Liquid helium breakdown as function of temperature and electrode roughness

The high dielectric dc strength of liquid helium can be explained by the effect of an energetic barrier against germinal vapor bubble elongation and runaway up to vapor discharge. The barrier normally rises in front of any cathode asperity where a germinal bubble may be produced from a collapsing vacuous cavity. After reaching a peak, the barrier changes into a decreasing tail, caused by significant vapor ionization. This so-called 'antibubble barrier' can be overcome at a sufficiently high field strength. For temperatures above the normal boiling point, the barrier peak must be lower than the threshold limit. At lower temperatures, the germinal bubbles may extend already into the falling tail, which favors runaway considerably. Nominal breakdown field strengths have been calculated assuming various surface roughness condition in the temperature range 2.5 to 4.5 K. A simple engineering formula for the roughness effect estimation is given.