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## Boltzmann relationIn a plasma, the *n*_{e}=*n*_{0}exp(eφ_{pl}/*k*_{B}*T*_{e})
## Additional recommended knowledgeThe reference for the potential is taken to be a position where the electron density is It can be derived in a particle view by equating the density of states to the physical density and applying the Boltzmann factor. Alternatively, it can be derived from the fluid equation for the electrons by equating the force density due to the electron pressure gradient assuming isothermal electrons, , to the force density due to the electric field on the electron charge density, . In many problems of plasma physics, it is not useful to calculate the electric potential on the basis of the Poisson equation because the electron and ion densities are not known Discrepancies with the Boltzmann relation can occur, for example, when oscillations occur so fast that the electrons cannot find a new equilibrium (see e.g. plasma oscillations) or when the electrons are prevented from moving by a magnetic field (see e.g. lower hybrid oscillations). |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Boltzmann_relation". A list of authors is available in Wikipedia. |