the accelerator: the geometric dimensions of the electron beam at the end of acceleration, the position of the electron beam in the vacuum chamber, and the behavior of the beam when the expanding (displacing) winding is switched on, namely the pitch of the unfolding spiral trajectory of the electrons. These beam parameters impose definite requirements on the dimensions and design of the extraction device and on its location in the accelerator chamber. Indeed, if the electron beam has a considerable vertical dimension at the end of the acceleration cycle during orbit expansion, then the vertical dimension of the deflecting capacitor must be taken at least no smaller than the height of the beam, in order to avoid loss of electrons. However, if the vertical dimension of the beam proves to be small, then there is absolutely no need to make the deflecting capacitor large and needlessly clutter the working region in the accelerator chamber.

Several methods are known for investigating beams in accelerators [14–16]. We studied the beam of accelerated electrons in the betatron chamber with the aid of probes made of KCl and NaCl crystals. The coloration of the crystals is a consequence of the formation of F-centers in alkali-halide crystals under the action of electrons and of the precipitation of colloidal alkali metal inside the crystal [17–19]. In our experiments the crystals had the form of a rectangular parallelepiped with dimensions from \(35 \times 25 \times 5\) to \(15 \times 15 \times 8\) mm; the surfaces of the crystals were polished.

The experimental arrangement for studying the electron beam with crystals is shown in Fig. 1. The crystal is mounted on a brass rod-holder, which can be moved without breaking the vacuum with an accuracy of up to 0.05 mm. To avoid bombardment of the crystal at the moment of injection by unaccelerated electrons, which also cause coloration of the crystal, the crystal is covered on all sides with aluminum foil—

… with a thickness of 30 µm. At the beginning of the experiment the crystal is withdrawn into a branch pipe of the chamber while the accelerator is adjusted to the nominal radiation; after this the crystal is inserted to the required depth and the exposure is made. To obtain a sharp image on the crystal, the exposure time was varied from 60 min at an accelerated-electron energy of 5 MeV to 30 min at 10 and 13 MeV. The exposure is related to the total dose received by the crystal during a run and therefore depends on the intensity of the radiation from the given betatron. Under the conditions of the experiment, the radiation intensity measured at a distance of 1 m from the tungsten target was only 0.7 roentgen/min. When the crystal was irradiated, the tungsten target was removed—raised together with the injector above the plane of the equilibrium orbit—so that the beam of accelerated electrons fell on the crystal, and the x-ray radiation from the crystal was monitored by an ionization chamber (Fig. 1).

Fig. 1. Determination of the dimensions of the electron beam by crystals.
1 — vacuum chamber; 2 — crystal; 3 — mechanism for moving the crystal; 4 — expansion winding; 5 — over-orbit injector; 6 — ionization chamber.

Changing the crystals is carried out through a detachable joint with a rubber seal, without disassembling the betatron electromagnet or repositioning the vacuum chamber, and consequently the electron orbit occupies the same spatial position in every case.

Fig. 2. Typical prints of the electron beam at different radii.

Photographs of the electron-beam prints on the crystals, shown in Fig. 2, are typical patterns from which one can judge the dimensions of the beam and the pitch of its spiral trajectory. The vertical dimension of the beam in all cases lies within 9–11 mm. At radii smaller than \(R = 159\) mm (the radius where \(n = 1\)), the beam is uniform in height and has a pitch close to 1 mm. At \(R > 159\) mm there is a considerable increase in the pitch of the spiral trajectory of the displaced beam and a noticeable division of it into three parts vertically. The most intense middle electron beam has, at the same time, the largest pitch. The intensity of the coloration of the crystal—

…was determined by means of an MF-4 microphotometer. In this process the dependences of the optical density of darkening \(S=f(x)\) and \(S=f(y)\) were obtained:

\[ S=\lg \frac{I_1}{I_2}, \]

where \(S\) is the optical density of darkening;
\(I_1\) is the intensity of the incident light;
\(I_2\) is the intensity of the transmitted light.

The directions \(x\) and \(y\) are shown in Fig. 2. From the curve \(S=f(x)\) the pitch of the spiral trajectory of the electrons is determined; from \(S=f(y)\), the vertical size of the beam. In doing so, a linear dependence is assumed between the density of darkening of the crystal and the number of electrons bombarding the crystal, i.e., that the coloration of the crystal is far from the saturation region, when further bombardment no longer increases the density of darkening. In the saturation region an NaCl crystal has a blue-purple coloration [17]. In our experiments the crystals had yellow and brown coloration.

Fig. 3. Determination of the vertical size of the beam.

Fig. 4. Determination of the pitch of the spiral trajectory at \(R=158\) mm.

Fig. 5. Determination of the pitch of the spiral trajectory at \(R=165\) mm.

Typical curves \(S=f(x)\) and \(S=f(y)\) are presented in Figs. 3–5. The vertical size of the beam, as is evident from Fig. 3, is \(9 \div 12\) mm. From the curves in Figs. 4 and 5 one can estimate the pitch of the electron trajectory. It is approximately 2 mm at \(R=158\) mm and 3.5 mm at \(R=165\) mm. For a more accurate determination of the pitch, knowledge of which is necessary in order to determine the location of the deflecting capacitor, graphical integration of these curves was used, i.e., a spatial…

…corresponding picture \(S=f(x,y)\) (Fig. 6) was constructed and the volume of the figure was calculated. To calculate the volume, the figure is divided by planes \((z,y)\) into separate layers \((I, II, III,\) etc.), and each layer is divided into parts by planes \((z,x)\). As a result, the volume of the resulting elements—parallelepipeds and pyramids—is calculated, and their summation gives the volume of the entire figure \(V_\Sigma\). Taking \(V_\Sigma=100\%\), we find the share of each layer \(V_I\), \(V_{II}\), etc., in the total volume \(V_\Sigma\), in percent. The volume of the figure as a function of distance \(V=f(x)\) is presented in Fig. 7. The dependence shows the percentage of electrons that can enter the gap of the deflecting capacitor, and the percentage of electrons lost on the front surface of the cutting plate of the capacitor. As is evident from the curves in Fig. 7, if the distance between the plates of the deflecting capacitor is equal to \(2\) mm, then almost all electrons will be captured by the capacitor. However, if the thickness of the cutting plate is \(0.05\) mm (the shaded region at the beginning of the graph), then up to \(33\%\) of the electrons will be lost on the front surface of the plate when the capacitor is installed at \(R=158\) mm, and up to \(16\%\) when it is installed at \(R=165\) mm. If all electrons that enter the gap of the deflecting capacitor are extracted from the accelerator chamber, then the percentage of extracted electrons, or extraction efficiency, will not exceed \(84\%\) when the capacitor is installed at \(R=165\) mm. Installing it at smaller radii is disadvantageous because of the increased loss of electrons on the front surface of the cutting plate due to the small pitch of the spiral trajectory (Fig. 7, curve \(R=158\) mm).

Fig. 6. Electron distribution in the beam at \(R=158\) mm.

Fig. 7. Pitch of the spiral trajectory and loss of electrons on a cutting plate \(0.05\) mm thick.

Thus, for the betatron investigated, the beam characteristics are as follows.

1. The height of the electron beam at the moment of expansion of the electron orbit is no more than \(12\) mm. Consequently, the height of the plates of the deflecting capacitor must be greater than \(12\) mm.

2. The pitch of the spiral trajectory of the electrons, small up to \(R=158\) mm, increases sharply near the limiting circumference—the circumference on which the electrons leave the region of action of the focusing forces of the accelerator magnetic field, \(R=163\) mm. The pitch of the spiral trajectory does not exceed \(2.5\) mm within the vacuum chamber of the accelerator. Consequently,

the distance between the plates of the deflecting capacitor should be of the order of 2–2.5 mm.

1. The distribution of the electron flux at a given pitch of the spiral trajectory is such that a larger number of electrons have a smaller pitch; therefore, on the front surface of a rather thin intercepting plate—50 μm—15–20% of the electrons will be lost.

2. The deflecting capacitor should be installed at \(R = 163\text{–}165\) mm.

3. The electron orbit lies in the median plane of the interpolar space. The orbit may leave this plane if, during assembly of the electromagnet, the profiled poles are displaced relative to one another. In this case, with the aid of crystals it is possible to determine the deviation of the orbit from the median plane and to indicate the cause producing the distortion of the orbit.

The author expresses gratitude to Professor A. A. Vorob'ev, under whose supervision the present work was carried out.

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