Dielectric-breakdown tests of water at 6 MV

EGG published 30 January 2009)We have conducted dielectric-breakdown tests on water subject to a single unipolar pulse. The peakvoltages used for the tests range from 5.8 to 6.8 MV; the effective pulse widths range from 0.60 to 1:1 s;and the effective areas tested range from 1:8 10

Reference [20] proposes that the characteristic time delay delay between the application of a voltage to a water-insulated anode-cathode gap, and the completion of dielectric failure of that gap, can be approximated as follows: In this expression stat is the statistical component of the delay time; i.e., the characteristic time between the application of the voltage and the appearance of free electrons and ions that initiate the formation of streamers in the water.We define form to be the formative component: the time required for the streamers to propagate across the gap and evolve sufficiently to produce complete dielectric failure.
To inhibit electrical breakdown, water-insulated components are usually designed to produce a nominally uniform electric field over most of the component's area.We assume that, when the area of a water-insulated system with a uniform field is sufficiently large, the appearance of free electrons and ions necessary to initiate a breakdown occurs somewhere in the system very early in the voltage pulse [20].Under this condition the statistical time delay stat can be neglected, and the breakdown delay is dominated by its formative component: In principle, dielectric breakdown dominated by the formative component can be studied with an electrode geometry that consists of a point anode and a planar cathode [20][21][22].Although measurements with an infinitely field-enhanced anode point and an infinitely extended flat cathode are not possible, a number of dielectric-breakdown measurements between a significantly field-enhanced anode electrode and a less-enhanced cathode have been described in the literature.
Using these measurements, Ref. [20] finds that complete dielectric failure is likely to occur in water between a fieldenhanced anode and a less-enhanced cathode when E p 0:330AE0:026 eff ¼ 0:135 AE 0:009: In this expression E p V p =d is the peak value in time of the spatially averaged electric field between the anode and cathode (in MV=cm, where V p is the peak voltage difference and d is the minimum distance between the electrodes), and eff is the temporal width (in s) of the voltage pulse at 63% of peak.This relation is based on 25 measurements for which 1 V p 4:10 MV, 1:25 d 22 cm, and 0:011 eff 0:6 s.
To develop a tentative design criterion for a large-area water-insulated system with a nominally uniform electric field, Ref. [20] further applies a safety factor to Eq. ( 3) by reducing the right-hand side by 20%: E p 0:330 eff 0:108 when A * 10 4 cm 2 ; (4 where A is the effective area of the system.Equation ( 4) assumes that the area of the system is sufficiently large to have a negligible statistical time delay, and hence that the breakdown delay is dominated by the formative component.Both Eqs. ( 3) and ( 4) assume that voltage pulses of interest have normalized time histories that are mathematically similar; under this condition, eff / delay $ form .
PHYSICAL REVIEW SPECIAL TOPICS -ACCELERATORS AND BEAMS 12, 010402 (2009) 1098-4402=09=12(1)=010402( 5) 010402-1 Ó 2009 The American Physical Society In this article, we describe three tests of Eq. ( 4), which we believe are the first performed under the following simultaneous conditions: (i) peak voltage !4:10 MV, (ii) AK gap !22 cm, (iii) effective pulse width !0:6 s, and (iv) effective anode area ! 10 4 cm 2 .Two of the tests were conducted on the 36-module ZR accelerator; the third was conducted on the Z-20 machine, which is a single ZR module used for component development.
All the tests were performed on one or more waterinsulated intermediate-storage capacitors.A crosssectional view of a single capacitor is presented by Fig. 1.The capacitor includes two coaxial electrodes.The inner radius of the outer electrode is 99 cm; the outer radius of the inner electrode is 56 cm; and the anodecathode gap is 43 cm.The total effective area of the anode of a single capacitor is 1:8 Â 10 5 cm 2 .The electric field at the anode is nominally uniform.The voltage across each capacitor was measured using the D-dot monitor described in Ref. [23].
The tests were conducted over the course of operating the ZR and Z-20 accelerators for various experiments, and were not performed on accelerator shots dedicated specifically to measuring the dielectric strength of water.Given the high voltages involved, large AK gaps, long pulse widths, and large areas, dedicated shots require a substantial investment of resources and hence are not readily conducted.For this reason, we report in this article results of tests that were performed during normal accelerator operation.
Results of the tests, along with those previously described in Ref. [20], are summarized by Table I.Two capacitors were used for the 5.8-MV test; the corresponding voltage pulses are plotted by Fig. 2. One capacitor was used for the 6.8-MV test; 20 were used for each of the five tests conducted at 6.1 MV.For the 6.8-and 6.1-MV tests, the voltage pulse applied to each capacitor was shortened by closing a switch that was connected to the capacitor's inner conductor.Correcting for the coaxial geometry, we find that the peak anode electric fields were 0.103, 0.121, and 0:108 MV=cm for the 5.8-, 6.8-, and 6.1-MV tests, respectively.
The values of E p 0:330 eff for all the tests are listed in Table I, and suggest that the results are consistent with Eq. ( 4).(The results are also consistent with the predictions of Woodworth and colleagues [26].) In addition to Eq. ( 3), other published water-dielectricbreakdown relations are considered; specifically [21,22,27,28]:  I. Conditions under which dielectric breakdown of water is observed not to occur.Each of these five observations was made on a large-area (A ! 10 4 cm 2 ) water-insulated system with a nominally uniform electric field.The quantity V p is the peak voltage difference between the anode and cathode, d is the minimum distance between the electrodes, E p V p =d, and eff is the temporal width of the voltage pulse at 63% of peak.The last column assumes E p is expressed in MV=cm, and eff in s.The Maxwell-Lab measurements were performed on a capacitor with coaxial electrodes that had outer and inner radii of 60 and 48 cm, respectively [22,24].The peak field E p given for the Maxwell measurements is that at the outer conductor (which was the anode), and is corrected for the coaxial geometry.The peak fields of the tests described in the present article are similarly corrected.The observations summarized in the table are consistent with the design criterion given by Eq. ( 4).

FIG. 1 .
FIG. 1. (Color) Cross-sectional view of a ZR-accelerator intermediate-storage capacitor.The two electrodes have outer and inner radii of 99 and 56 cm, respectively.

TABLE II .
Comparison of the results summarized by Table I with the predictions of Eqs. ( ). FIG. 2. (Color) Time histories of the voltage applied to the two ZR intermediate-storage capacitors that were used for the 5.8-MV test.DIELECTRIC-BREAKDOWN TESTS OF . . .Phys.Rev. ST Accel.Beams 12, 010402 (2009) 010402-3