Question

Stepwise Ionization by Electron Impact. Estimate a stepwise ionization rate coefficient in Ar at electron temperatures of 0.5 and 1 eV, assuming quasi-equilibrium between plasma electrons and electronic excitation of atoms. Comment on why the stepwise ionization is a preferential one in thermal plasmas and less important in non-thermal discharges.

Answer 1

Answer well the Ionization due to an electron impact occurs when the energy of the electron exceeds the ionization energy of the particle, which is E_i = 15.76 eV for Argon

Ionization due to an electron impact can be easily described by the equation,

Ar + e^- Ar⁺ + 2 e^-                                                   equation 1

This leads to the process , where ionization happens by first excitation of an atom and following ionization of the excited atom. Excited argon atoms are labeled below as Ar*.

This process of stepwise ionization can be described by,

Ar + e^- Ar* + e^- Ar⁺ + 2e-                                          equation 2

For simplified use in numerical simulations, rate coefficients are often described by simple but remarkably accurate "Arrhenius Equation" for the temperature dependence of reaction rates which gives the quantitative basis of a relationship between the activation energy & the reaction rate at which a reaction proceeds in dependence of the temperature.

The rate coefficient is written As -

k_f (T_e) = A T^s exp [-E_i / k_B T_e]

where, A is a constant pre-factor on the order of 10^-16 and s = 1, 5 is an exponent determinated by approximation.

Based on the relative temperatures of an electrons, ions and neutrals, plasmas are classified as "thermal" or "non-thermal". Thermal plasmas have electrons and a heavy particles at the same temperature.

Therefore, an analysis of existing rate coefficient models is needed. .