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A potential relaxation instability (PRI), which causes a periodic motion of a potential jump and plasma expansion accompanying a high-density fluctuation level (Â¿60 percent), is observed in a bounded discharge plasma. The instability is found to create a high electron drift velocity and a spatial growth of density and potential fluctuations, and to accelerate a test wave. An additional supplement of a plasma into the boundary suppresses the instability. At the same time, the fluctuation decreases (<5 percent) and the frequency difference of the wave spectrum between nth and (n - 1) th (n is an integer) higher harmonics decreases as the frequency increases. However, when the potential relaxation instability is excited, this frequency difference keeps constant.