SELECTION OF SYNCHRONIZING DEVICES FOR INDUCTION ACCELERATORS

L. M. ANAN'EV, M. M. SHTEIN

(Presented by the scientific seminar of the Department of Industrial Electronics)

The extremal character of the dependence of the radiation-dose power generated by a betatron on the injection moment largely determines the stability of accelerator operation in the presence of disturbing factors, and leads to the necessity of a careful and well-founded selection of the corresponding synchronizing devices.

At present, the most frequently required moment, or phase, of injection is obtained by delaying the pulse generated by the magnetic-field zero-value sensor—a peaker—by means of biasing, or by electronic circuits. However, the indicated method of obtaining the injection phase is not the only one, and synchronization can be obtained from any periodic process associated with the operation of the betatron: the magnetic field in the gap, the magnetizing current in the coil, or the voltage on the electromagnet (Fig. 1).

The difficulty of selecting synchronizing devices is determined not only by the variety of possible methods of synchronization, but also by the difference in the excitation regimes of betatron electromagnets. Thus, with mixed excitation of the electromagnet, the rate of change of the magnetic field when passing through the zero value decreases sharply, which makes it difficult to use a peaker [1].

For a more substantiated selection of synchronization circuits, an analysis was carried out of the synchronization methods presented in Fig. 1, taking into account the following requirements:

1. Ensuring the necessary stability of the electron injection moment.

2. Simplicity and convenience of electrical adjustment of the injection phase.

3. The possibility of introducing automatic phase correction as a function of the principal destabilizing factors: the voltage and frequency of the supply network. Such correction makes it possible to increase the stability of operation of the betatron installation [2, 3].

4. The possibility of creating simple and reliable control circuits.

Despite the large number of works devoted to synchronization problems, the requirements for the time stability of control circuits have not been defined with sufficient clarity.

An attempt at a theoretical estimate of the time stability of synchronization devices was made in [4]. It follows from this work that, near the maximum, the relative change in intensity is equal to

\[ \frac{\Delta I}{I}=\frac{r_0}{b_0}\frac{\Delta t_i}{t_i}, \]

where \(r_0\) is the radius of the equilibrium orbit,
\(b_0\) is the half-width of the working gap,
\(\dfrac{\Delta t_i}{t_i}\) is the relative change in the injection phase.

We have experimentally measured, on small betatrons, the dependences \(I=f(t_i)\) under various conditions. For them

\[ \frac{\Delta I}{I}=(2.4 \div 3)\frac{\Delta t_i}{t_i}. \]

These data make it possible to estimate approximately the temporal instability of the circuit, which should not exceed \(0.5 \div 1\%\), so that the intensity instability caused by the synchronization circuit itself is no more than \(3 \div 5\%\). For high-energy installations the permissible temporal instability, in all probability, must be still smaller.

The greatest use at present has been gained by the control circuit in which the signal from the peaker starts an electronic delay circuit [5, 6]. As the delaying device, a blocking oscillator is usually used, with pulse-duration control by changing the grid bias of a normally cut-off tube (Fig. 2). In this case the temporal stability of the synchronization circuit is determined mainly by the stability of the duration of the multivibrator pulse.

Fig. 1. Diagram of possible synchronization arrangements.

Column headings in the diagram: “method of regulation”; “signal sensor”; “initial quantity.”

Diagram labels:

• Magnetization → Peaker → magnetic flux
• Controlled delay line → Peaker → magnetic flux
• Delay by electronic circuit → Peaker → magnetic flux
• Phase-shifting bridge with limiter → Coil → magnetic flux
• Delay by electronic circuit → Coil → magnetic flux
• Integrator with discriminator → Coil → magnetic flux
• RLC circuit with discriminator → Coil → magnetic flux
• Magnetization → Peak transformer → magnetizing current
• Delay by electronic circuit → Shunt → magnetizing current
• Phase-shifting bridge → Shunt → magnetizing current
• Limiter → Shunt → magnetizing current
• Magnetization → Peak transformer → voltage
• Delay by electronic circuit → Divider or voltage transformer → voltage
• Phase-shifting bridge → Divider or voltage transformer → voltage
• Integrator → Divider or voltage transformer → voltage
• magnetic flux, magnetizing current, voltage → electron injection

The circuit shown in Fig. 2 was subjected to experimental investigation. For changes in anode voltage within \(\pm 5\%\), the instability did not exceed \(\pm 0.3\%\). The pulse duration of the multivibrator, when the filament voltage is changed, depends strongly on the magnitude of the anode load (Fig. 3).

Thus, with careful design and selection of parameters, the stability of synchronization circuits with a blocking oscillator can be brought to \(0.6 \div 0.7\%\). When a phantastron circuit is used, the temporal stability can be improved [7].

A drawback of electronic delay circuits is that, in order to compensate for changes in the voltage of the power supply, it is necessary to intro-

additional devices. If the electromagnet and the injection circuit are supplied by an unstabilized voltage, the required change in the delay duration is equal to

\[ \frac{\Delta t_i}{t_i} = -\frac{1}{2} \left[ \frac{\Delta U_{1m}+\Delta\left(U_{3m}\cos\varphi_3\right)+\Delta\left(U_{5m}\cos\varphi_5\right)+\cdots}{U_{1m}} \right], \]

where \(U_{1m}, U_{3m}, U_{5m}\ldots\) are the amplitudes of the first, third, fifth, etc. harmonics of the supply voltage,

\[ \varphi_3,\ \varphi_5,\ldots \]

are the phases of these harmonics.

In synchronization circuits with pick-up feeding, the pulse generated by the pick-up is delayed relative to the instant at which the magnetic field passes through zero by a time \(t_i\), determined by the bias current \(I_{\text{п}}\) and the magnetic-field strength \(H_{\text{п}m}\) at the place where the pick-up is installed.

Fig. 2

\[ t_i=\frac{K_{\text{п}} I_{\text{п}}}{H_{\text{п}m}\omega}, \]

where \(K_{\text{п}}\) is a proportionality coefficient depending on the construction of the pick-up.

The moment of injection is determined only by the bias current \(I_{\text{п}}\), and its time stability can be made sufficiently high.

The advantage of the circuit with pick-up feeding, compared with electronic delay, is the automatic compensation of changes in the voltage and frequency of the electromagnet power supply. If there is no phase shift between the magnetic fields at the pick-up installation point and on the equilibrium orbit, the change in the bias current is determined only by deviations of the injection voltage \(U_i\) and is found from the expression

\[ \frac{\Delta J_{\text{п}}}{J_{\text{п}}} = \frac{\Delta U_i}{2U_i}. \]

Since the injection circuit consumes little power, stabilization of the injection voltage presents no difficulty. In this

case, the optimum injection conditions are maintained at an unchanged magnetizing current.

Among the above methods of synchronization, one may single out those in which the output quantity of the sensor is a voltage. They are all characterized by the fact that between the voltage and the magnetic flux there is a phase shift by an angle of the order of \(\pi/2\).

Analysis of the most characteristic cases has shown that, despite their simplicity, noise immunity, and the possibility in some cases of compensating destabilizing factors, the use of these methods for ordinary betatron power-supply circuits is inadvisable. This is due to the fact that, as a result of the large constant shift between the flux and the voltage, the time instability of the synchronization circuits must not exceed \(0.01\%\), which is difficult to ensure in practice.

Fig. 3

For betatrons with mixed excitation, especially at high bias levels, when the angle of shift between the zero value of the magnetic field and the voltage is small, this method of synchronization may find application. A variant of the circuit using, as sensors, turns placed in the interpole space and subsequent discrimination of the voltage at a definite level was tested during the adjustment of a betatron with mixed excitation, PMB-5, and gave satisfactory results.

When considering synchronization systems based on the magnetizing current, one should take into account the various power-supply circuits for the electromagnet windings. If the betatron has two windings, an exciting winding and a magnetizing winding, only the current of the magnetizing winding can be chosen as the reference signal. For this case a vector diagram was constructed and an analytical expression was found for the shift angle between the current and the magnetic flux. This relation is rather complicated: it includes the frequency of the supply network \(\omega\), the ohmic resistance of the magnetizing winding \(r_2\), the capacitance and loss-angle tangent \(\delta\) of the compensating capacitor bank \(C\), and the leakage inductances.

Neglecting the nonlinearity of the electromagnet and the leakage inductances, the expression for the relative shift angle may be written as follows:

\[ \frac{\Delta \alpha}{\alpha} = \frac{\omega r_2 C}{\omega r_2 C+\operatorname{tg}\delta} \left( \frac{\Delta \omega}{\omega} + \frac{\Delta r_2}{r_2} + \frac{\Delta C}{C} \right) + \frac{\operatorname{tg}\delta}{\omega r_2 C+\operatorname{tg}\delta} \cdot \frac{\Delta \operatorname{tg}\delta}{\operatorname{tg}\delta}. \]

Experiments also made it possible to establish that, for such a power-supply circuit of the electromagnet, the relation between the magnetizing current and the magnetic flux is determined by a number of quantities that are difficult to control: the shift angle depends in a complicated way on the supply voltage, and the temperature dependence of the angle \(\alpha\) is also substantial. The factors considered lead to significant time variations of the injection instant and to radiation instability. Therefore, the use of this synchronization method—

...synchronization for betatrons with an excitation and magnetizing winding is, in all probability, inexpedient.

If a betatron has only a magnetizing winding, which most often is fed from a step-up transformer, the phase-shift angle between the current and the flux depends on the magnitude of the reactive and active components of the total resistance of the magnetic circuit and on the design dimensions of the electromagnet. An approximate expression for the phase-shift angle has the form:

\[ \alpha = \frac{\rho_x} {\rho_R+\dfrac{\delta_0 k_c r_n}{2\sqrt{2}\,\mu_0 l_{\mathrm{av}}\sigma r_0}}, \]

where \(\rho_x\) and \(\rho_R\) are the specific reactive and active resistance of the steel of the magnetic core,

\[ \begin{aligned} l_{\mathrm{av}}&\text{— length of the mean line of force of the magnetic flux in the steel,}\\ k_c&\text{— steel filling factor,}\\ \delta_0&\text{— gap at the equilibrium orbit,}\\ r_n&\text{— outer radius of the pole,}\\ \sigma&\text{— leakage coefficient of the electromagnet poles.} \end{aligned} \]

The absolute value of the phase-shift angle for transportable betatrons at a frequency of 50 Hz is of the order of 30 μsec. The dependence of the angle \(\alpha\) on the supply voltage is determined by the specific active resistance \(\rho_R\), since \(\rho_x\) is almost independent of induction [8]. In the range of induction values \(10 \div 15\) kGs the active resistance \(\rho_R\) increases sharply, but for betatrons the magnetic resistance of the air gap is considerably greater than the resistance of the steel magnetic core; therefore the decrease of the angle \(\alpha\) with increasing voltage is insignificant.

The dependence of the phase-shift angle \(\alpha\) on the frequency of the supply network is completely determined by the specific reactive resistance \(\rho_x\), which depends on frequency in the same way as the losses in steel, i.e., to the power 1.3.

The decrease of the phase-shift angle \(\alpha\) when the supply voltage changes from zero to its maximum is small and is of the order of 5 μsec at a frequency of 50 Hz. Temperature changes of the angle \(\alpha\) were within the limits of experimental error.

Thus, the analysis carried out above of various methods of synchronization makes it possible to establish that a circuit with pre-magnetization of the peaker is capable of ensuring the creation of simpler and more stable synchronization systems. If, for one reason or another, obtaining the required injection instant by feeding the peaker is undesirable, an electronic delay circuit should be used. For installations in which the use of a peaker is fundamentally impossible (for example, with mixed excitation of the electromagnet), synchronization systems using the magnetic flux must be used; and for betatrons with a single excitation winding, using the magnetizing current.

REFERENCES

1. Yu. P. Yarushkin. Candidate dissertation. Tomsk, TPI, 1965.

2. V. M. Razin. Izv. TPI, vol. 87, 206, 1957.

3. N. Ya. Makarov. Candidate dissertation, Tomsk, TPI, 1966.

4. L. M. Anan’ev, Ya. S. Pekker. Dependence of the radiation intensity of a betatron on the injection phase. Abstracts of reports of the Sixth Inter-University Conference on Electron Accelerators, Tomsk, 1966.

5. L. M. Anan’ev, V. L. Chakhlov, Ya. A. Sharashin, M. M. Shtein. Transportable small-size betatron PMB-3, PNTPO, No. 2-64-624/14, GOSINTI, Moscow, 1964.

6. Betatron B-25/10. Technical description and operating instructions, NIIEYaI, Tomsk, 1963.

7. L. A. Meerovich, Kh. G. Zelichenko. Pulse Engineering. “Sov. radio,” Moscow, 1953.

8. B. K. Bul’. Fundamentals of the Theory and Calculation of Magnetic Circuits. Energiya, Moscow—Leningrad, 1964.