Dynamics of plasmas

Let us begin this sampler of elementary plasma dynamics by discussing one, most characteristic, mode of plasma motion, paradoxically called the “electrostatic wave”. Suppose that all space were filled uniformly by free particles all of one charge q, with a number per unit volume n. These particles are found at time zero with various coordinates x. Let us follow a small motion for a short time after time zero, designating their position at time t by $\mathrm{\zeta \hspace{0.17em}=\hspace{0.17em}\zeta (t,}\mathrm{x}\mathrm{).}$ In this extremely simple situation, Newton’s laws and one of Maxwell’s equations suffice to give a complete solution of the problem. Newton tells us that for each of the particles.

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