Consider an initially uniform plasma in which the electron and ion number densities are each equal ton. By some external means, let a one dimensional perturbation occur such that the electrons in an infinite plane (the (y, z) plane) are displaced by a small amount x, as indicated in Fig. 11.

(a) Using Gauss's law, show that the electric field that appears across the perturbed plane is given by

(b) Show that the equation of motion (Newton's second law) for each electron, under the action of this electric field, is

Verify that this is the equation of a harmonic oscillator of fr equency

Figure 11.

Transcribed Image Text:

E = : (ne) x