OSCILLATIONS IN THE PLASMA SHEATH

The behavior of the ion plasma sheath next to a wall is investigated under a sinusoidal-in-time perturbation of the potential of the wall. A collisionless sheath is assumed, and the ion density distribution is considered to remain at the steady state value, with only the electron distribution being perturbed. The collisionless macroscopic plasma equations are solved by a perturbation procedure, using an exact equation for the steady state potential distribution. A second order differential equation which is linear, but which has variable coefficients is obtained for the perturbation. This equation is transformed into the form of a wave equation with variable propagation constant so that the analytical behavior can be deduced. One observes that above a certain range of frequencies, but below the plasma frequency of the uniform plasma, the perturbation may propagate over a finite region which may begin away from the wall. A numerical integration of the equation is performed, using an asymptotic approximation in order to obtain the boundary conditions. The predicted oscillations are seen to occur, and two resonances in the sheath are found at frequencies below the plasma frequency.