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A semi-analytic model of collisionless sheath in plasma immersion ion implantation (PI3) for a step bias with finite rise time in cylindrical geometry has been developed. The model takes into account the formation of the presheath, predicts the sheath overshooting and its further recovery to the steady-state Child value. To verify the model, a sheath dynamics has been investigated experimentally on a 30-kV PI3 setup using the positively biased Langmuir probe technique. The measurements have been carried out in argon and helium plasmas of inductively coupled and hot cathode plasma sources. The model predictions agreed well with the experimental results.