Paschen curves are presented for hollow cathodes with diameters varying from 5 mm to 1.5 mm. The curves obey similar functions of (pd), where p is the argon gas pressure and d is the hollow diameter. The curves exhibit similar properties in terms of the location of the breakdown voltage minima. The breakdown voltage increases monotonically for decreasing hollow diameter. The shapes of the various curves and the (pd) minima location are unaffected by aspect ratio.
P. D. Mixon, S. T. Griffin, and J. C. Williams, "Breakdown Voltage Scaling Characteristics of an Argon Hollow Cathode Discharge," Appl. Spectrosc. 47, 1567-1570 (1993)