STRUCTURAL DIAGRAM OF A BETATRON AS A CONTROL OBJECT

A. A. VOROB'EV, V. M. RAZIN

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

On the basis of an analysis of the phenomena in the individual units and elements of a betatron installation, it appears possible to compile the expanded structural diagram shown in Fig. 1. This diagram must reflect all the static and dynamic properties of the individual units and elements of the betatron in their interrelation. Let us give some explanations of the diagram.

The dynamic properties of the betatron electromagnet are represented by element 1. Taking into account the presence of large nonmagnetic gaps in the betatron electromagnet, this part can apparently be represented in the form of a certain linear dynamic system with the corresponding transfer function. Those values of the magnetic induction on the equilibrium orbit which have definite values at the moment of injection and at the moment of displacement are recorded by means of pulse elements 21 and 10, which close the circuit at the instants \(t = t_{\phi i}\) and \(t = t_{\phi c}\).

The heater power-supply system of the injector cathode is represented in the structural diagram by an inertial nonlinear element 6 and a non-inertial nonlinear element 7. If there is an automatic-control circuit for the injector emission current, the dynamic properties of the measuring and regulating parts must be represented by dynamic element 8 with a summing or measuring element 18, to whose input the disturbance \(U_{\mathrm{sh}}\) may be applied.

The properties of the system for forming the voltage pulse are represented by dynamic element 15, which has feedback through element 16 in the case of automatic stabilization, i.e., regulation of the voltage amplitude.

The required value of the injection voltage is set by means of summing device 20, to whose input the disturbance \(U_{\mathrm{sh}}\) is applied.

The conditions for electron capture into the betatron acceleration mode are represented by the complex nonlinear element 2, to whose inputs are applied variables in the form of the injector emission current \(I_{\mathrm{e}}\), the injection voltage \(U_i\), the injection phase \(t_{\phi i}\), and the magnetic induction on the equilibrium orbit \(B_{Dz}(t_{\phi i})\) at the moment of injection.

Here we note that line 17—15 fixes the moment of physical realization of the injection voltage pulse, whereas line 17—2 corresponds to fixing the very instant of electron capture into acceleration. The influence of various factors, including various disturbances, is taken into account by summing element 17.

The pulsed nature of betatron operation is taken into account by pulse element 3, and the time expended on the acceleration process is represented by delay element 4. Line 7—15 corresponds to accounting for the influence of the emission current of the injector cathode on the amplitude of the injection voltage, while line 15—7 indicates the dependence of the cathode emission current on the amplitude of the injection-voltage pulse.

Element 5 corresponds to the dynamic properties of the system intended for measurement and automatic regulation of the mean value of the radiation dose rate.

Nonlinear inertia-free element 9, together with multiplier element 11 and pulse element 10, models an equation indicating the dependence of the energy of the accelerated electrons on the displacement phase, while element 12 corresponds to the system for measuring and regulating the energy level of the accelerated electrons, if such a system is present. The required value of the energy of the accelerated electrons is set in summing element 19, to whose input the corresponding disturbances are also applied.

The influence of the energy of the accelerated electrons on the radiation dose rate is taken into account by nonlinear inertia-free element 13, which represents an approximately cubic dependence on energy, and by multiplier element 14, which performs, as it were, modulation of the radiation-dose-rate pulses with allowance for the energy level of the displaced electrons. In the absence of stabilization of the injection voltage, the radiation dose rate will be approximately proportional to the fourth power of the mains voltage.

A preliminary examination of the structural diagram of the betatron installation makes it possible to draw the following conclusions:

1. The betatron, together with the power-supply, monitoring, control, and regulation systems, constitutes a single, rather complex cybernetic system with two outputs in terms of the charge \(Q\) and energy \(W\) of the accelerated electrons; the number of inputs of this system, in a first approximation, is determined by the number of parameters under the influence of the operator and by the number of certain conditional points of application of signals of external and internal disturbances, as shown in Fig. 1.

2. In the cybernetic system under consideration there are various cross feedbacks, i.e., here there is so-called coupled regulation of certain parameters.

3. In terms of its principle of operation, this cybernetic system is pulsed.

4. The system contains a considerable number of nonlinear elements, to which linearized methods of investigation are not applicable. Only some of the units and elements of the betatron installation can be represented approximately in the form of linear dynamic elements, and for them the corresponding transfer functions can be found.

Fig. 1. Structural diagram of the betatron installation.