Estimation of Spark Voltage and Spark Length Due to ESD Just before Collision between Charged Metal Spheres Using Measurement Waveforms of Radiated Electric Fields

Originally, the spark voltage Vs and spark length δ of ESD (Electrostatic Discharge) that occurs just before the collision of charged metal objects are unknown and difficult to measure directly. In this study, concerning the collision ESD between charged metal spheres where both spark voltage and spark length are unknown, to begin with, a breakdown potential gradient EB (=Vs/δ ) is obtained by fitting the calculated waveform of the radiated electric field normalized to its first peak value, derived from the Rompe-Weizel spark resistance law, to the first falling edge of the normalized measurement waveform. Thereby the method of estimating the spark length δ from the first peak of the measured waveform is presented. Using this method, the spark voltage and spark length are actually estimated for the measurement waveforms of radiated electric fields due to ESDs between charged metal spheres from a high-voltage source through a high resistance in our previous study and ESDs for friction-charged metal spheres conducted by Pommerenke and his group. The effectiveness of the estimation method is validated by comparing these estimated results with the standard Paschen's curve, its empirical formulas and the measured spark lengths between the charged metal spheres with different fixed gaps.