ON THE USE OF A BETATRON AS AN ELECTRON INJECTOR IN HIGH-ENERGY SYNCHROTRONS

A. A. VOROB'EV, G. I. DIMOV

When choosing the type of injector for electron synchrotrons, the following are mainly taken into account:

1) the number of electrons that can be introduced into the synchrotron in each acceleration cycle;

2) the value of the injection energy that it is reasonable to adopt for one or another type of injector.

It is necessary to strive for large numbers of electrons introduced into the synchrotron. In synchrotrons currently in operation, after each acceleration cycle, \(10^8 \div 10^{10}\) electrons are obtained.

Increasing the injection energy gives certain advantages with respect to the main unit of the synchrotron—the electromagnet. An increase in the injection energy is accompanied by a considerable reduction in the weight and dimensions of the electromagnet and in the power of its supply. At a sufficiently high injection value, the need for preliminary induction or synchrophasotron acceleration of the electrons in the synchrotron chamber disappears.

In evaluating one or another type of auxiliary accelerator used as a synchrotron injector, one should take into account not the average current of the electrons accelerated in this accelerator, but the number of electrons that can be introduced from this accelerator into the synchrotron chamber. Electrons can be introduced into the synchrotron chamber with a sufficiently small energy spread, with sufficiently small divergence in the direction of velocities, and with a sufficiently small transverse beam cross section. For synchrotrons of \(1 \div 2\) Bev, the permissible energy spread of the introduced electrons is \(1 \div 0.1\%\), the permissible input divergence of the electron beam is \(10^{-2} \div 10^{-3}\) radian, and the permissible cross section of the electron beam is \(1\ \text{cm}^2\). For synchrotrons of higher energies, the tolerances on energy spread and beam divergence decrease.

The introduction of electrons into the synchrotron chamber is carried out during a short interval—the injection time. In synchrotrons with an energy of the order of \(1 \div 2\) Bev, electron injection is carried out during several revolutions, and the injection time is inversely proportional to the rate of rise of the magnetic field, proportional to the injection energy, and usually does not exceed \(5\ \mu\text{sec}\). In synchrotrons of higher energies, above \(6\) Bev, electron injection is carried out during 1 revolution, and the injection time does not exceed \(1\ \mu\text{sec}\).

Only a small fraction of the electrons introduced into the chamber is captured into acceleration in the synchrotron. Usually this fraction has a value of the order of 0.1.

The greatest possibilities for ensuring the injection of a large number of electrons are offered by high-voltage accelerators with a pulse transformer (pulse current of the order of \(10\ a\)) and by rectified-voltage generators (pulse current \(0.1 \div 1\ a\)). The electron beam from these accelerators has a small divergence and a high “instantaneous” monoenergeticity. However, the injection energy that these accelerators can provide is comparatively small. In practice, a pulse transformer can be built for a voltage of \(1 \div 1.5\ \text{MeV}\), and a rectified-voltage generator for a voltage of \(2 \div 3\ \text{MeV}\). Injectors of this type may be used in synchrotrons with energies of the order of \(1 \div 2\ \text{BeV}\), with preliminary acceleration in the synchrotron chamber.

For synchrotrons with energies of \(1 \div 2\ \text{BeV}\), an electron cyclotron—microtron—can serve as the injector. The microtron makes it possible to obtain electron currents of the order of \(10\ \text{mA}\) (in the microtron of the Swedish synchrotron at \(1200\ \text{MeV}\), the electron current is \(20\ \text{mA}\)). The spread of electron energies is \(0.03 \div 0.05\%\). The microtron can ensure capture into synchrotron acceleration of \(10^{10} \div 10^{11}\) electrons. In practice, it is reasonable to construct a microtron for an energy of \(4 \div 8\ \text{MeV}\). Such a comparatively high injection energy makes it possible to dispense with preliminary acceleration in the synchrotron chamber; at the same time, the weight of the electromagnet and the power of its supply may be comparatively small.

A satisfactory type of injector is a traveling-wave linear accelerator. A linear accelerator makes it possible to inject electrons with very high energy and can be used in synchrotrons for very high energies, of \(6\) and more \(\text{BeV}\). Modern linear accelerators make it possible to obtain pulse currents of about \(100\ \text{mA}\). In this case the electron beam has a broad energy spectrum, \(3 \div 5\%\) of the nominal energy. Therefore only approximately one tenth of the electrons can be introduced into the synchrotron, i.e., the useful electron current from the linear accelerator does not exceed \(10\ \text{mA}\). The linear accelerator ensures capture into acceleration of the order of \(10^{10}\) electrons.

It should be noted that the current of electrons accelerated in a linear accelerator is limited by the power of the radio-frequency generators.

It is proposed to use an induction accelerator—a betatron—as the electron injector into a synchrotron. The betatron is a simple and small accelerator installation in comparison with other types of injectors. The betatron, like the linear accelerator, makes it possible to inject electrons with very high energy.

In modern betatrons, with an injection energy of \(30 \div 40\ \text{keV}\), and with a sufficiently large working cross section of the chamber, the electron current circulating in the orbit reaches \(1\ a\). In this case the number of electrons accelerated per cycle is \(10^{11}\).

At present, extraction of electrons from the betatron chamber has been accomplished. Thus Gund and Reich [1] extracted from a betatron \(70\%\) of the electrons at an energy of \(6\ \text{MeV}\) by means of an electrostatic deflector. Foot and Petree [2], using a pulsed magnetic deflector, extracted from a betatron about \(60\%\) of the electrons at an energy of \(24\ \text{MeV}\). They also carried out extraction of electrons at energies up to \(50\ \text{MeV}\). At the Tomsk Polytechnic Institute, B. A. Kononov extracted electrons with an energy of \(10\ \text{MeV}\) from a betatron by means of a pulsed electric deflector, with an efficiency of \(30\%\).

For the electron beam extracted from a betatron, small divergence and cross section can be achieved. Foot and Petree obtained an extracted beam with a divergence of the order of \(0.01\) radian in air, with a cross section of \(3 \times 5\ \text{mm}^2\). B. A. Kononov obtained a beam with a divergence of the order of \(0.1\) radian in air, with a cross section of \(6 \times 10\ \text{mm}^2\). In vacuum, the divergence of the beam decreases.

An electron beam with the indicated characteristics is not difficult to focus into a beam with an even smaller divergence and with the same cross section. The time for extracting electrons from a betatron can be made less than 1 μsec. Foote and Petry carried out electron extraction in approximately 1 μsec. The monoenergeticity of the electrons from a betatron is high, especially when the electrons are extracted at the “peak” of the current pulse feeding the betatron electromagnet.

Thus, all the electrons extracted from the betatron can be introduced into the synchrotron chamber. If \(10^{12}\) electrons are accelerated per cycle in the betatron, \(10^9 \div 10^{10}\) electrons can be accelerated per cycle in the synchrotron.

In the betatron, the number of electrons accelerated per cycle is not limited by the power of the accelerating system and is determined only by the conditions of electron injection into the betatron. And the conditions of electron injection into a betatron can be considerably improved. Already at the present time, with injection

Labels in the diagram: electrostatic deflector of the synchrotron; rotating and focusing magnet; stabilized DC voltage sources with smooth regulation; correcting magnets of vertical rotations and displacements; magnetic lenses with weak-gradient field; stabilized power circuit for the betatron electromagnet; from the cycle-setting generator, \(t_b\); pulsed betatron; to the power circuit of the synchrotron electromagnet, \(t_c\); deflector; betatron injector; magnetic field of the synchrotron; magnetic field of the betatron; power circuit of the betatron injector; power circuit of the betatron deflector; from the magnetic-field level sensor of the synchrotron, \(t_i\); \(t_b\)—start of betatron operation; \(t_c\)—start of synchrotron operation; \(t_i\)—moment of injection of electrons into the synchrotron.

Fig. 1. Functional diagram of the injection system of a pulsed synchrotron.

of electrons in a constant guiding magnetic field (which has been accomplished, for example, by Schittenhelm [3]), an increase in the circulating

[[unclear: beginning of line]] electron current in the betatron to 10 a. Another way of increasing the number of electrons accelerated in the betatron is to raise the injection energy. The latter can be achieved by using, as the betatron injector, a high-voltage tube with a pulse transformer.

In Fig. 1 we present a possible functional diagram of an injection system with a betatron for the case of pulsed operation of the synchrotron.

The diagram shows two focusing lenses, which make it possible, even with a considerable divergence of the electrons at the exit from the betatron, to obtain a parallel beam of small cross section. With a small divergence of the betatron electron beam, of the order of 0.01 radian, one lens may suffice.

Magnetic lenses with alternating-sign gradient and a rotating focusing magnet with rotating inserts make it possible to focus the electron beam separately in the vertical and horizontal planes.

The magnetic and electric fields of the injection channel are static. Having these fields follow the injection energy presents great technical difficulties.

The supply of the betatron electromagnet must be stabilized. Extraction of electrons from the betatron must be carried out in the vicinity of the “peak” of the betatron magnetic-field pulse. Since in this vicinity the magnetic field changes only weakly, one may allow oscillation of the moment of electron extraction relative to the “peak” of the pulse over a considerable interval (of the order of 10 μsec) without appreciable oscillation of the energy of the injected electrons. Oscillations of the moment of electron extraction arise because of instability of the time interval \(t_c - t_b\) (Fig. 1) and instability of the supply of the synchrotron electromagnet.

The stability of the supply of the inflector and of the turning and correcting magnets is determined by the required accuracy of the direction of injection of the electron beam.

The stability of the supply of the magnetic lenses is determined by the permissible divergence of the electron beam upon injection.

The stability of the supply of the betatron electromagnet is determined by the required stability of the injection energy and by the stability of the turning magnetic and electric fields of the injection channel.

References

1. Gund K., Reich H., Zs. f. Phys., 126, 383, 1949
2. Foote R., Petree B., Rev. Sci. Instr., 25, 694–698, 1954
3. Schittenhelm R., Arch. techn. Messen, No. 236, 205–208, 1953.