Water-dielectric-breakdown relation for the design of large-area multimegavolt pulsed-power systems

We have developed an empirical electrical-breakdown relation that can be used to design large-area water-insulated pulsed-power systems. Such systems often form an integral part of multiterawatt pulsed-power accelerators, and may be incorporated in future petawatt-class machines. We find that complete dielectric failure is likely to occur in water between a significantly field-enhanced anode and a less-enhanced cathode when $E_p{\tau }_{\mathrm{eff}}^{0.330\pm 0.026}=0.135\pm 0.009$. In this expression $E_p\equiv V_p/d$ is the peak value in time of the spatially averaged electric field between the anode and cathode (in $\mathrm{MV}/\mathrm{cm}$), $V_p$ is the peak voltage across the electrodes, $d$ is the distance between the anode and cathode, and ${\tau }_{\mathrm{eff}}$ is the temporal width (in $\mu \mathrm{s}$) of the voltage pulse at 63% of peak. This relation is based on 25 measurements for which $1\le V_p\le 4.10\mathrm{MV}$, $1.25\le d\le 22\mathrm{cm}$, and $0.011\le {\tau }_{\mathrm{eff}}\le 0.6\mu \mathrm{s}$. The normalized standard deviation of the differences between these measurements and the associated predictions of the relation is 12%.

Figure 1

The peak electric field required to achieve complete dielectric failure $E_p$ as a function of the effective pulse width ${\tau }_{\mathrm{eff}}$. Each of the 25 measurements plotted here was obtained with a significantly field-enhanced anode and a less-enhanced cathode, as described in Refs. 27, 42, 43, 44, 45, 46, 50. This data is summarized in Table . We define $E_p$ as $V_p/d$, where $V_p$ is the peak voltage in time across the anode-cathode gap, and $d$ is the length of the gap. We define ${\tau }_{\mathrm{eff}}$ to be the width of the voltage pulse at 63% of peak. It appears that the data are more consistent with Eq. (5) than Eq. (7).