Some Circuit Elements of a Semiconductor Optimizer of Betatron Gamma-Radiation Intensity

V. M. Razin, V. P. Sherstobitov

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

It is known that, in order to obtain the maximum radiation of a betatron, optimizers, or extremal regulators, are used; preference is given here to optimizers with rectangular modulation of the principal controlled parameter—the phase of electron injection into the accelerating chamber. The main units in this case are the integrator, comparison circuit, actuating device, modulator, pulse selector, and other auxiliary circuits. A wide variety of implementations of the main units is possible. However, existing extremal regulators have a number of fundamental shortcomings: slowing of the search for the maximum due to the use of modulation with a small constant amplitude; considerable oscillation of the operating point in the vicinity of the maximum when the time constant of the comparing detectors is small; and deterioration of the dynamic properties of the optimizer when the time constants of the comparing detectors are increased.

The authors of the present work proposed ideas for improving optimizers, which were reported at the Fifth Interuniversity Conference on Electron Accelerators in Tomsk in March 1964.

Modulation with variable amplitude was proposed, as well as a circuit for combining the comparison time of a pair of radiation pulses and a circuit for automatic search of the range of operating injection phases.

Information on the considerations underlying the improved optimizer can be found in the proceedings of the aforementioned conference, while the aim of the present article is to examine the technical principles of constructing the principal units of the optimizer and to provide recommendations for implementing them with semiconductor devices.

Actuating device. As the actuating device, a peak transformer is used, with the phase of the pulses shifted by passing the magnetizing current through a regulating winding. The peak transformer may be installed in the field of the betatron electromagnet or connected to the mains.

Modulator with a variable modulating action on the injection phase. Modulation of the phase of the injection pulses is carried out by a magnetizing current through a special winding (the modulating winding) of the peak transformer. In this circuit a law of variation of the am-

…of the amplitude of the modulating current or of the phase of electron injection according to the formula

\[ \delta T=\delta T_0-aI', \tag{1} \]

where \(\delta T_0\) is the initial amplitude at \(I'=0\);

\(I'\) is the intensity of the betatron gamma radiation at the given instant of time in the absence of modulation;

\(a\) is a dimensional proportionality coefficient.

Here one-sided rectangular pulse modulation is assumed, in which a magnetizing current is applied during the pulse. Changing the amplitude according to formula 1 is easy to implement, since it is only necessary to perform subtraction and multiplication by a constant coefficient.

When the radiation intensity \(I'\) reaches a certain level, the optimizer is transformed into a system with a constant modulating action. For this purpose \(I'\) is limited at the level \(I_0\).

The modulator circuit is shown in Fig. 1.

The initial amplitude \(\delta T_0\) is obtained from the current from the control trigger TU, which is started by negative pulses from the signal winding of the peaking transformer (positive pulses are used to control the injection circuit). The current is then amplified by transistor \(T\).

Resistance \(R_1\) is intended for adjusting \(\delta T_0\).

The collector circuit of the control trigger is supplied with a negative voltage, and the emitter circuit with a positive one, so that the voltage at the collector of any transistor may have either sign depending on the state of the trigger.

Pulses \(I'\) of positive polarity are rectified and create a current through resistance \(R_2\) in such a way that the resulting base current of the open transistor \(T\) corresponds to the value \(\delta T\). The coefficient \(a\) is adjusted by a variable resistance.

Fig. 1. Circuit of a modulator with variable modulation depth.

Radiation-pulse selector. To obtain information on the direction of motion of the operating point along the injection-phase axis, the compared pairs of pulses must be switched through separate channels.

Fig. 2. Circuit for selecting radiation pulses of one channel.

Pulse selection is carried out by means of transistor switches. The circuit of one of the comparison channels is shown in Fig. 2 (channel \(I''\) when the modulating current flows through the winding of the peaking transformer).

For radiation pulses \(I''\), when the biasing modulating current flows, the detector \(D_2 R_3 C_3\) is opened when transistor \(T_2\) of the \(npn\) type is closed; this transistor is controlled by the trigger TrU shown in the circuit in Fig. 1.

The gain of the decoupling amplifier on \(T_1\) varies, depending on the state of TrU, within the following limits:

\[ K_{\max} \simeq \frac{R_2}{R_1}, \]

\[ K_{\min} \simeq \frac{R_T}{R_1}. \tag{2} \]

Here \(R_1, R_2\) are the resistances of the circuit in Fig. 2,
\(R_T\) is the resistance of the open transistor \(T_2\).

To ensure reliable cutoff it is necessary to satisfy the condition

\[ R_1 \gg R_T . \tag{3} \]

The resistances \(R_1\) and \(R_2\) should be chosen from the condition of ensuring an allowable time constant for charging the capacitance \(C_3\).

Circuit for matching the comparison times of a pair of radiation pulses. If the pulses being compared occur successively in time, then, when they are applied to detectors with a small time constant connected at the input of the integrator, considerable fluctuations of the voltage at the integrator from pulse to pulse will be observed. Small time constants of the comparison detectors are necessary for high-speed tracking of the radiation maximum, since the latter may rapidly shift along the phase axis.

In the optimizer described, a circuit for matching the comparison times of a pair of pulses is used; in simplified form it is presented in Fig. 3.

Fig. 3. Circuit of a channel with storage of radiation pulses.

At the input of the circuit there is connected a decoupling amplifier similar to that shown in Fig. 2.

The capacitance \(C_2\) performs the functions of a storage device and a voltage inverter by means of transistor switches. The trigger TrU helps to select the pulses of the required channel (in the present case, pulses \(I'\)).

At the moment of arrival of \(I''\), transistor \(T_1\) is opened by means of the waiting multivibrator \(M\), operating synchronously with the circuit that resets the accelerated electrons in the betatron from the orbit onto the target. The multivibrator \(M\) also forms a pulse that removes the residual charge from the capacitance \(C_2\) after transfer of part of the voltage to the capacitance \(C_3\). This is accomplished

with the aid of the blocks \(M\) and TrU. The pulse \(J'\), in the absence of a modulating action, arrives when transistor \(T_2\) is open and capacitor \(C_2\) is charged through it and \(D_2\) (\(T_1\) and \(T_3\) are closed). The voltage on the capacitor is retained until the appearance of \(J''\) (by this time transistor \(T_2\) is already closed). Then \(T_1\) opens and, through it and diode \(D_3\), capacitor \(C_3\) is charged (synchronously with the charging process of capacitor \(C_3\) in the circuit of Fig. 2).

When TrU passes from the state \(J''\) to the state \(J'\), a pulse is again formed by the multivibrator \(M\), and capacitor \(C_2\) is completely discharged through transistors \(T_1\) and \(T_3\), and the circuit is prepared for storing a new pulse \(J'\).

In the calculation it should be taken into account that the collector current of the transistors depends only slightly on the collector voltage and depends mainly on the controlling base current.

The condition for charging \(C_2\) to the amplitude value of the input voltage can be written approximately, taking the collector current to be constant at the moment of charging,

\[ \frac{I_z \cdot t_i}{C_2} \gg U_{\max}, \tag{4} \]

where \(I_z\) is the charging current,
\(t_i\) is the duration of the radiation pulse,
\(U_{\max}\) is the maximum signal amplitude (a voltage proportional to the maximum radiation intensity).

When the charge is transferred from capacitor \(C_2\) to capacitor \(C_3\), the voltage on the latter will not exceed the value

\[ U_{C3} \le \frac{C_2}{C_2 + C_3}\, U_{\max}. \tag{5} \]

In this case condition 4 is written in the form

\[ \frac{I_p \cdot t_m (C_2 + C_3)}{C_2 \cdot C_3} \gg U_{\max}, \tag{4′} \]

where \(I_p\) is the current of charge transfer from capacitor \(C_2\) to capacitor \(C_3\),
\(t_m\) is the pulse duration of the monostable multivibrator \(M\) (the duration of the open state of transistor \(T_1\)).

The relations given make it possible to choose correctly the parameters of the circuit elements.

The charge-storage time of capacitor \(C_2\) depends on the reverse resistances of the diodes and the resistances of the closed transistors. In this circuit it is better to use silicon elements throughout; however, it is sufficient to use the silicon diode \(D_1\) and transistor \(T_1\).

Circuit of the output stage of the integrator. The known difficulty is the implementation of dc integrators using transistors because of the strong zero drift. However, for the optimizer it is possible to use dc amplifiers with modest drift compensation, since it operates in the following mode.

Figure 4 shows the circuit of the output stage of an integrator with a bipolar output relative to ground.

Thus, through the regulating winding of the peak transformer, the magnetizing current can flow in both directions. The transition from a unipolar circuit to a bipolar one is carried out with the aid of transistor \(T_1\) (\(npn\)), connected in a common-base circuit. The collector current of this transistor flows through resistor \(R_5\) and the base of \(T_2\).

With the aid of the variable resistance \(R_5\), the zero of the integrator can be set.

Fig. 4. Output stage of the integrator.

The limits of variation of the voltage in this case will be:

upper limit \(U_k \approx E_{\mathrm{e}}\),

lower limit

\[ U_k \approx E_k \cdot \frac{R_4}{R_3 + R_4}. \]

The remaining units of the optimizer are made according to standard circuits.