COMPUTING DEVICE FOR CONTROLLING THE INJECTION PHASE OF A BETATRON

V. M. Razin, V. L. Ryabukhin

(Presented by the scientific seminar of the Department of Mathematical and Computing Instruments and Devices)

One of the main reasons affecting the magnitude and stability of betatron radiation is the requirement of exact fulfillment of the injection condition, which, according to [1], can be written in the form

\[ t_i=\frac{k\sqrt{U_i(U_i+1.02)}}{U_m}, \tag{1} \]

where
\(t_i\) is the time in seconds;
\(U_i\) is the injection voltage in megavolts;
\(U_m\) is the voltage taken from the additional winding of the electromagnet, in volts;
\(k\) is a constant coefficient.

The required accuracy in determining and setting the injection instant [1] can be provided by a digital computing device which, depending on the adopted algorithm for solving expression (1), may have several design variants.

Let us consider some of them.

Constructing the device as a digital computer performing all arithmetic operations will obviously not be optimal. To eliminate the division operation, expression (1) can be represented in the form

\[ t_i=f(U_i)\cdot f(U_m), \tag{2} \]

where

\[ f(U_i)=\sqrt{U_i(U_i+1.02)}, \tag{3} \]

\[ f(U_m)=\frac{k}{U_m}. \tag{4} \]

The solution of expression (2) can be obtained with the aid of a specialized computing device that carries out multiplication of functions (3) and (4), while the determination of the function values themselves is performed either by functional converters or by means of a read-only memory device (ROM). The advantage of a device of the functional-converter type is the simplicity of performing the multiplication operation (digital potentiometer), the simplicity of the operating logic and, consequently, of the control device. The disadvantages of this device include the complexity of constructing and adjusting high-precision functional converters, and stringent requirements on the power supplies.

tion and radio components, and low noise immunity. Since the information arrives at the input in the form of pulsed and alternating voltage, repeated transformations of the signals from one form to another lead to a loss of the required accuracy.

Figure 1 shows a block diagram of a specialized computing device that uses the determination of the values (3) and (4) by means of a ROM, where

I — converting device: 1 — channel switch; 2 — analog-to-digital converter (ADC).

II — ROM: 3 — address system; 4 — matrix \(f(U_i)\); 5 — matrix \(f(U_m)\); 6 — \(k_0\) coefficient generator.

III — multiplying device: 10 — control device, 11 — adder; 12 — multiplier register.

IV — digital-to-analog converter: 7 — trigger; 8 — gate; 9 — counter.

Fig. 1. Block diagram of the computing device for controlling the injection phase of a betatron, where I — converting device: 1 — channel switch; 2 — analog-to-digital converter.
II — ROM: 3 — address system; 4 and 5 — matrices \(f(U_i)\) and \(f(U_m)\); 6 — \(K_0\) coefficient generator.
III — multiplying device: 10 — control device; 11 — adder; 12 — multiplier register.
IV — digital-to-analog converter: 7 — trigger; 8 — gate; 9 — counter.

The circuit of the device was developed for a 30-MeV betatron having the following parameters: \(r_0 = 25\ \text{cm}\), \(U_i = 40\ \text{kV}\), and \(H_m\).

The values \(U_i\) and \(H_m\) may vary within the range \(\pm 12.5\%\) without impairing the operability of the device.

The use of such a device with other betatrons encounters difficulties associated with changing the values of the functions stored in the ROM and, consequently, with replacing the storage matrices. To eliminate this drawback, the following algorithm was adopted for determining the values of the injection phase:

\[ t_i = k_0 \cdot f(U_i) \cdot f(U_m), \tag{5} \]

where \(k_0\) is a proportionality coefficient that depends on the type of betatron and is determined experimentally.

It can be shown that the change in the functions (3) and (4), when their arguments vary from their maximum value down to the level 0.75 \((\pm 12.5\%)\), is smooth in character. Therefore, for new values of \(U_i\) and \(U_m\), the character of the change in the functions will remain the same, but in order to obtain the correct

for the solution, their product must be multiplied by the correction coefficient \(k_0\).

Let us consider the operation of the device shown in Fig. 1.

At the moment when a pulse from the magnetic-field zero sensor arrives at the input of the device, channel switch 1 switches ADC-2 into the mode of converting the amplitude of the injection pulse. After the conversion is completed, the parallel ten-bit binary code corresponding to the pulse amplitude, entering address system 3, excites in it the required output bus, as a result of which the value of the function \(f(U_i)\) is issued from the matrix \(f(U_i)\)—4 to adder 11. Selection of the required matrix is carried out by the channel switch. The value of the coefficient \(k_0\) is written into the multiplier register. The multiplication operation begins with the most significant bits. The shifting of the adder and the register is performed toward the more significant bits. After the multiplication operation is completed, the most significant bits of the product \(k_0 \cdot f(U_i)\) are written into the multiplier register, and the adder is cleared, as a result of which the product is rounded.

At the moment when the voltage \(U_m\) reaches its amplitude value, ADC-2 begins to operate again, and at its output a binary code of the input value \(U_m\) is formed; according to this code, the required value of the function \(f(U_m)\) is selected from the matrix \(f(U_m)\)—5, after which the value \(f(U_m)\) is multiplied by the value \(k_0 \cdot f(U_i)\). The final result of the product is transferred from the multiplier register, in the form of a parallel ten-bit inverse code, to counter 9. When a pulse arrives from the zero-field sensor, trigger 7 opens gate 8, and pulses with a repetition frequency of 10 MHz begin to arrive at the input of the counter, which is simultaneously the counter of an analog-to-digital converter. The overflow pulse of the counter serves to start the injection circuit. This completes the operating cycle. Determination of the injection time in the next period proceeds similarly. The maximum time for the device to enter the mode of determining and setting the injection time is two periods of variation of the line frequency.

Tests of the prototype of the computing device showed the high reliability of its operation, as well as the advisability of using it both as an autonomous regulator of the betatron injection phase and in combination with other devices that set the injection time depending on the output radiation, which will make it possible to sharply increase the stability of the radiation.

REFERENCES

1. V. M. Razin, V. L. Ryabukhin. On the question of developing a computing device for regulating the injection phase of a betatron. This collection.