Experimental Study of Losses in a Betatron Power Supply Circuit with Unipolar Current Pulses
Abstract Generated abstract
This paper experimentally investigates energy losses in the oscillatory power supply circuit of a betatron using unipolar current pulses, focusing on losses in the electromagnet steel and in an IM-3-100 capacitor bank. Comparing unipolar and sinusoidal operating modes at circuit frequencies around 50 Hz and capacitor voltages up to 1000 V, the authors measure total circuit losses and separate contributions from magnetic core and capacitor elements. The results indicate that unipolar remagnetization reduces steel losses relative to sinusoidal excitation, while unipolar capacitor voltage reduces losses in IM-type capacitors by roughly two to three times. These reductions suggest that betatron oscillatory circuit frequency and acceleration-cycle repetition rate can be increased without worsening thermal conditions or capacitor service life.
Full Text
EXPERIMENTAL STUDY OF LOSSES IN THE POWER-SUPPLY CIRCUIT OF A BETATRON WITH UNIPOLAR CURRENT PULSES
V. V. Ivashin, E. G. Furman
(Presented by the scientific seminar of the departments of electrical machines and general electrical engineering)
When calculating power-supply circuits for betatrons with unipolar current pulses and pulsed input of energy into the oscillatory circuit, it is necessary to know the value of the loss energy \(Q_R\) per one current pulse in the accelerator electromagnet. The value of the energy \(Q_R\) determines the parameters of the storage-capacitor charging circuit, the power of the power supply, the thermal regime of the circuit elements, etc.
The use of unipolar sinusoidal current pulses to excite the electromagnet leads to the fact that, over one remagnetization cycle, the ratio of losses in the steel due to hysteresis and eddy currents changes in comparison with the sinusoidal regime.
It is also known that operation of a capacitor bank in a unipolar regime leads to a reduction of losses in the capacitor in comparison with the sinusoidal mode of operation [2]. The reduction of losses in capacitors makes it possible to use, in power-supply circuits, not expensive cosine capacitors, but cheaper and smaller capacitors, for example capacitors of the IM-3-100 type.
In the general case, the losses in the oscillatory circuit are calculated as
\[ p_{\text{ob}} = \sum p_i . \tag{1} \]
where \(P_i\) are the losses in the elements of the oscillatory circuit.
If the losses in the active elements are calculated rather simply and accurately, then calculation of the losses in the steel of the magnetic core and in the capacitor bank, with the existing operating regime of the electromagnet and the storage unit, presents considerable difficulty.
In this work an experimental study was carried out of the degree of reduction of energy losses in the betatron electromagnet and in the capacitor bank at a capacitor voltage up to \(1000\ \text{V}\), during the transition from the sinusoidal operating regime to a regime unipolar in current in the magnet and in voltage on the capacitors.
Figure 1 shows the circuits for carrying out the experiment and the curves of the change in current and voltage in them for the sinusoidal (a) and unipolar (b) operating regimes.
Figure 2 gives the envelopes of the amplitude values of the voltages under unipolar and sinusoidal excitation of the electromagnet \(L\) from a capacitor bank of capacitance \(400 \cdot 10^{-6}\), composed of four
Fig. 1. Circuits for carrying out the experiments and curves of current and voltage variation
Fig. 2. Graphs of the envelopes of the amplitude values of the voltage on the capacitance in the unipolar (upper) and sinusoidal mode
pulse oil-paper capacitors of type IM-3-100. The natural frequency of the circuit in both modes is equal to 50 Hz. From Fig. 2 it is seen that, in the unipolar operating mode of the circuit, the losses are substantially smaller than in the sinusoidal mode. Since the losses in the copper and in the switching devices during operation of the circuit in the unipolar mode are equal to the losses in these same elements in the sinusoidal mode (with the exception of the shaded region in Fig. 1), the reduction of losses in the circuit occurs owing to their reduction in the electromagnet and in the capacitor bank.
Losses in the Steel
Dynamic losses in steel under magnetization reversal in a sinusoidal field are calculated with sufficient accuracy by the formula [3]
\[ P_{\text{st}}=\left[aB_m^2\frac{f}{50}+b\cdot B_m^2\left(\frac{f}{50}\right)^2\right]\cdot G \quad (\text{W}), \tag{2} \]
where \(a\) and \(b\) are the coefficients of hysteresis and eddy-current losses, W/kg;
\(B_m\) is the maximum induction,
\(f\) is the magnetization-reversal frequency,
\(G\) is the weight, kg.
Fig. 3. Magnetic flux (a), dynamic hysteresis loop (b), and induced eddy currents under unipolar magnetization reversal of a ferromagnet (c)
When the core is remagnetized in a unipolar field (Fig. 3 a, b), the hysteresis loop is established on a partial cycle and begins with the maximum residual induction \(B_{rm}\). The hysteresis loop in the unipolar mode is flatter, i.e., the average dynamic permeability of the ferromagnet decreases, as is clearly seen in Fig. 3, b.
As the experiments showed, with unipolar remagnetization of the core the hysteresis losses per one current pulse are approximately four times smaller than the losses per one remagnetization cycle in a sinusoidal field of the same magnitude. The eddy-current losses at frequencies up to 500 Hz under unipolar and sinusoidal remagnetization of the ferromagnet are practically equal, since the establishment time of the eddy currents \(t_{\text{ust}}\) (Fig. 3, c) is considerably less than the duration of the current pulse \(t_i\) through the betatron electromagnet.
The experiments were carried out on an electromagnet weighing 170 kg, made of steel grade É12, with an almost uniform distribution of induction over the cross section of the magnetic circuit and with a variable air gap. The losses in the magnetic circuit at a maximum induction of 1.02 T and unipolar remagnetization amounted to 350 W, while in the sinusoidal mode they were 554 W, i.e., they decreased by a factor of 1.6.
The studies performed show that, with unipolar supply of the electromagnet, the losses in the steel can be determined from the formula
\[ P_{\text{st}}=\left[\frac{a}{2}B_m^2\cdot \frac{f}{50}+b\cdot B_m^2\left(\frac{f}{50}\right)^2\right]\cdot G\cdot \frac{N}{2f}\;(\text{W}), \tag{3} \]
where \(f\) is the natural frequency of the oscillatory circuit,
\(N\) is the number of current pulses per second.
For this reason, the frequency \(f_0\) of the oscillatory \(LC\) circuit in the unipolar mode may be increased by approximately a factor of \(K\) in comparison with the sinusoidal mode, for the same losses in the electromagnet of the \(LC\) circuit, which has frequency \(f_c\).
\[ K=\frac{f_0}{f_c}=\sqrt{\frac{625}{4b^2 f_c^2}+50\frac{a}{b f_c}+1-\frac{25a}{2b f_c}}. \tag{4} \]
In the general case, the coefficient \(K\) depends on the ratio of losses in the steel due to eddy currents and hysteresis. For example, for steel É12 (for which
\[ a=2.4\,\frac{\text{W}}{\text{kg}},\qquad b=0.8\,\frac{\text{W}}{\text{kg}} \]
) the circuit frequency can be increased, with unipolar supply, by a factor of 1.4 in comparison with the sinusoidal mode, which gives an increase in the repetition frequency of acceleration cycles in the accelerator by approximately a factor of 2.8.
Losses in IM-3-100 Type Capacitors
The energy losses in a capacitor, in the general case, consist of the following components:
a) losses in the dielectric;
b) losses in the metallic parts,
and in the sinusoidal mode they are calculated by the formula [4]
\[ P_c=2\Pi f U_c^2\cdot C\cdot \operatorname{tg}\delta+P_m\;(\text{W}), \tag{5} \]
where \(U_c^2\) is the effective value of the voltage across the capacitance, V,
\(C\) is the capacitance, F,
\(\operatorname{tg}\delta\) is the dielectric loss angle,
\(P_m\) is the loss in the metallic parts of the capacitor.
The value of \(\operatorname{tg}\delta\) for oil-paper capacitors varies within
within the range \((30 \div 100)\cdot 10^{-4}\) and have a complex dependence on the magnitude of the applied voltage [5].
Dielectric losses under alternating voltage are mainly due to ionization processes, which occur in the layers of the liquid dielectric [4, 5] when the electric-field strength in the dielectric exceeds \(5\ \text{kV/mm}\).
In [5], oscillograms are presented of active current surges through a standard section of an IM-type capacitor under sinusoidal voltage and a superposed dc component. Surges of active current occur when the sign of the voltage changes on the leading part of the half-sinusoid.
A number of authors [2, 4, 5] have noted that if the field in a capacitor changes sign only slightly or does not change sign at all, then the losses in them decrease in comparison with a sinusoidal field of the same frequency.
Experiments to determine losses in IM-3-100 capacitors were carried out using the circuits of Fig. 1, \(a\), \(b\), in unipolar and sinusoidal modes, with the natural frequency of the circuits \(50\ \text{Hz}\).
The experiment consisted of the following: the total losses in the oscillatory circuit were measured and the losses in the circuit elements were determined, while the losses in the steel were measured experimentally.
Table 1
| \(U_m(t)\) [V] | 1000 | 900 | 800 | 100 | 600 |
|---|---|---|---|---|---|
| \(Q_{co}\) (J) | 0.95 | 0.76 | 0.60 | 0.43 | 0.367 |
| \(Q_{cs}\) (J) | 4.02 | 3.21 | 2.50 | 1.80 | 1.02 |
Table 1 gives the results of measuring losses in an IM-3-100 capacitor in the unipolar mode, \(Q_{co}\), for one current pulse in the electromagnet, while the negative overshoot \(-\Delta U_c\) amounted to \(0.12\,U_{ct}\) (Fig. 1, \(b\)); and for one period in the sinusoidal operating mode, \(Q_{cs}\).
Since the losses in the capacitor depend practically linearly on frequency, in the unipolar mode the losses can be calculated from the formula
\[ P_{co}=Q_{co}\cdot N \qquad (\text{W}) \tag{6} \]
It is shown in [4] that the lifetime of a capacitor is determined by the losses in the dielectric; consequently, in the unipolar mode it is possible to increase significantly the electric-field strength in the capacitor in comparison with the sinusoidal mode, or to increase the repetition frequency of the accelerator acceleration cycles.
Thus, at the maximum voltage on the capacitance of \(1000\ \text{V}\) (electric-field strength \(12.5\ \text{kV/mm}\)), the circuit frequency in the unipolar mode can be increased, in our case, by a factor of 2.1 in comparison with the sinusoidal mode, without reducing the service life of the capacitor bank, which will lead to an increase in the acceleration cycles by approximately a factor of 4.2.
In the future, in order to obtain a complete picture of the change in losses in capacitors, it is necessary to measure losses in capacitors at higher electric-field strengths in the dielectric.
Conclusions
- With unipolar remagnetization of the core, the losses in the steel are smaller than in the sinusoidal remagnetization mode, which makes it possible to increase the natural frequency of the accelerator oscillatory circuit in continuous operation without worsening the thermal conditions of the electromagnet.
- With a unipolar voltage on the capacitor bank, the losses in IM-type capacitors are two to three times smaller than in the sinusoidal mode. This leads to a significant increase in the service life of the storage unit and in a number of cases makes it possible to use compact high-capacitance pulse capacitors in betatron power-supply circuits.
REFERENCES
-
V. V. Ivashin. An economical thyristor circuit for supplying a compact betatron. Report at the VII Interuniversity Conference on Electron Accelerators. Tomsk, September 3–7, 1968.
-
Carruthers R. “Energy storage for thermonuclear research.” Pros IUSTZ ELECTZ Euqs A-106, suppe, No. 2, 1959.
-
V. V. Druzhinin. Magnetic Properties of Electrical Steels. Gosenergoizdat, 1962.
-
V. T. Rene. Calculation and Design of Electrical Capacitors. Kiev, 1966.
-
G. S. Kuchinskii. Paper-Oil Insulation in High-Voltage Structures. Gosenergoizdat, 1967.