Instabilities and double-layer formation are systematically investigated on a bounded collisionless system with electron beam penetrating through a plasma. The Buneman instability is observed at low beam currents. Above a critical current, there appears a sudden nonoscillatory potential drop due to the Pierce instability, which traps ions in the potential well. This collisionless ion trapping provides a new formation mechanism of the double layer, which is controlled by changing the speed of the potential drop.The Buneman instability (electron-ion twostream instability)' has been expected to be one of the most effective heating mechanisms in a current-carrying plasma. " To our knowledge, however, no clear-cut experiment on this instability has been published, except our preliminary report. It is a strong convective instability, and boundary effects are quite important for experiments on the instability. There are two types of boundary: a periodic boundary and a boundary of electron-beam injection. The former corresponds to the torus experiment of Hamberger and Jancarik, ' in which the spectrum of fluctuations was analyzed and the anomalous resistivity was said to be attributed to the Buneman instability. The latter situation was first realized by Nezlin etal. ' They observed unstabj. e oscillations and a virtual cathode due to the Pierce instability, ' although their theory is not suitable to the experiment as will be shown later. On the other hand, laminar' and turbulent' double layers were observed under this situation, where trapped electrons were, respectively, supplied externally and produced by the turbulent electron-electron two-stream instability. Trapped ions were also pointed out to be important for the double-layer formation. The mechanism of their initial production, however, was not explained clearly. In this Letter, we identify the Buneman instability in an electron beam-plasma system under a reasonable consideration of the boundary effect, and demonstrate a subsequent potential drop due to the Pierce instability, which provides a new mechanism of double-layer formation based on collisionless ion trapping. The dispersion equation in an infinite plasma with beam electrons is given by k'[1 -~,'/((u-kV)' -(u, .'/(u']+ k D' = 0, where kD (= &u, /v, ) is the Debye wave number of plasma electrons; U and v, are the electron-beam 3 3 MbL/m U I I (b), PI BI