Bohm criterion

The Debye sheath (also electrostatic sheath) is a layer in a plasma which has a greater density of positive ions, and hence an overall excess positive charge, that balances an opposite negative charge on the surface of a material with which it is in contact. The thickness of such a layer is several Debye lengths thick, a value whose size depends on various characteristics of plasma (e.g. temperature, density, etc.).

A Debye sheath arises in a plasma because the electrons usually have a temperature on the order of magnitude or greater than that of the ions and are much lighter. Consequently, they are faster than the ions by at least a factor of ${\displaystyle {\sqrt {m_{\mathrm {i} }/m_{\mathrm {e} }}}}$. At the interface to a material surface, therefore, the electrons will fly out of the plasma, charging the surface negative relative to the bulk plasma. Due to Debye shielding, the scale length of the transition region will be the Debye length ${\displaystyle \lambda _{\mathrm {D} }}$. As the potential increases, more and more electrons are reflected by the sheath potential. An equilibrium is finally reached when the potential difference is a few times the electron temperature.

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