INFLUENCE OF MAINS-VOLTAGE INSTABILITY ON THE FAST COMPONENT OF RANDOM FLUCTUATIONS IN THE PULSE INTENSITY OF γ-RADIATION FROM THE SB-25 BETATRON

V. A. MOSKALEV, Yu. A. GROMOV

It was noted in [1] that the pulse intensity of the bremsstrahlung radiation of a betatron exhibits a pronounced irregularity in time, i.e., in the course of normal operation of the accelerator it fluctuates from one acceleration cycle to the next over wide limits (Fig. 1).

Among the factors that should have a substantial influence on the fast component of the drift of the radiation pulse intensity, one may note such a factor as fluctuations of the mains voltage. The electromagnet, the injector filament, and all electronic circuits are powered from the mains (the injection circuits, inflection, displacement, the UBS), and when the mains voltage changes, changes in their output parameters are detected after a certain time or instantaneously. The spectrum of mains-voltage fluctuations is broad and occupies the band from 0 to 50 Hz (Fig. 2).

Fig. 1. Fluctuations of the radiation pulse intensity at the 60% level

On this basis it may be assumed that the magnitude of the variance of the intensity fluctuations from one acceleration cycle to the next should be strongly related to the magnitude of the variance of the mains-voltage fluctuations.

To test this assumption, an experiment was carried out consisting in the simultaneous recording of fluctuations of the mains voltage and of the pulse intensity of the betatron radiation.

The recording was performed on the high-current SB-25 (“Luch”) betatron with the aid of a pulse recorder specially developed for this purpose.

statistical studies of betatron operation from acceleration cycle to acceleration cycle [2]. The recording time was taken to be 1 minute. Operator intervention was thereby excluded. Realizations of 15 sec duration were studied, as required for obtaining reliable statistical characteristics of the relationship, since the decay time of the autocorrelation function of the pulsed-radiation process in terms of intensity is 0.02 sec [1]. Preliminary processing of the obtained

Fig. 2. Fluctuations of the mains voltage at the 98% level

realizations showed that, during 30–40 sec after detuning the betatron to the radiation maximum, the process of fluctuations of the radiation intensity can be regarded as ergodic and stationary; the distribution laws of the fluctuations of the mains voltage and of the radiation intensity are close to normal. Therefore, during this time interval after detuning the betatron to the radiation maximum, one may confidently use the obtained estimates of the relationship and, with a specified confidence probability, regard the calculations as reliable.

From the recording results, a systematized correlation field was obtained (Fig. 3). Here the amplitudes of fluctuations of the mains voltage \(x\) and of the pulsed radiation intensity \(y\) were divided into 13 intervals. The size of one interval for \(x\) corresponded to 0.1% of the value of the mathematical expectation \(m_x\), taken as 100%; the size of one interval for \(y\) was 3.6% of \(m_y\). From the data of the correlation field, the correlation ratio \(\eta_{y/x}\), characterizing the degree of association of the variability of \(y\) with the variability of \(x\), was found:

\[ \eta_{y/x} = \sqrt{\frac{S^2_{y/x}}{S^2_y}}, \]

where \(S^2_y\) is the total variance of the fluctuations of \(y\);

\(S^2_{y/x}\) is the part of the total variance of the fluctuations of \(y\) caused by the influence of fluctuations of \(x\) on the magnitude of \(S^2_y\).

The calculations gave the values \(S_y = 10\%\), \(S_{y/x} = 1.6\%\), \(\eta_{y/x} = 0.16\). From correlation analysis [3], this degree of association may be considered reliable if:

\[ \frac{\eta \sqrt{n}}{(1-\eta^2)} > l, \]

where \(l\) is a number associated with the confidence probability \(P\) and calculated from the normal distribution function; \(n\) is the sample size.

The confidence intervals within which the value of the correlation ratio lies are estimated by the formulas:

\[ \eta_{\min}=\eta-\frac{l(1-\eta^2)}{\sqrt{n}};\qquad \eta_{\max}=\eta+\frac{l(1-\eta^2)}{\sqrt{n}}. \]

For a confidence probability \(P=0.95\) we have \(l=1.96\) [3], whence

\[ \frac{\eta\sqrt{n}}{(1-\eta^2)}=4.35;\qquad \frac{l(1-\eta^2)}{\sqrt{n}}=0.07, \]

which indicates a reliable correlation having the value \(\eta_{x/y}=0.16\pm0.07\).

Of the magnitude of the fluctuation of \(y\), equal to \(2S_y\), only 16% (if \(\eta_{y/x}=0.16\) is taken) is due to fluctuations of \(x\). Since \(2S_y=20\%\),

Fig. 3. Correlation field of fluctuations of the pulse intensity of radiation as a function of fluctuations of the mains voltage

then, of these, 3.2% are due to fluctuations of \(x\), while the remaining 16.8% are due to unknown causes.

Thus, it follows from the experiment that the fluctuation of the betatron radiation intensity from acceleration cycle to acceleration cycle cannot be explained by instability of the mains voltage.

Simultaneous recording of all betatron parameters that, to some degree, affect the magnitude of the pulse intensity of the betatron radiation is necessary, since instability of the circuits may be caused not only by changes in the mains voltage, but also by a number of other causes.

REFERENCES

1. V. A. Vorob’ev, G. P. Tarasov. Izv. vuzov, “Fizika,” No. 12, 139, Tomsk State University Press, Tomsk, 1968.

2. V. A. Moskalev, Yu. A. Gromov. Apparatus for recording pulse parameters of a betatron, Izv. TPI, vol. 193, Tomsk, 1970 (in press).

3. N. V. Smirnov, I. V. Dunin-Barkovskii. Course in Probability Theory and Mathematical Statistics. Nauka Publishing House, Moscow, 1969.