On the structure of the charged near-electrode sheath in a plasma with degenerate electrons

A nonlinear self-consistent theory of a stationary charged near-electrode sheath in a plasma with a quantum-degenerate electron component is developed. The theory is based on the gasdynamic two-liquid description of the plasma, such that its degenerate component satisfies the equation of state for a cold Fermi gas (in the Thomas—Fermi approximation), while the classical component satisfies the equation of state for an ideal gas (in the isothermal approximation). A generalized Bohm criterion is derived for the existence of a stationary sheath, as well as the criterion of the formation of a double-layer-type structure in the sheath. The theory is illustrated by numerical examples of various structures (of the monolayer and the double-layer type) in the sheath.

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