Electron temperature

Temperature is a statistical quantity. The formal definition is T = dU/dS, 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, ${\displaystyle \langle E\rangle =(3/2)\langle k_{B}T\rangle }$.

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 8.6173324(78)×10⁻⁵ eV; this factor is the ratio of the Boltzmann constant to the elementary charge. Each eV is equivalent to 11,605 kelvin. It can be calculated by the relation,${\displaystyle \langle E=k_{B}T\rangle }$.

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