It is shown that the local approximation for electron distribution function (EDF) determination at plasma periphery, where the ambipolar field is dominant, is not applicable even at high pressures when the characteristic plasma size exceeds the energy relaxation length of the electrons R > λε. Therefore, consistent results can be obtained only when solving the complete kinetic equation in both energy and spatial variables (i.e. it is necessary to solve nonlocal kinetic equation).

A method for the calculation of the nonlocal electron distribution function (EDF) with programs commonly used for solving the one-dimensional Boltzmann kinetic equation (e.g., COMSOL Multiphysics) was proposed and implemented. The capabilities of the proposed method were illustrated using the example of the positive column plasma in argon. Significant differences between the local and nonlocal EDFs were observed, especially at the plasma periphery. This can result in significant differences in the electron transport coefficients and reaction rate constants for electron-induced processes. The proposed approach increases the precision of the numerical modeling of gas discharge devices and equipment.

The influence of electron-electron collisions on the formation of a nonlocal electron distribution function (EDF) and other characteristics of the electron gas are analyzed. Correct expressions for the coefficients in the integral of electron-electron collisions are obtained that are suitable for substitution into the kinetic Boltzmann equation averaged over the volume. This method of EDF calculation is implemented in COMSOL Multiphysics software. The example of positive column plasma in argon shows that accounting for electron-electron collisions leads both to differences between nonlocal and local EDFs and to dependence on the ionization degree.

The influence of metastable atoms on formation of the nonlocal electron distribution function (EDF) and other characteristics of gas-discharge plasma in argon is investigated in this paper. Superelastic collisions of electrons with metastable atoms strongly affect the shape of the EDF, the behavior of reaction rate constants, and other plasma characteristics. An interesting phenomenon of EDF replication emerges with a period of excitation threshold; this effect can increase the rate constants of excitation and ionization processes by several orders of magnitude, especially at the periphery of the plasma volume. Thus, collisions between electrons and metastable atoms are important in the formation of a nonlocal EDF, and neglecting them can lead to large errors in calculations of plasma characteristics.

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