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## The Maxwell-Boltzmann approximation for ion kinetic modeling

In this short paper with C. Bardos, F. Golse, and R. Sentis, we are aimed to justify the Maxwell-Boltzmann approximation from kinetic models, widely used in the literature for electrons density distribution; namely, the relation

$\displaystyle n_e =e^{q_{e} \phi / \theta }$

in which ${n_e, q_e, \theta,\phi}$ denote the electrons density, the elementary charge, the electron temperature, and the electric potential.