Beam double layer in a bounded plasma

A study is made of the properties of a beam double layer in a plasma between two conducting electrodes held at a fixed potential. The dispersion relation for electron oscillations is derived using the hydrodynamic approximation and with allowance for the boundary conditions. The dispersion relation obtained shows that a weak double layer is unstable. The instability growth rate is studied as a function of both the position of the layer and the potential difference between the electrodes.