The distribution of discharge amplitudes of randomly colliding charged spheres

If portable devices such as smartphones or tablets are carried e.g. in a backpack, tribo-electric charging due to metallic objects can lead to impulsive discharges and damage of the device. The discharge voltages are random because of the random movement of the objects. In previous experiments, spherical metallic objects and various non-conducting materials such as rubber, nylon, and plastic were assembled in a shaker to emulate the backpack and its movements. Discharge events were recorded using a linearly polarized Vivaldi antenna and, performing some 1000 experiments, histograms of the maximum detected field strengths were assembled. In our present paper, we refine the previously proposed procedure by explicitly deconvolving the impact of the linear polarization on the measured field strength. We compute the histogram of the discharge voltage between the spherical objects, propose a Gamma probability density to characterize its statistics and compute its parameters b and p for various assemblies of the non-conducting materials. The proposed procedure can be used to estimate the probability of failure of tribo-electrically charged devices.