GVM calibration using a capacitive divider

Nuclear Instruments and Methods in Physics Research A244 (1986) 221-224 North-Holland, Amsterdam

221

GVM CALIBRATION USING A CAPACITIVE DIVIDER D. C A M I N a n d S. T A U Departamento de Fisiea, CNEA, Au. del Libertador 8250, 1429, Buenos Aires, Argentina

A new method for calibrating a generating voltmeter of a tandem accelerator is described. The capacitive divider formed by the capacitor pick-off plate and a polyestyrene capacitor is used to measure the terminal potential. The capacitance between the CPO and the terminal is calculgted and measured. The dc voltage developed in the capacitive divider is measured and plotted against GVM reading. A correction factor is obtained and used for true voltage readings during the column voltage test. Results of this test are also given.

1. Introduction The extremely high voltage present at the terminal of electrostatic accelerators is normally measured using a generating voltmeter (GVM) [1]. For accurate readings the GVM has to be calibrated and this can only be done once a beam is passed through the machine and the energy of the beam is obtained by measuring the magnetic strength of the analyzing magnet. One of the important steps in the assembly of the accelerator is the column voltage test. At this step there is of course no beam available and therefore another method of GVM calibration is required. Either a resistor voltage divider or the knowledge of the relationship between the terminal voltage and the column corona current of other similar machines are normally used. A new method for GVM calibration, used during the column voltage test of our 20 UD tandem accelerator (Tandar), is described in this report [2]. The method of the capacitive divider utilizes the capacitor pick-off plate in an unusual way to measure dc voltage.

determinated by the simple equation (see fig. 1). V2_ V1

C1 Cl-~'C 2 '

and if C2 >> CI:

v2=

C1

v,.

This is valid providing that both capacitors hold the same charge. Therefore, in order to measure V2, a very high impedancc instrument is required to avoid loss of charge in C2. In this particular application, C~ is the capacitance composed by the capacitor pick-off and the terminal. C2 is the parallel combination of a iealdess polyestyrene capacitor and the capacitance existing between the feed-through electrode of the CPO and ground. V~ is the terminal potential to be determined. As C l has a capacitance of approximately 0.01 pF, using C2 = 10000 pF a scale factor of 0.01/10000 = 1 V / M V is obtained. Besides, using a 1012 9 input resistance voltmeter, the time constant of the measuring

2. Capacitive divider If two capacitors are connected in series and a voltage Vl is applied across them, the voltage ratio is

V2

ic, l C2

Fig. 1. Capacitive divider. 0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Fig. 2. View of terminal and tank considered in Cceo evaluation. IV. BEAM TRANSPORT SYSTEMS

222

D. Camin, S. Tau / GVM calibration ~.~TANK WALL - - "--TERMINAL CPOtt

- ~___~.-_1'~ 5000pF

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Fig. 3. Circuit used for the measurement of Ccr o.

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Fig. 4. Results obtained with the circuit of fig. 3.

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D. Camin, S. Tau / GVM calibration

223

VGVM~ 1.2

1.1 1,0 0.9

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Vr =o(VGw- (~ VT = ~.77VovM'0.077 (Mv)

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Fig. 5. GVM indication against CPO voltage. circuit is 10000 p F x 1012 ~ -- 10000 s, sufficiently high to perform the G V M calibration without losing accuracy.

t~

3. Determination of the cap~itance between CPO and terminal

90

The terminal and the tank form a coaxial cylindric capacitor. Although the electric field distorts at the terminal edges, it is fairly homogeneous at its middle. We could calculate the capacitance of a slice of a coaxial capacitor formed by the terminal and the tank (see fig. 2). If d c is the capacitance and d l the slice's length, then dc

1

-d-7= 24.]2 log(R/r)

pF

" 70

I

'J"

m_l.

The capacitance per unit of outer surface area is dc dA

24.12 1 2~rR Iog(R/r)

p F m -2.

uZl

Since the area of the CPO is small, we could state Ccp°

d c ~rD 2 dA 4

24.12 1 'n'D 2 2~rR I o g ( R / r ) 4 '

D2 Ccp o = 3.015 R l o g ( R / r )

pF,

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w~aere D is the C P O diameter in meters. In our case we had D = 0.211 m, R--- 3.81 m, r = 1.27 m

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tJMNCORONACURRENT [)4A]

Fig. 6. Percentage of full gradient vs column corona current for different NEC accelerators. IV. BEAM TRANSPORT SYSTEMS

224

D. Camin, S. Tau / G VM calibration

Therefore we obtain Copo = 0.0738 pF. This value is 10% smaller than the one measured using technique described in sect. 4. It is assumed in the calculation that the CPO is part of the tank wall and that there are no discontinuities. In practice the CPO is mounted on a base which is slightly separated from the tank wall and therefore a field distortion probably occurs.

4. Measurement of the capacitance CcPo For the measurement of this capacitance, the circuit shown in fig. 3 was assembled. The terminal was biased with a variable 0-50 kV dc power supply. V2 was measured with a very high impedance voltmeter (Keithley 616). The CPO teflon insulator was thoroughly cleaned to avoid leakage. C2 was a polyestyrene capacitor with a nominal value of 5 kpF (actual value --- 5290 pF). A test was made to check the measurement's stability. C2 was charged to a fixed voltage (1.5 V) and the voltmeter showed a stable value for a long time (the reading decreased 18 mV/min). The Keithley 616 voltmeter has an input impedance greater than 10 ~2 I2, therefore the time constant of the measuring circuit was estimated to be higher than 5000 s. To avoid other leakage paths all the connectors had been thoroughly cleaned. In order to include all stray capacitances C2 was measured, after being mounted, using a capacitance meter. Starting with VI = 0 and V2 = 0 we raised the voltage in steps of 5 kV. Upon reaching a maximum of 50 kV we decreased the voltage in steps of 5 kV. The values obtained for V2 are plotted in fig. 4. The capacitance Ccv~ was calculated in each case as

the GVM gain can be adjusted to change the GVM scale. The calibration was made before the insulating gas SF6 was pumped into the tank. For that reason the first spark disrupted at a relatively low terminal voltage, i.e. 2 MV. The spark originated a drop in the terminal voltage recorded by the GVM indication. Part of the discharge current circulated between the terminal and CPO plate. Capacitor C~ was then partially discharged. After the spark occurred, the terminal voltage continued to rise and also did V2. The slope of the straight line is preserved as it depends on the C I / C 2 ratio. But a discontinuity in the plot is observed as Cl holds less charge than C2. Nevertheless, the values taken below 2 MV were sufficient to extrapolate the straight line to higher values.

6. Reliability of the method at high terminal voltage Since the GVM is linear in a wide range of terminal voltages, the same calibration factor obtained at 2 MV was used to correct the GVM readings at high terminal voltage during the column strength voltage test. At the same time the values of colunm corona current have been measured. Having these values it was possible to determine the terminal voltage according to data of voltage versus corona current obtained in similar machines (Oak Ridge 25URC and Jaeri 20UR) or in bench test of a single module (NEC). Fig. 6 shows a plot of terminal voltage versus column corona current for the three different methods. The vertical axis represents the terminal voltage per module in terms of percentage of full gradient. A close correspondence between NEC and GVM readings is observed. An independent check of the GVM calibration was provided by the elastic scattering of 12C on 12C. The results thus obtained agree within 5%.

Ccvo = XC2,

where K is the slope of the straight line adjusted in the V2 =f(V1) plot. The average value was Cceo = 0.0815 pF.

5. GVM calibration Once the value of Ccr,o was determined, the terminal voltage was raised up and VGVr~ was plotted against Vz as shown in fig. 5. The Vr scale is obtained dividing V2 by C I / C 2 (in our case 0.0815 pF/5290 pF = 15.4 V/MV). Next, the GVM calibration factor a = (VT ,8)/VGvr~ is obtained by least square fitting with a straight line, the values taken up to 1.6 MV. Therefore, to obtain the true value in MV, the GVM readings have to be multiplied by a (in our case = 1.77). Alternatively,

7. Conclusions The capacitive divider method is a simple way of calibrating the GVM. Values taken at low terminal voltage seem to be reliable at high potentials. Special precautions have to be taken to avoid loss of charge balance due either to leakage in C2 or sparks in the terminal. A correspondence is observed between the proposed method and other used so far.

References [11 J.O. Thrump, F.J. Stafford and R.J. Van de GraML Rev. Sci. Instr. 11 (1940) 54. [2] E. PErez Ferreira et al., Nucl. Instr. and Meth. 220 (1984) 37.