  We report results from a study on electrical breakdown in liquid helium using
near-uniform-field stainless steel electrodes with a stressed area of
$\sim$0.725 cm$^2$. The distribution of the breakdown field is obtained for
temperatures between 1.7 K and 4.0 K, pressures between the saturated vapor
pressure and 626 Torr, and with electrodes of different surface polishes. A
data-based approach for determining the electrode-surface-area scaling of the
breakdown field is presented. The dependence of the breakdown probability on
the field strength as extracted from the breakdown field distribution data is
used to show that breakdown is a surface phenomenon closely correlated with
Fowler-Nordheim field emission from asperities on the cathode. We show that the
results from this analysis provides an explanation for the supposed electrode
gap-size effect and also allows for a determination of the breakdown-field
distribution for arbitrary shaped electrodes. Most importantly, the analysis
method presented in this work can be extended to other noble liquids to explore
the dependencies for electrical breakdown in those media.
