Electron temperature

Temperature is a statistical quantity whose formal definition is

${\displaystyle T=\left({\frac {\partial U}{\partial S}}\right)_{V,N},}$

or the change in internal energy with respect to entropy, holding volume and particle number constant. A practical definition comes from the fact that the atoms, molecules, or whatever particles in a system have an average kinetic energy. The average means to average over the kinetic energy of all the particles in a system.

If the velocities of a group of electrons, e.g., in a plasma, follow a Maxwell–Boltzmann distribution, then the electron temperature is defined as the temperature of that distribution. For other distributions, not assumed to be in equilibrium or have a temperature, two-thirds of the average energy is often referred to as the temperature, since for a Maxwell–Boltzmann distribution with three degrees of freedom, ${\displaystyle \langle E\rangle =(3/2)\,k_{\text{B}}T}$.

The SI unit of temperature is the kelvin (K), but using the above relation the electron temperature is often expressed in terms of the energy unit electronvolt (eV). Each kelvin (1 K) corresponds to 8.617 333 262...×10–5 eV; this factor is the ratio of the Boltzmann constant to the elementary charge.[1] Each eV is equivalent to 11,605 kelvins, which can be calculated by the relation ${\displaystyle \langle E\rangle =k_{\text{B}}T}$.

The electron temperature of a plasma can be several orders of magnitude higher than the temperature of the neutral species or of the ions. This is a result of two facts. Firstly, many plasma sources heat the electrons more strongly than the ions. Secondly, atoms and ions are much heavier than electrons, and energy transfer in a two-body collision is much more efficient if the masses are similar. Therefore, equilibration of the temperature happens very slowly, and is not achieved during the time range of the observation.

References

1. Mohr, Peter J.; Newell, David B.; Taylor, Barry N.; Tiesenga, E. (20 May 2019). "CODATA Energy conversion factor: Factor x for relating K to eV". The NIST Reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology. Retrieved 11 November 2019.