Boltzmann relation

In a plasma, the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium. In a plasma, the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium. In many situations, the electron density of a plasma is assumed to behave according to the Boltzmann relation, due to their small mass and high mobility. If the local electrostatic potentials at two nearby locations are φ1 and φ2, the Boltzmann relation for the electrons takes the form: where ne is the electron number density, Te the temperature of the plasma, and kB is Boltzmann constant. A simple derivation of the Boltzmann relation for the electrons can be obtained using the momentum fluid equation of the two-fluid model of plasma physics in absence of a magnetic field. When the electrons reach dynamic equilibrium, the inertial and the collisional terms of the momentum equations are zero, and the only terms left in the equation are the pressure and electric terms. For an isothermal fluid, the pressure force takes the form