Electrostatic marginal stability of a one-dimensional inhomogeneous finite plasma

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Abstract
The marginal stability of an inhomogeneous finite plasma, at equilibrium with an electric field, is investigated for linear electrostatic perturbations with a time dependence e-i omega t. A set of equilibria with a variable parameter is introduced, which equilibria, as well as their perturbations, should only depend on a single inhomogeneity variable. The perturbed electric field should vanish at the boundaries. The paper concerns the instability of equilibria in the vicinity of a marginal one admitting an omega =0 mode. The corresponding growth rate is derived explicitly in the case of special properties of the marginal equilibrium. A corresponding example is discussed.

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