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.
[1] If the local electrostatic potentials at two nearby locations are φ1 and φ2, the Boltzmann relation for the electrons takes the form:[2] where ne is the electron number density, Te is the temperature of the plasma, and kB is the 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.
For an isothermal fluid, the pressure force takes the form while the electric term is Integration leads to the expression given above.
If the electron density is known and the assumptions hold sufficiently well, the electric potential can be calculated simply from the Boltzmann relation.