When the macroscopic neutrality of a plasma is instantaneously perturbed by external means, the electrons react in

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When the macroscopic neutrality of a plasma is instantaneously perturbed by external means, the electrons react in a such a way as to give rise to oscillations at the electron plasma frequency

Consider these oscillations, but including the motion of the ions. Show that in this case the natural frequency of oscillation of the net charge density is given by

where

Use the linearized equations of continuity and of momentum for each species, and Poisson equation, considering only the electric force due to the internal charge separation.

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