Radiated Electric Field and its Intensity Limit due to Low Voltage Collision ESD Following Modified Paschen Curve

Previously published studies have shown that the radiated electric field due to collision ESD (electrostatic discharge) between metal spheres charged below 1000 V increases as the spark voltage decreases, reaching a maximum around 600 V before declining further. However, the reason for this specific behavior remains unclear. In this paper, the underlying cause is considered based on the mechanism using the modified Paschen curve for microgaps in air at atmospheric pressure, derived by Radmilovic. This curve predicts a sharp reduction in spark voltage below the Paschen minimum due to electron field emission from the cathode. For spark lengths above the Paschen minimum, we assume that the deviation of the spark voltage from the standard Paschen curve is due to a breakdown mechanism dominated by field-emitted electrons. By applying Radmilovic's theory to determine a threshold value of the local electric field for initiating field emission, we verify that for estimated spark lengths below about 600 V, the spark voltages deviate downward from the standard Paschen curve, decreasing along the corresponding theoretical Radmilovic curve. Consequently the breakdown potential gradient does not increase significantly as the spark voltage decreases, limiting the intensity of the radiated electric field during collision ESD.