Statistical analysis of breakdown voltages in helium: Critical anomalies and gas-liquid transition

We conducted a comprehensive statistical analysis of the breakdown-voltage variations in helium near its critical point (5.2 K) using Weibull distribution analysis and Shannon entropy evaluation. Through detailed measurements at temperatures ranging from 5.1 to 5.5 K and densities from 5 to 115kg/m^{3}, we discovered two significant phenomena. First, in the liquidlike region above the critical density, we identified two distinct breakdown mechanisms with different Weibull shape parameters: a high-variability mode associated with bubble-mediated breakdown and a low-variability mode resembling gas-phase breakdown. The contribution of the bubble-mediated mode increases systematically with density, emerging at pressures 0.01-0.02 MPa above the critical pressure line. Second, the statistical variation in breakdown voltages shows a notable reduction near the critical density (≈69.6kg/m^{3}), particularly at temperatures close to the critical point. This reduction in the statistical spread was consistently observed through both the Weibull distribution analysis and Shannon entropy evaluation, with the latter providing a distribution-independent measure of voltage variations applicable across all fluid states from gaslike to liquidlike regions. The reduced statistical variation near the critical point presents an intriguing contrast with the enhanced density fluctuation characteristic of this region, suggesting a complex interplay between the fluid structure and breakdown mechanisms. These findings reveal previously unknown aspects of the breakdown phenomena in highly fluctuating fluids and provide insights into the relationship between fluid structure and electrical breakdown characteristics.