Abstract
The derivation of moment equations for the theoretical description of electrons is of interest for modelling of gas discharge plasmas and semiconductor devices. Usually, certain artificial closure assumptions are applied in order to derive a closed system of moment equations from the electron Boltzmann equation. Here, a novel four-moment model for the description of electrons in nonthermal plasmas is derived by an expansion of the electron velocity distribution function in Legendre polynomials. The proposed system of partial differential equations is consistently closed by definition of transport coefficients that are determined by solving the electron Boltzmann equation and are then used in the fluid calculations as function of the mean electron energy. It is shown that the four-moment model can be simplified to a new drift-diffusion approximation for electrons without loss of accuracy, if the characteristic frequency of the electric field alteration in the discharge is small in comparison with the momentum dissipation frequency of the electrons. Results obtained by the proposed fluid models are compared to those of a conventional drift-diffusion approximation as well as to kinetic results using the example of low pressure argon plasmas. It is shown that the results provided by the new approaches are in good agreement with kinetic results and strongly improve the accuracy of fluid descriptions of gas discharges.
Highlights
Nonthermal plasmas are widely used in many technical applications including plasma display panels, energy saving lamps, devices for microbial decontamination and ozonizers [1,2,3,4]
Results obtained by the proposed fluid models are compared to those of a conventional drift-diffusion approximation as well as to kinetic results using the example of low pressure argon plasmas
A new system of moment equations for the description of electrons in nonthermal plasmas was derived by an expansion of the electron velocity distribution function in Legendre polynomials and the definition of transport coefficients that are determined by means of the localmean-energy approximation
Summary
Nonthermal plasmas are widely used in many technical applications including plasma display panels, energy saving lamps, devices for microbial decontamination and ozonizers [1,2,3,4]. They are characterized by low gas temperatures Tg in the range from 300 to 1000 K and comparatively high mean electron energies e between 1 and 10 eV, where 1 eV corresponds to temperature of 11605 K. Results are compared to those of a conventional drift-diffusion model frequently used [24,25] and to kinetically obtained results at the example of argon gas discharge plasmas
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