SYNCHRONIZATION CIRCUIT FOR A PULSED BETATRON

M. M. Shtein

(Submitted by the Research Institute of Nuclear Physics, Electronics, and Automation)

Powering a betatron with unipolar current pulses improves its technical and economic characteristics [1]. The pulsed nature of the excitation of the electromagnet imposes a number of specific requirements on the construction of the synchronization circuit, whose main task consists in setting the moment of injection. The use of synchronization circuits developed for betatrons with continuous power supply often proves ineffective, and sometimes simply impossible. Traditional synchronization circuits are, as a rule, constructed using a peak-transformer sensor of the zero field value, which provides a reference signal, while the required delay is obtained by premagnetizing the sensor or by means of electronic circuits [2].

With pulsed power supply, when the betatron electromagnet is connected to a charged capacitor bank, a signal is induced in the winding of the peak-transformer sensor and oscillatory processes arise, disrupting the operation of the synchronization circuit.

In addition, one of the requirements imposed on the synchronization circuit is the possibility of automatic correction of the injection moment depending on destabilizing factors and, in particular, changes in the supply-network voltage [3]. With pulsed power supply of the betatron, along with random changes in the supply voltage, pulsations are observed that are associated with the fact that the pulse frequency is, as a rule, higher than the network frequency. Thus, in the synchronization circuit of a pulsed betatron such correction must necessarily be provided.

Synchronization of the injection moment consists in matching the velocity of the injected electrons with the field magnitude on the equilibrium orbit. In this case the maximum charge is captured into acceleration. At small injection voltages the matching is determined by the following expression:

\[ B_i = \frac{3.37\sqrt{U_i}}{r_0}, \tag{1} \]

where

\[ \begin{aligned} B_i &\text{ — the value of the induction on the equilibrium orbit } r_0;\\ U_i &\text{ — the injection voltage.} \end{aligned} \]

If the value of the emf in the turns enclosing the contour is known, then the magnitude of the induction inside this contour at any point can be found, to within a constant factor, as:

\[ B(t)=k\int_0^t e(t)dt+B_{\text{res}}; \tag{2} \]

\(B_{\text{res}}\) is the residual or initial value of the induction, determined by the presence of the ferromagnetic core.

In expression (2) nonlinear effects are not taken into account. This should not lead to significant errors, since in the magnetic circuit of the betatron there is a large air gap and, on the other hand, the field at the moment of injection is small.

It may be assumed that the emf \(e(t)\) is proportional to the voltage on the capacitor bank, and before the moment of injection it has not had time to change appreciably; then the moment of injection is approximately found as

\[ t_i=\frac{B_i-B_{\text{res}}}{ke(0)} \, ; \tag{3} \]

Let us first consider the effect of residual induction. As follows from expression (3), if the residual induction is proportional to the supply voltage, then its presence leads to a decrease in the required delay by a constant amount, which can easily be taken into account. In reality, however, the magnitude of the residual induction depends in a complicated way on the supply voltage and, in the region of high voltages, decreases as the voltage increases.

Fig. 1

Figure 1 gives the dependence of the residual induction on voltage, measured for a small-size betatron of energy \(6\) MeV at a pulse frequency of \(200\) Hz. Within the limits of the permissible fluctuations of the supply voltage, \(10\%\), the magnitude of the residual induction changes on average by \(0.2\) G.

This is not a very large value, since the field at the moment of injection in the investigated betatron is approximately \(100\) G and the required change in the moment of injection will be about \(0.2\%\); nevertheless, as follows from [4], when increased demands are placed on the stability of the betatron radiation, the effect of residual induction must be taken into account. In betatrons of medium and higher energies, residual induction will have a stronger effect because of the larger absolute value and because of the decrease of the field at the moment of injection. Expression (2) shows that it is desirable to construct the synchronization circuit so that it performs the same operation of integrating the emf (supply voltage) as the betatron electromagnet. In this case there will be automatic correction of the moment of injection according to the required law in accordance with the change in the supply voltage.

The author has developed and experimentally tested a circuit implementing such a principle in simplified form (Fig. 2). Its basis is a single-cycle magnetic amplifier \(MU\), serving as an element of the...

delay [5]. The operating winding of the amplifier \(W_p\), in series with which the load resistance \(R_{\mathrm{n}}\) is connected, is supplied by the voltage \(e(t)\), taken from turns wound on the central core of the betatron.

An approximate analysis of the operation of the circuit can be carried out using the magnetization curve of the MU core (Fig. 3). The initial state \(1(B_n, H_n)\) is determined by the ampere-turns of the control \(i_y W_y\) and compensating \(i_k W_k\) windings:

\[ H_n=\frac{i_y W_y+i_k W_k}{l_{\mathrm{ct}}}, \tag{4} \]

where

\(l_{\mathrm{ct}}\) is the mean length of the line of force of the MU core.

When the voltage \(e(t)\) is applied, the operating point moves to the ascending branch of the hysteresis characteristic (point 2), and after a certain time the core enters saturation (point 3).

Fig. 2

Fig. 3

At the moment when the core passes into saturation, a voltage drop is formed across the resistance; through the Zener diode \(D_2\) and the differentiating circuit \(C_q R_q\) it opens the thyristor \(T_1\), which forms the trigger pulse of the injection circuit. When the voltage \(e(t)\) becomes equal to zero or negative, the core returns to its initial state. The delay duration is regulated by changing \(H_n\) (4).

If the demagnetizing action of the windings \(W_y\) and \(W_k\), as well as the increase of current in the operating winding over the section \(1\text{–}2\), are not taken into account, then the moment of injection can be found by solving the following equation:

\[ B_s-B_n=\frac{1}{S_{\mathrm{ct}}W_p}\int_0^{t_i}\left[e(t)-\frac{\Delta H l_{\mathrm{ct}}R_{\mathrm{n}}}{W_p}\right]dt, \tag{5} \]

where

\(S_{\mathrm{ct}}\) is the cross section of the MU core.

In order that equation (5) correspond to (2), it is necessary to satisfy the condition

\[ \frac{\Delta H l_{\mathrm{ct}}R_{\mathrm{n}}}{W_p}\ll e(t); \tag{6} \]

The latter can be achieved by an appropriate choice of the circuit elements, parameters, and core material. As the material it is desirable to use steels with low coercive force and a sharply pronounced saturation region, for example, permalloy 50NP, 65NP, etc.

The use of the MU makes it possible very simply to correct the injection instant as a function of various destabilizing factors. In the present circuit such correction is carried out by the injection voltage \(U_i\), which is taken from the charging capacitance of the injection circuit. The required change in the injection instant for small fluctuations of the injection voltage can be found from (1)

\[ \frac{\Delta t_i}{t_i}=\frac{\Delta U_i}{2U_i}; \tag{7} \]

Consequently, for the best correction the ampere-turns of the correcting winding \(i_k W_k\) must be equal to \(i_y W_y\).

In an analogous way, correction can be carried out that takes into account the influence of the residual induction, etc.

The results of an experimental check of the developed circuit are given in Fig. 4. Curve 1 shows the dependence of the relative dose power on the supply voltage during manual adjustment to the maximum,

Fig. 4

i.e., it characterizes the maximum possible dose at the given supply voltage. Curve 2 was obtained in the following way. For the nominal supply voltage the betatron was adjusted to the maximum, and then, without touching the adjustment knobs, the supply voltage was varied and the dose power was recorded. The correcting winding \(W_k\) was connected in this case. Dependence 3 was taken with the correction switched off. Analysis of the results obtained shows that, despite its simplicity, the correction is sufficiently effective, especially for large deviations of the supply voltage. To obtain the maximum possible output, a more detailed allowance for all factors affecting the magnitude of the radiation is necessary.

LITERATURE

1. A. A. Geizer et al. A small-size betatron with increased specific characteristics. Present collection.

2. L. M. Anan’ev et al. Induction Electron Accelerator—Betatron. Gosatomizdat, 1961.

1. L. M. Ananyev, M. M. Shtein. Izv. TPI, vol. 180, 53, 1971.
2. L. M. Ananyev, M. M. Shtein. Izv. TPI, vol. 180, 3, 1971.
3. M. A. Rozenblat. Magnetic Elements of Automation. TEI, 1969.