General method for analyzing small-amplitude waves

All plasma phenomena can be described by combining Maxwell's equations with the Lorentz force equation where the latter is represented by the Vlasov, the two-fluid, or the MHD approximation. The subject of linear plasma waves provides a good introduction to the study of plasma phenomena because linear waves are relatively simple to analyze and yet demonstrate many essential features of plasma behavior.

Linear analysis, a straightforward method applicable to any set of partial differential equations describing a physical system, reveals the physical system's simplest non-trivial, self-consistent dynamical behavior. In the context of plasma dynamics, the method is as follows:

1. By making appropriate physical assumptions, the general Maxwell–Lorentz system of equations is reduced to the simplest set of equations characterizing the phenomena under consideration.

2. An equilibrium solution is determined for this set of equations. The equilibrium might be trivial such that densities are uniform, the plasma is neutral, and all velocities are zero. However, less trivial equilibria could also be invoked where there are density gradients or flow velocities. Equilibrium quantities are designated by the subscript 0, indicating “zero-order” in smallness.

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