Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 156　　　　　　　　　　　　　　　　　　　　　　　　　　　1969

ACCELERATING SYSTEM FOR THE SYNCHROPHASOTRON MODE OF A 300 MeV SYNCHROTRON

B. A. SOLNTSEV, V. I. TOLMACHEV

Injection of electrons in the 300 MeV synchrotron is carried out at an energy of 260 keV. The velocity of the electrons at this energy is only 0.75 of the speed of light. The increase in energy in the initial part of the cycle is accompanied by an increase in the velocity of the electrons and by a change in their revolution period in the orbit. The frequency of the accelerating electric field in this part of the acceleration cycle must likewise change. The character of the change in the frequency of the accelerating electric field and the change in the controlling magnetic field determine the behavior of the orbit radius in time and the number of electrons captured into acceleration. The dependence of frequency on time that ensures constancy of the orbit radius [1] is

\[ f(t)=\frac{ceBR_0}{2\pi R_0S}\, \frac{1}{\sqrt{E_0^2+(eBR_0)^2}}, \tag{1} \]

where \(B\) is the magnetic field on the orbit of radius \(R_0\),
\(S\) is the orbit shape coefficient,
\(E_0\) is the electron rest energy.

For the 300 MeV synchrotron \(R_0=95\) cm, \(S=1.32\). The law of frequency variation, taking into account the character of the rise of the controlling magnetic field, is shown in Fig. 1. It follows from the figure that the range of frequency variation lies within \((28.16—37.505)\) MHz, with the greatest changes in frequency occurring during the first 140–200 μsec after injection. Thereafter the frequency changes little and, after approximately 500 μsec, remains practically constant.

Thus, it is expedient to divide the entire acceleration cycle into two stages. The first stage—the stage of synchrophasotron acceleration—covers the region of frequency variation. This period is comparatively short, and here, as the source of high-frequency power, a generator using pulse tubes may be employed, capable of developing sufficient power in the specified frequency band. The second stage occupies the main part of the acceleration cycle, but since acceleration is carried out at a constant frequency, ordinary oscillator tubes may be used here. An estimate of the tolerances for deviation of the frequency from the specified value shows that the most stringent requirements are imposed on the initial frequency, which must be maintained with an accuracy of 0.3%.

In the synchrotron, paired toroidal resonators—a broadband and a narrowband one—are used as the accelerating device. To avoid electron losses during the transition from the synchrophasotron stage of acceleration to the synchrotron stage, by exciting oscillations in the narrowband resonator [5] the frequency during the transition is changed

Fig. 1. Law of variation of the frequency of the accelerating voltage

abruptly from 37 MHz to 37.5 MHz. Thus, the period of synchrophasotron acceleration lasts 330 μsec. The magnitude of the accelerating voltage in the first stage is 600 V and increases to 1000 V in the second stage as a result of the increase in the growth rate of the controlling magnetic field.

Fig. 2. Block diagram of the accelerating system

The only available method for carrying out the frequency-variation program in our case, as, however, in other accelerators with a similar frequency deviation, is the use of ferrites. All other existing methods of frequency modulation either cannot provide the specified frequency deviation or have poor stability of parameters. The block diagram of the accelerating system for the synchrophasotron stage of acceleration is shown in Fig. 2.

For supplying the accelerating device, both self-oscillators and generators with independent excitation may be used. In the usual cases of frequency modulation, multistage generators with independent excitation have a number of advantages over self-oscillators. Their principal advantage is that the frequency is formed at low power levels, where the influence of destabilizing factors is smaller. However, when there is a large frequency deviation, the intermediate stages must be broadband. This circumstance leads to a tendency of the amplifiers toward self-excitation. The first version of the generator, consisting of an exciter with ferrite inductance and five amplification stages, proved unreliable precisely for this reason. At present a generator is used consisting of a frequency-modulated self-oscillator of about 3 kW power and an amplifier providing an output power of the order of 6 kW. The generator circuit is shown in Fig. 3. The basis for choosing the self-oscillator circuit was the following considerations.

Fig. 3. Schematic circuit of the generator

The following considerations were used. To obtain frequency modulation as a result of a change in inductance, both single-circuit generators and two-circuit generators may be used. The advantage of two-circuit self-oscillators over single-circuit ones is the possibility of independently adjusting the frequency and the feedback [3]. In a single-circuit generator, when the frequency is changed, the feedback coefficient inevitably changes and, as a consequence, so does the generated power.

The choice of ferrite for a single-circuit scheme presents no difficulties. It is sufficient that the coefficient of change of the magnetic permeability of the ferrite

\[ \kappa_\mu=\frac{\mu_{\max}}{\mu_{\min}} \]

be no less than the square of the frequency-tuning coefficient

\[ \kappa_f=\frac{f_{\max}}{f_{\min}};\quad \kappa_\mu \geq \kappa_f^2 \ [2]. \]

For two-circuit generators there is no such simple and obvious relation between \(\kappa_\mu\) and \(\kappa_f\). Calculation shows that, in the case where one of the circuits of the self-oscillator is tuned, the required value of \(\kappa_\mu\) depends on the ratio of the inductances of the circuits. Fig. 4 gives the dependence of \(\kappa_\mu\) on the ratio of the inductances of the self-oscillator circuits \(k_\phi=\dfrac{L_1}{L_2}\) with a common grid and ob-

...with a common anode, providing the necessary frequency overlap. It can be seen from the figure that the higher the requirement on the constancy of the power generated over the range, the higher the required ferrite \(k_\mu\). Uniformity of voltage over the range is bought at the price of increasing the ferrite tuning range. As for the circuit with a common cathode, its properties, as a two-circuit arrangement, are considerably weaker. Thus, two-circuit arrangements have no substantial advantages over a single-circuit arrangement.

Starting from this, the self-oscillator was assembled according to the usual two-stroke, three-point circuit with capacitive coupling. Experience in operation with the synchrotron showed that the nonuniformity of the accelerating voltage is small, and this nonuniformity can be considerably reduced by tuning the amplifier and introducing negative feedback. The generator circuit consists of a two-turn inductance coil wound on 3 ferrite rings of diameter 13 cm and total cross section \(12\ \text{cm}^2\). An analogous coil is used for coupling to the output stage. The high-frequency induction in the ferrite does not exceed the permissible value and is \(140\ \text{G}\). The ferrite rings are placed in the gap of an electromagnet, through whose windings flows a current whose magnitude and waveform determine the frequency-modulation program. Such a system makes it possible to simplify considerably the power-supply circuits of the electromagnet and to reduce the magnitude of the modulating current.

Fig. 4. Dependence of \(K_\mu\) on \(K_\Phi\) for a self-oscillator with a common grid and with a common anode

Fig. 5. Circuit for forming the modulating current

The tolerance for deviations of the law of frequency variation from the specified one is considerably less stringent than for the initial frequency. The tolerance for deviation of the modulating current is further relaxed by the circumstance that, in the absence of current, the self-oscillator frequency is close to the initial one. If the initial frequency is \(f_{\text{n}}\), then the permissible current deviations at frequency \(f\) are

\[ \frac{\Delta I}{I}=\frac{f}{f-f_{\text{n}}}\frac{\Delta f}{f}. \tag{2} \]

A characteristic feature is that here the tolerance decreases with increasing frequency and becomes most stringent toward the end of the synchrophaso-

tron stage, where it reaches a value of (1.5–2)%. Such comparatively low requirements on the modulating current made it possible to use the simple shaping circuit shown in Fig. 5.

The amplifier is assembled according to a push-pull circuit with a grounded grid. In each arm of the amplifier, two GI-14B tubes are installed in parallel. The shunt resistance of the resonator, to provide the specified passband, is 30 ohms; therefore the amplifier must deliver 6 kW of power to the load. The tubes deliver this power at an anode voltage of 6 kV. To couple to the load, two coaxial cables with a characteristic impedance of 75 ohms each are used; thus the amplifier load is symmetrical. The cable length is chosen to be \(\lambda/2\). The use of a cable of length \(\lambda/4\) would make it possible to increase the shunt resistance of the resonator by a factor of \(\sqrt{2}\) and to reduce the consumed power [6]. However, the complexity of tuning such a system and undesirable transformations do not permit its advantages to be realized.

Fig. 6. Time relationships of pulses in the generator

Both stages of the generator have anode modulation by rectangular pulses, with the output stage being switched on later so that the transients when the self-oscillator is switched on have time to die out. The self-oscillator modulator and the output-stage modulator operate on the principle of partial discharge of a storage capacitance through a thyratron [4]. The processes occurring in the generator are illustrated in Fig. 6.

REFERENCES

1. M. S. Rabinovich. Proceedings of FIAN USSR. Vol. X, 1958.
2. V. I. Kaganov. Low- and Medium-Power Radio Transmitters. Moscow—Leningrad, “Energiya,” 1964.
3. B. P. Terent’ev. Radio Transmitting Devices. Svyazizdat, 1963.
4. V. A. Borisov, G. N. Ostreiko, V. S. Panasyuk, L. I. Yudin. PTE, No. 4, 1963.
5. O. Wernholm. Arkiv för Fysyk B. 26, 1964.
6. A. Susini. Some wide-band quarter wavelength line coupling circuits. CERN 64-48, 20 November, 1964.