POWER SUPPLY CIRCUIT FOR A BETATRON ELECTROMAGNET WITH TRIANGULAR CURRENT PULSES

V. V. Ivashin, E. G. Furman

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

In accelerator technology, power-supply circuits in the form of an oscillatory circuit—capacitor bank–accelerator electromagnet—tuned to the frequency of the power source have found wide application. Such a circuit, however, has a number of substantial drawbacks, the principal one being that the second half-wave of the sinusoidal current is not used for acceleration purposes. Pulse power-supply circuits for accelerator electromagnets from capacitive energy-storage units are known in which both half-waves of the current pulse are used for acceleration purposes. In this case the most economical power-supply circuits are those in which the capacitive storage unit operates in a voltage-unipolar mode [1, 2, 3]. A voltage-unipolar mode of operation of the storage capacitor ensures a reduction in losses (and an increase in service life) by no less than a factor of 4–6 in comparison with a bipolar mode of operation. This makes it possible to use high-energy pulse capacitors in power-supply circuits and thereby substantially reduce the weight of the capacitor bank without reducing its service life in comparison with the sinusoidal mode [4].

The most rational form of the magnetic cycle in the electromagnet of a betatron is the triangular form. Unipolar circuits in principle make it possible to obtain a triangular form of current pulses by interrupting the process of discharging the capacitance into the electromagnet at angles smaller than \(\pi/2\) of the discharge period and to carry out, through reverse valves, recovery of the magnetic-field energy into the capacitor bank. For example, already at an angle of 75 electrical degrees the energy losses in the electromagnet winding are reduced by a factor of 2.96, and at an angle of \(60^\circ\)—by a factor of 12. The maximum value of the current and of the magnet field is then reduced, respectively, by only 3.5% and 13%. The use of circuits with a triangular form of the magnet current makes it possible substantially to increase the frequency of acceleration pulses and, consequently, also the average intensity of its radiation [1].

Figure 1 shows the simplest power-supply circuit for a betatron electromagnet with triangular current pulses. The capacitive storage unit \(C_1\), through the controlled valves \(T_1\), \(T_2\) and the reverse diodes \(D_1\) and \(D_3\), \(D_4\), \(D_5\), is connected to the winding of the electromagnet \(L_m\). In parallel with the diodes \(D_4\), \(D_5\) are connected the commutating capacitors \(C_3\), \(C_4\), which have a charging circuit consisting of the diode \(D_5\) and the inductance \(L_1\). Sequentially-

in series with diodes \(D_1\) and \(D_2\) are the windings of a saturable reactor, whose magnetic core is premagnetized by the electromagnet current. To compensate for losses in the accelerator oscillatory circuit and to stabilize the maximum value of the energy of the \(LC\) circuit, pulsed injection of energy from a dc source is used [3,5]. The pulsed energy-injection circuit consists of a buffer capacitance \(C_2\), a charging inductance \(L_2\), and a controlled valve \(T_3\).

In the initial state the capacitor \(C_1\) is charged to the required voltage level; there is no energy in the remaining elements of the power circuit of the supply system. When control pulses arrive at

Fig. 1. Power-supply circuit of an electromagnet with triangular current pulses

the thyristors \(T_1\) and \(T_2\), the capacitor \(C_1\) begins to discharge into the electromagnet. At the same time the capacitors \(C_3\) and \(C_4\) begin to charge through diode \(D_5\) and the charging inductance \(L_1\). When the voltages on the capacitors \(C_3\), \(C_4\), and \(C_1\) become equal, the diodes \(D_1\) and \(D_2\) open, and in the interval \(t_2—t_3\) the saturable reactor begins to be remagnetized under the action of the difference between the capacitor voltages. At the time \(t_3\) the reactor saturates, and under the action of the voltages of the capacitors \(C_3\) and \(C_4\), which are greater than the voltage of the capacitor \(C_1\), the thyristors \(T_1\) and \(T_2\) are turned off. The electromagnet current is commutated from the thyristor circuit into the circuit consisting of capacitor \(C_4\), the winding of the saturable reactor, diode \(D_2\), capacitor \(C_1\), diode \(D_1\), the winding of the saturable reactor, and capacitor \(C_3\). In this process the capacitors \(C_3\) and \(C_4\) are completely discharged by the electromagnet current and are shunted, respectively, by the diodes \(D_3\) and \(D_4\). The energy of the commutating capacitors is converted into the energy of the magnetic field of the electromagnet, owing to which the current in it increases by the amount \(\Delta I\). By the time the capacitors \(C_3\) and \(C_4\) have discharged, energy remains in the charging inductance and is converted into the energy of the electric field of the storage capacitor \(C_1\). Injection of energy from the supply source

to compensate losses in the circuit takes place on the falling part of the magnet-current pulse; for this purpose thyristor \(T_3\) is opened after the current has been transferred from the thyristors to the diodes. The input of energy is accompanied by a decrease in the duration of the current fall in the electromagnet.

In the same way it is possible to form trapezoidal fields in the electromagnet, which may be required when the electrons are extracted slowly. For this it is necessary to connect separate saturation chokes in series with diodes \(D_1\) and \(D_2\), and, by changing the parameters of the commutating capacitors or the inductances of the charging chokes, to separate in time the instant of current commutation of thyristor \(T_1\) relative to \(T_2\).

Regulation of the current-commutation angle of the thyristors can be carried out by changing the inductance of choke \(L_1\). If valve \(D_5\) is made controllable, then, by changing the instant at which valve \(D_5\) is switched on relative to the instant at which thyristors \(T_1, T_2\) are switched on, it is possible to regulate the current-commutation angle of the thyristors without changing the magnitude of the charging inductance.

A distinctive feature of the circuit is that the forced commutation of the current from the controlled valves into the uncontrolled ones is carried out without the use of special controlled devices, which increases reliability and simplifies operation of the power-supply circuit.

The energy stored in the inductance and capacitors of the commutating circuit is many times smaller than the energy of the capacitive storage bank; therefore, with a sufficiently high degree of accuracy, the differential equation of the capacitor-charging process can be written as

\[ L_1 \frac{C_3 \cdot C_4}{C_3 + C_4}\,\frac{dU_c(t)}{dt} + 2U_c(t) = U_{cm}\cdot \cos \omega t, \tag{1} \]

where \(\omega\) is the natural angular frequency of the \(C_1 L\) circuit. The solution of this equation is

\[ U_{c3}(t)=U_{c4}(t)= \frac{u_{cm}\cdot \omega_1^2}{2(\omega^2-\omega_1^2)} \left(\cos \omega t-\cos \omega_1 t\right), \tag{2} \]

where \(\omega_1\) is the angular frequency of the \(L_1, C_3, C_4\) circuit. The instant at which diodes \(D_1\) and \(D_2\) are switched on, i.e., the instant of equality of the voltages of the commutating capacitors and of the storage capacitor, can be expressed as

\[ \omega t_2 = \arccos \frac{1}{4} \left(1-\frac{\omega^2-\omega_1^2}{\omega_1^2+\omega^2}\right). \tag{3} \]

The magnitude of the current-commutation angle of thyristors \(T_1\) and \(T_2\) depends only on the ratio of the frequencies of the circuits \(L, C_1\) and \(C_3, L_1, C_4\). Figure 2 gives the dependences of the magnitude of the commutation angle on the ratio of the frequencies of these circuits. Dependence 1 is given for the case when capacitors \(C_3\) and \(C_4\) have separate charging inductances; dependence 2, when they have a common one, Fig. 1. The flux linkage of the commutating choke depends on the voltage difference between the commutating capacitors \(C_3\) or \(C_4\) and the storage capacitor \(C_1\), and on the remagnetization time of the choke \(t_3 - t_2\), Fig. 1. The flux linkage of the choke can be determined as

\[ \Psi = \int_{t_2}^{t_3} |U_{c3}(t)-U_{c1}(t)|\,dt = \frac{\Delta U \cdot t_{\mathrm{B}}\cdot I_m \cdot \sin \omega t_2} {2U_{cm}\cdot C(\omega+\omega_1)}, \tag{4} \]

where \(C\) is the equivalent capacitance of the two series-connected capacitors \(C_3\) and \(C_4\); \(t_v\) is the time allotted to the thyristors for recovery of their blocking properties; \(I_m\) is the maximum value of the electromagnet current when the storage capacitor is fully discharged.

The values of the commutating capacitors and of the charging inductance depend mainly on the recovery time of the blocking properties of thyristors \(T_1, T_2\) and on the thyristor current commutation angle. The recovery time of the blocking properties is determined as

\[ t_v=\frac{\Delta U\cdot C_1\cdot C_3}{I_m(C_1+C_3)\sin\omega t_3}. \tag{5} \]

Fig. 2. Dependence of the change in the current commutation angle on the ratio of the frequencies of the power and commutating circuits: 1— for separate charging inductances of the commutating capacitors, 2— for a common charging inductance

Experimental verification of the circuit was carried out on a betatron electromagnet with a repetition rate of 50 pulses/sec and magnetic-field energy of \(3\cdot10^3\) J. The maximum value of the electromagnet current was 1020 A. Controlled commutating devices used were TL2-200-8 thyristors, with a recovery time of \(100\cdot10^{-6}\) sec. The thyristor current commutation angle was varied within \(30\div85\) electrical degrees. The natural frequency of the power circuit was 45 Hz. The energy stored in the commutating capacitors and in the charging inductance at a commutation angle of 75 electrical degrees amounts to 15% of the energy of storage capacitor \(C_1\). Of this, 12% of the energy enters the electromagnet field during current commutation, owing to which the field is boosted at its maximum value, while 3% of the energy remains in the charging inductance. During formation of the current decay in the electromagnet, this energy enters the storage capacitor. If high-frequency thyristors of the TCh type with a recovery time of about \(5\cdot10^{-6}\) sec are used, the energy stored in the commutating circuit will be about 1% of the energy of the storage capacitor. In the circuit considered, it is possible to recharge the commutating capacitors from a separate power source. In this case, along with boosting of the magnetic field, energy input is also provided to compensate for circuit losses. In the circuit, elements of the commutating circuit can be used for purposes of electron displacement; for example, displacement windings can be connected in series with diodes \(D_3\) and \(D_4\).

The average values of the currents of the thyristors and diodes in the circuit considered are practically equal to one another and, for quasi-triangular current pulses, can be determined as

\[ I_{\mathrm{av}}=\frac{I_m}{\pi}(1-\cos\omega t_k)\cdot t_i\cdot N, \tag{6} \]

where

\[ \omega t_k \]

is the current commutation angle of the thyristors,

\[ t_i \]

is the duration of the electromagnet current pulse,

$N$ is the number of pulses per second.

The maximum voltage applied to the thyristors and diodes ($T_1$, $T_2$, $D_1$, $D_2$) is equal to the amplitude voltage of the storage capacitor; and the power of the switching devices $T_1$ or $D_1$, required for switching the energy of the magnetic field equal to $Q_m$, is determined as

\[ P=\frac{4\cdot Q_m \cdot \omega t_k \cdot N}{\pi(1+\cos \omega t_k)}, \tag{7} \]

and the total power of the controlled devices of the circuit is equal to $4P$.

At present, domestic industry has mastered the production of tablet-type thyristors and diodes that make it possible to switch powers up to $10^6$ W. The use of such thyristors in power-supply circuits for high-current betatrons will make it possible, with two thyristors ($T_1$, $T_2$, Fig. 1), to switch an energy of $5\cdot 10^3$ J at 200 pulses/sec. The use of high-frequency thyristors of the TCh type with a recovery time of $5\cdot 10^{-6}$ sec will make it possible to create power-supply circuits for betatrons with energies of 200 J at $(2 \div 3)\cdot 10^3$ acceleration pulses per second.

REFERENCES

1. V. V. Ivashin, G. A. Sipailov. Generator of unipolar current pulses of triangular and trapezoidal form. PTE, No. 5, 1966.

2. “Scientific Papers.” Moscow, Izv. RIAN SSSR, vol. 9, 1967.

3. V. V. Ivashin. Economical thyristor circuit for supplying a betatron electromagnet. In the collection “Electron Accelerators.” Issue 3, Atomizdat, 1970.

4. V. V. Ivashin, E. G. Furman. Experimental study of losses in a betatron power-supply circuit with unipolar pulses. Izv. TPI, vol. 212, TTU Publishing House, 1971.

5. E. G. Furman. Stabilization of the energy of the accelerator oscillatory circuit. PTE, No. 5, 1971.