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The sheath and presheath relaxation in front of an electrode biased to high negative voltage pulses is investigated on the basis of ion fluid equations as well as of a particle-in-cell/Monte Carlo simulation. The electrons are assumed to be Boltzmann distributed and the ions are governed by charge exchange collisions. The electron Debye length is small compared to the ion mean free path. Switching on a high negative voltage, three phases on different time scales may be distinguished: the matrix extraction phase, the sheath expansion phase, and the presheath relaxation initiated by a rarefaction wave. Correspondingly, switching off a high negative voltage results in a fillup process followed by a sheath constriction and by a compression wave rearranging the presheath. All these phenomena are mixed if voltage pulses of finite duration are applied. We present numerical results exhibiting typical relaxation phenomena for single pulses as well as for periodic pulses with various frequencies and pulse forms. Results for the particularly important matrix extraction phase are compared with an analytic step model of the homogeneous matrix sheath [K.-U. Riemann and Th. Daube, J. Appl. Phy. 86, 1202 (1999)]. © 2002 American Institute of Physics.