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

Abstract

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 ${E}_{p}{\ensuremath{\tau}}_{\mathrm{eff}}^{0.330\ifmmode\pm\else\textpm\fi{}0.026}=0.135\ifmmode\pm\else\textpm\fi{}0.009$. In this expression ${E}_{p}\ensuremath{\equiv}{V}_{p}/d$ 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 ${\ensuremath{\tau}}_{\mathrm{eff}}$ is the temporal width (in $\ensuremath{\mu}\mathrm{s}$) of the voltage pulse at 63% of peak. This relation is based on 25 measurements for which $1\ensuremath{\le}{V}_{p}\ensuremath{\le}4.10\text{ }\mathrm{MV}$, $1.25\ensuremath{\le}d\ensuremath{\le}22\text{ }\mathrm{cm}$, and $0.011\ensuremath{\le}{\ensuremath{\tau}}_{\mathrm{eff}}\ensuremath{\le}0.6\text{ }\ensuremath{\mu}\mathrm{s}$. The normalized standard deviation of the differences between these measurements and the associated predictions of the relation is 12%.