EXTREMAL REGULATOR OF THE INTENSITY OF BETATRON RADIATION

E. M. BELOV, N. Ya. MAKAROV, I. E. NAATS

Presented by the scientific seminar of the Scientific Research Institute of Electrical Measurements

The problem of ordinary regulation differs from extremal regulation and, as is known, reduces to maintaining, with the required accuracy, equality between the actual value and a previously specified value of the regulated quantity. The latter may be either constant (automatic stabilization) or variable (programmed regulation, tracking systems).

In systems of extremal regulation, the value of the regulated quantity is not known in advance and is not specified; regulation reduces to finding and maintaining with the required accuracy the extremum of the regulated quantity, which varies in time according to a law not known in advance. To carry out extremal regulation, knowledge of all the functional dependences determining the magnitude and position of the extremum is not required; it is necessary only that an extremum exist.

The extremum regulator of the intensity of betatron radiation is based on the operating principle of a regulator with “memory” of the extremum, with forced variation of the input coordinate “\(x\)” at a constant rate.

The maximum value of \(y\), reached at the moment \(t\), is recorded by a special “memory” device. After passing through the maximum, the current value of the coordinate \(y\) is compared with its extremal value and, when the difference \(\delta = y_{\max} - y\) reaches the specified value \(\delta_{\max}\), the direction of variation of the coordinate \(y\) is reversed and the memory is removed. The coordinate \(y\) again begins to increase, approaching the extremum from the other side; subsequently the process is repeated.

Since the dependence of the radiation intensity on the generation phase of the injection pulse sometimes has a double-peaked characteristic, use of the gradient method under these conditions is difficult.

The block diagram of the extremum regulator of radiation intensity is shown in Fig. 1: 1 — the controlled object (induction accelerator); 2 — radiation sensor (the “Kaktus” roentgenometer); 3 — error-signal processing system; 4 — automatic extremum-search system; 5 — regulating device (injection circuit).

The schematic diagram of the radiation sensor is shown in Fig. 2.

The signal, proportional to the magnitude of the radiation intensity and obtained in the ionization chamber, is amplified by a dc amplifier built around \(L_1\)-6Zh3P, inverted (\(L_2\)-6N15P), and

Fig. 1. Block diagram of the extremum regulator of betatron radiation intensity.

is fed to the control grid of \(L_3\)-6Zh10P of the harmonic-oscillation generator, modulating them in amplitude.

Fig. 2. Schematic circuit of the radiation sensor.

The inductive coupling of the generator with the input circuit of the first stage of the error-signal processing system makes it easy to transmit the measured signal from the radiation-sensor circuit, which has no common pole with the error-signal processing circuit, to other circuits of the regulator. The schematic circuit of the error-signal processing system is shown in Fig. 3.

The principle of operation of such a system is as follows. During operation of the regulator in the automatic search mode for the extremum, the phase of the injection pulse passes through all values from zero to \(30 \div 60\ \mu\text{s}\), depending on the maximum energy of the accelerated electrons and the amplitude of the injection pulse. In this process, capacitor \(C_8\) in the peak-detector circuit, built around \(L_4\)-6N8 and \(L_5\ \tfrac{1}{2}\ 6Kh6, is charged to the voltage corresponding to the maximum radiation intensity, while capacitor \(C_{11}\) is charged to the voltage corresponding to the current value of the radiation intensity.

Fig. 3. Schematic diagram of the error-signal processing system.

The voltages obtained, \(u_1\) and \(u_2\), are fed to the subtracting circuit \(L_{16}\)-6N8 and \(\frac{1}{2}L_7\)-6N8, which produces the error signal \(\delta = k(u_1-u_2)\), determining the duration of the control pulse of the flip-flop relay \(L_8\)-6N8.

The tube \(L_7\)-6N8 in the amplitude-comparator circuit serves as a current stabilizer, which makes it possible to ensure linearity of the cascade characteristic.

\[ \delta_{\max}=k\cdot (u_{\max}-u_{\sim}), \tag{1} \]

where \(k\) is the gain factor;
\(u_{\max}\) is the maximum value of the voltage on the reference-coordinate integrator;
\(u_{\sim}\) is the value of the voltage on the current-coordinate integrator.

The control device of the error-signal processing system is a monostable multivibrator generating pulses of variable duration with a maximum overlap factor \(k_{\mathrm{p}}\cong 8\). The duration of the pulses of the monostable multivibrator is a linear function, in the operating range, of the mismatch signal and may be represented in the form

\[ \tau=\tau_{\max}\left(1-\frac{\delta}{\delta_{\max}}\right), \tag{2} \]

where \(\tau_{\max}\) is the maximum duration of the pulse generated by the multivibrator;
\(\delta_{\max}\) is the maximum value of the mismatch signal.

The control pulse is applied to the automatic-search system, the schematic circuit of which is shown in Fig. 4. The automatic-search system includes the regulating cascade \(L_{10}\)-6Zh4, operating in the sawtooth-voltage generation mode during search and in the dc-amplifier mode when tracking the extremum of the radiation intensity.

Fig. 4. Schematic circuit of the automatic-search system.

In the search mode, the sawtooth voltage from the output of the regulating cascade, through the matching cascade \(\frac{1}{2}L_7\)-6N8, is applied to the tracking multivibrator \(L_{11}\)-6N8, changing the duration of its output pulse. The tracking multivibrator is synchronized by pulses from the field sensor of the betatron magnet; by the trailing edge of its output pulse it triggers the shaping cascade \(L_{12}\)-6N8 and, through the cathode follower \(L_{13}\)-6P3, the injection circuit.

After a certain time, necessary for storing the maximum of the radiation intensity, the switch \(k_1\) is turned on, and the processing system

of the error signal proves to be connected with the automatic extremum-search system. The operating principle of such a system can be traced from the static characteristic \(I=f(\varphi)\) as the scanning injection pulse moves along the phase axis \(\varphi\).

For \(\delta \to 0\) to the left of the maximum value of the radiation intensity—\(I_{\max}\) (motion toward \(\varphi_{\max}\))—the duration of the control pulse of the multivibrator \((L_9)\) \(\tau_u \to \tau_{\max}\), as a result of which the negative voltage drop in the diode circuit of \(1/2\,L_9\text{-}6X6\) increases, thereby reducing the rate of change of the sawtooth voltage of the regulating stage \(L_{10}\). Thus, the change in the phase of the injection pulse as the latter moves toward \(I_{\max}\) becomes slowed.

When the injection pulse passes the value \(\varphi_{\max}\), at which the radiation intensity is maximal, a mismatch signal appears which reduces the duration of the control pulse, causing the sawtooth voltage to move in the reverse direction. The tracking circuit is phased in such a way that, for the mismatch signal \(\delta=0\), the phase of the injection pulse decreases. Owing to this, a slowed motion toward the maximum of the radiation intensity is ensured, but now from the other side; moreover, the regulating stage \(L_9\) operates practically in the dc-amplifier mode.

The duration of the pulse of the tracking multivibrator is then reduced and, consequently, \(\varphi \to \varphi_{\max}\), but now from the right along the characteristic.

Obviously, again \(\delta \to 0\) and \(\tau_u \to \tau_{\max}\) when the injection pulse passes the values \(\varphi=\varphi_{\max}\), \(\delta=0\), and the process is repeated again.

The amplitude of the oscillations is determined by the sensitivity of the circuit and by the period of inertia of the regulator and the object; therefore these parameters are subject to experimental verification.

Switch \(K_2\) ensures operation of the regulator in the mode of a stabilizer of radiation intensity at any required level of radiation intensity.

Experimental verification of the extremum regulator

The purpose of the experimental verification of the extremum regulator was to determine the practical possibility of extremal regulation of the radiation intensity of a betatron. If such regulation is possible, it is necessary to determine the effective value of the radiation intensity \(I_{\mathrm{eff}}\), the amplitude of the oscillations about the maximum, and the period of these oscillations.

In designing the extremum regulator, the characteristic of the betatron shown in Fig. 5 was used, for an accelerator with a maximum energy of the accelerated electrons of up to \(15\,\mathrm{MeV}\). The total time for traversing the characteristic from 0 to \(50\,\mu\mathrm{s}\) was chosen to be 2 seconds; in this case the change in phase of the injection pulse with each subsequent pulse was \(0.5\,\mu\mathrm{s}\) at a pulse repetition frequency of \(50\,\mathrm{Hz}\).

The experimental verification of the extremum regulator was carried out on a betatron with a maximum energy of the accelerated electrons of \(15\,\mathrm{MeV}\); in this case the regulated radiation intensity reached up to \(0.95\,I_{\max}\).

A secondary test of the extremum regulator was carried out on a betatron with a maximum energy of accelerated electrons up to 30 MeV. In this case the radiation intensity reached \((0.6 \div 0.7) I_{\max}\). Such

Fig. 5. Static characteristic of a 15 MeV betatron.

a decrease in the radiation intensity is due to the peaked character of the dependence of the radiation intensity on the generation phase of the injection pulse for this accelerator, Fig. 6. Tracking of the maximum

Fig. 6. Static characteristic of a 30 MeV betatron.

of the radiation intensity, with a sufficiently narrow peak characteristic (about \(2\ \mu\text{sec}\)), is difficult because the “memory” device of the reference coordinate proved unable to hold—

store in “memory” the maximum value of the radiation intensity during the time required to search for the extremum (about 2 seconds).

The amplitude of the self-oscillations was approximately \(0.15 I_{\max}\), and they occurred around the point \(I \simeq (0.6 \div 0.7) I_{\max}\) with a frequency of about 10 Hz. In order to create better conditions for storing the maximum value of the radiation intensity, it would have been possible to increase the time of traversal of the characteristic (the period), but, on the other hand, this would have led to an increase in the inertia of the regulator and, consequently, to a decrease in \(I_{\mathrm{eff}}\).

It is evident that it is necessary to introduce into the regulator circuit an auxiliary device that would store the maximum radiation-intensity value for a sufficiently narrow static characteristic of the controlled object, using the optimum time for traversing it.

Conclusions

1. The use of an extremal regulator of radiation intensity with forced variation of the input coordinate and storage of the extremum is advisable for accelerators with a maximum accelerated-electron energy of up to 30 MeV.

2. When using an extremum regulator on a betatron with \(E = 30\) MeV, it is necessary to introduce additionally into the reference-coordinate circuit a device for “operational memory” and to use a device with the optimum traversal time of the static characteristic of the controlled object.

References

1. E. M. Belov, I. E. Naats. Extremal regulator of gamma-radiation intensity. Author’s certificate No. 141 912.

2. E. M. Belov, V. N. Titov. Device for regulating the gamma-radiation intensity of a betatron. Author’s certificate No. 140 505.