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High-voltage sheath dynamics near a negatively biased substrate in cathodic arc plasmas are investigated using a biased electrical probe. Since the sheath is devoid of electrons, the sheath boundary can be inferred from the position where a positively biased probe draws no electron current. The extent of the sheath is primarily dependent on the plasma density, the ion velocity and the applied voltage. Using insulating substrates, the sheath boundary eventually retracts due to a dynamic reduction in the applied voltage. This reduction is caused by positive charge accumulation on the insulator surface. The collapse time of the sheath is dependent on the plasma density and the substrate characteristics. We believe this to be the first direct observation of the reduction in the width of the high-voltage sheath when implanting an electrical insulator using plasma-based ion implantation (PBII). This information is important when determining the optimal parameters for plasma-based ion implantation of insulators. Our measurements are compared with theoretical predictions based on the Child-Langmuir equations for high-voltage sheaths. By choosing appropriate values for the secondary electron coefficient the theory could be made to fit the experimental data. A discussion of the validity of the choice of secondary electron coefficients is presented.