BETATRON WITHOUT AN IRON YOKE AND POLES

G. I. Dimov and D. A. Noskov

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

Abandoning the bulky iron electromagnet is one of the ways of creating a compact, portable betatron. With the abandonment of the iron electromagnet, the possibility opens up of obtaining high magnetic-field strengths not limited by the saturation of iron, and, consequently, the possibility of creating an accelerator with small radial dimensions. In addition, the magnetic field produced by an electromagnet without iron has a good phase structure and great static homogeneity, which is also a major advantage of an electromagnet of this type.

These attractive possibilities have drawn the attention of researchers in various countries. In the Soviet Union, Sweden, and England, attempts were made to build and operate a betatron with a complete absence of iron.

As a result of these works it has been shown that electromagnets of this type have two major shortcomings. First, to create a magnetic field with the aid of such electromagnets, tens of times more reactive energy is expended in comparison with electromagnets with iron, i.e., they require a bulky power-supply circuit; second, to create high magnetic-field strengths a high current density in the coils is required, as a result of which only pulsed operation is possible.

To reduce the power consumed by the betatron, to reduce the current density in the coils, and to simplify the design of the electromagnet, it is expedient to make electromagnets with central iron cores. The introduction of iron cores reduces by hundreds of times the energy required to create the accelerating flux, which constitutes a large part of all the energy consumed by a betatron without iron. The dimensions and weight of the electromagnet of a betatron of this type, as in the case of a complete absence of iron, are small. Here, however, the reduction in the dimensions of the electromagnet is already limited by the saturation of the cores. The reduction in dimensions and weight is achieved only at the expense of the absence of iron poles and a magnetic yoke.

A betatron with an electromagnet of this type (with iron cores) was designed in 1949 in Holland, at the Eindhoven laboratory, for an energy of 8 MeV [1]. The betatron electromagnet consists of two coils with two iron cores. Its weight is almost 7 times less than the weight of an iron betatron of corresponding energy. However, the energy expenditures for creating the magnetic field in this betatron are still very large, and the current density in the coils is high.

Data on the calculation, startup, and operating characteristics of such betatrons have not been published. Therefore, in the laboratory of the Tomsk Polytechnic Institute, work was undertaken with the aim of studying an electromagnet with iron-free cores and finding its most rational design, and also with the aim of studying the operating characteristics of iron-free betatrons.

Fig. 1

Labels in the figure: adjusting bolt; centering tube; central core; accelerating chamber; winding; coil cheek; electron gun; support disk; water ring; coil cheek; spacer; struts.

The authors calculated, designed, and built a betatron without an iron yoke and poles for an energy of up to 10 MeV, with an equilibrium-orbit radius of 9.5 cm. The betatron consists of an electromagnet, producing a magnetic field of the configuration necessary for electron acceleration, a vacuum chamber, a power-supply circuit for the electromagnet, electron injection and dumping circuits, and other auxiliary circuits.

The betatron electromagnet consists of two coaxial coils of rectangular cross section with two central cores (Fig. 1). Each coil has 34 turns with a cross section of 56 mm² (six parallel branches). The central cores are assembled from radial plates and cre—

are located at the center of the coils in a getinaks tube by means of a screw, with which the gap between the cores can be smoothly adjusted. The magnetic guiding field of the required configuration is produced between the coils, where the glass accelerating chamber, with a cross section of \(7\ \mathrm{cm} \times 5\ \mathrm{cm}\), is also placed.

The advantage of this electromagnet design is its simplicity of manufacture, convenience in operation, and the possibility of easily changing certain parameters and characteristics of the magnetic field. The radius of the equilibrium orbit is readily changed by varying the gap between the central cores and by varying the distance between the coils; in this case the exponent of the decrease of the magnetic-field intensity, “\(n\),” changes only slightly. Changing the length of the cores entails both a change in the radius of the equilibrium orbit and a change in the exponent “\(n\)” (while the character of the dependence of the exponent “\(n\)” on the radius changes only slightly).

Although the betatron built at the Tomsk Polytechnic Institute has a supply power six times smaller than that of the Dutch betatron, this power still remains considerably greater than that of a betatron with an iron magnetic circuit for the corresponding energy.

The electrical power-supply circuit consists of a gas-discharge rectifier, through which a capacitor bank of capacitance \(90\ \mu\mathrm{F}\) is charged, discharging through an ignitron into the electromagnet coils. The voltage on the capacitor bank is \(8500\ \mathrm{V}\), the current amplitude through the electromagnet coils is \(2400\ \mathrm{A}\), the duration of the current pulses is \(0.001\ \mathrm{s}\), and the repetition frequency is 2 pulses per second.

The absence of a powerful switching device did not make it possible to operate the betatron at the calculated energy. Using an I-100/1000 ignitron and applying reverse-voltage suppression, we operated the betatron at an energy of about \(2.5\ \mathrm{MeV}\) (reduced mode: voltage \(2000\ \mathrm{V}\) at a current of about \(600\ \mathrm{A}\), repetition frequency about 20 pulses per second).

For operation in the pulsed mode, a simplified injection circuit was used, consisting of a capacitor, a variable resistor, and a pulse transformer connected in series and connected in parallel with the electromagnet coils.

The characteristics of the magnetic field of a betatron without an iron yoke and poles differ somewhat from the characteristics of the field produced in the interpole space of an ordinary betatron. For example, upon displacement from the central plane, the value of “\(n\)” in the ironless version decreases, whereas in the ordinary version it changes hardly at all. The phase and static inhomogeneities of the magnetic field are considerably smaller than in betatrons with an iron magnetic circuit.

In the course of investigating the operating features of a betatron without an iron yoke and poles, certain dependences were established that are of importance for betatrons of any design.

Thus, for example, it was established that inside the accelerating chamber there exists a range of values of the equilibrium-orbit radius within which its change does not affect the radiation intensity. It was shown that, with the aid of the potential function, one can preliminarily determine the optimal radius of the equilibrium orbit. The experimental optimum differs from the theoretical one by \(3\ \mathrm{mm}\).

In investigations of the dependence of the radiation intensity on the configuration of the magnetic field, it was shown that a more illustrative characteristic of the focusing properties of this field is the potential function of its focusing forces. When the exponent “\(n\)” on the orbit is changed from 0.5 to 0.72, the height of the potential barrier of the focusing magnetic forces remains practically unchanged; the radiation intensity also does not change. For values of “\(n\)” on the orbit of 0.25 and 0.36, the height of the potential

of the barrier decreases considerably; the radiation intensity in these cases also drops sharply.

In the course of the experiments it was established that changing the position of the electron gun within the limits of 5–7 mm has little effect on the radiation intensity.

Studies of the dependence of the radiation intensity on the pulse duration, other conditions being equal, showed that for the given betatron design and the given circuits the radiation intensity changes only slightly at the above pulse frequencies of 350 and 750 cps, and decreases substantially at a frequency of 1000 cps and higher. Extending our conclusions to betatrons powered by alternating current, one may say that each particular design has a frequency range within which the radiation intensity is proportional to the frequency. Outside the limits of this range the proportionality is violated.

In addition to the betatron with two coils, a more economical design of the electromagnet of a betatron without an iron yoke and poles was developed in the laboratory of the Tomsk Polytechnic Institute (developed by G. I. Dimov, L. M. Anan’ev, and S. V. Khoroshilov).

Fig. 2

A distinctive feature of this betatron electromagnet design is that the guiding field is produced by a system of five coils (Fig. 2). The introduction of the middle coils makes it possible to dispense with a considerable central gap in the core, leads to a more favorable configuration of the guiding field, and increases, in the axial direction, the region of the magnetic guiding field. The introduction of an inner coil with an oppositely directed flux makes it possible to increase the length of the core and reduce the consumption of reactive energy, which makes it possible to increase the repetition frequency to 50 pulses per second. The use of this coil

has also a negative aspect: the radial size of the electromagnet increases.

A 5 MeV betatron with an electromagnet of this type has an equilibrium-orbit radius of 10 cm (cores made of transformer steel Э42). The weight of the electromagnet is 60 kg.

In terms of supply power, this design is already not inferior to a betatron with an iron magnetic circuit when the latter is supplied with industrial-frequency current. The electromagnet of a 5 MeV betatron consumes a current of 60 A at a voltage of 3000 V and with a pulse duration of 0.002 sec.

However, this electromagnet design is not perfect either. By reducing the pulse duration and using steel with a higher magnetic induction for the cores, one can construct a betatron of this type for energies up to 10 MeV with higher technical and economic characteristics, not inferior in average intensity to a betatron with an iron yoke operating at industrial frequency.

REFERENCES

1. Bietman und Oele, Phil. Tech. Rund. No. 3, 1949.