Resonant absorption and the electrostatic oscillations of a cold inhomogeneous plasma

Small amplitude electrostatic oscillations of a cold inhomogeneous plasma are investigated using a wave number expansion procedure. The method allows the inclusion of both monotonic and non-monotonic density profiles. The collective modes of oscillation obtained are a phenomenon of spectral concentration and allow the system to satisfy the initial conditions imposed upon it. The temporal decay of these modes coincides with an increase in the oscillations of the continuous spectrum. This time behaviour is shown to be independent of the damping time scale obtained when a finite collision frequency is included. The collective modes do not contribute to the heating of the plasma. Absorption of energy from the incident wave occurs in the steady state at those locations where the forcing frequency matches the local plasma frequency. (author)