Variational description of the positive column with two-step ionization

Steady-state positive column calculations can sometimes be simplified by writing the electron diffusion rate in terms of an effective length, thereby replacing a Laplacian with an algebraic quantity. When the electron continuity equation is purely linear in electron density, the characteristic diffusion length is useful for this purpose, since it can be used to relate the electron diffusion loss rate to the dimensions of a plasma and to calculate the electron temperature or operating electric field. If additional, nonlinear processes are introduced, the characteristic diffusion length is no longer appropriate for representing the diffusion rate. This paper presents a simple yet exact definition of a generalized diffusion length for calculations of the spatially averaged electron density in plasmas with electron production and loss rates linear and quadratic in electron density. This generalized effective diffusion length properly accounts for the average effect of electron diffusion for all possible signs and relative magnitudes of the linear and quadratic rates. Some properties of the effective diffusion length differ significantly from those of the characteristic diffusion length, which represents a special limiting case. Problems with other definitions of an effective diffusion length are discussed.

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Populations in the metastable and the resonance levels of argon and stepwise ionization effects in a low-pressure argon positive column

Ferreira

Loureiro

Ricard

1985

Journal of Applied Physics

269

114

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The contribution of the ionization from the two metastable and the two resonance levels of argon to the total ionization rate in a low-pressure argon positive column is investigated theoretically and experimentally. A simple yet self-consistent discharge model is developed by coupling the balance between the electron total production and loss rates to the steady-state rate balance equations for the excited states. The predictions of this model, i.e., the maintenance field for the positive column and the populations in the individual excited states as a function of the gas pressure and the discharge current are compared with the experiment (0.05<p<1 Torr; 0.2<I<20 mA; φ=2.6-cm-i.d. discharge tube). It is shown that stepwise ionization becomes predominant for pressures larger than a few tenths of a Torr even for the lowest currents of this experiment. The predicted values of the maintenance field are considerably lower than those that would be required to sustain the discharge by ground-state ionization and compare favorably with the measurements. The calculated populations in the metastable states also compare reasonably well with the experiment. The discrepancies are, however, quite large in the case of the resonance levels owing, presumably, to the lack of accuracy of the theoretical escape factors for the resonance radiation.

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Variational description of the positive column with two-step ionization

Cited by 7 publications

References 10 publications

Distribution of electron concentrations in a discharge with nonlinear sources for the appearance and disappearance of particles

Distribution of electron concentrations in a discharge with nonlinear sources for the appearance and disappearance of particles

The diffusion length for gas discharge columns with electron production and loss rates linear and quadratic in electron density

Populations in the metastable and the resonance levels of argon and stepwise ionization effects in a low-pressure argon positive column

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