Abstract
A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.
Highlights
Electric discharge in gases [1,2,3] has played a significant role in the emergence and development of modern physics, and in addition to its many applications in science and technology [4,5,6,7], it remains a field for experimental and theoretical research [8,9,10]
A nonlinear model has been introduced for the positive column of DC glow discharge in a pure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment, process and having the two-step ionization process of the metastable excited states, too
Since the optimization of small signal gain and overall efficiency of these lasers is strongly dependent on the discharge conditions, so it requires further theoretical understanding in this area. It has been already discovered, in the positive column (PC) of the glow discharge (GD), there is an equation between electron characteristic energy, kTe, and the similarity variable, nR or pR where n is overall particle density of media, p is overall pressure of the media and R is the internal radius of the discharge vessel, no matter it is DC or AC discharge [14,15,16,17]
Summary
Electric discharge in gases [1,2,3] has played a significant role in the emergence and development of modern physics, and in addition to its many applications in science and technology [4,5,6,7], it remains a field for experimental and theoretical research [8,9,10]. Since the optimization of small signal gain and overall efficiency of these lasers is strongly dependent on the discharge conditions, so it requires further theoretical understanding in this area It has been already discovered, in the positive column (PC) of the glow discharge (GD), there is an equation between electron characteristic energy, kTe, and the similarity variable, nR or pR where n is overall particle density of media, p is overall pressure of the media and R is the internal radius of the discharge vessel, no matter it is DC or AC discharge [14,15,16,17]. Results of an investigation on the generalized equation of the characteristic electron energy kTe on the similarity variable of the glow discharge N R, where N is the total particle density of the media and R is the internal radius of the discharge vessel, have been reported. There is an experimental work which has been done on the media of the glow discharge of the CO2 laser [19] and shows the dependence of the kTe to the similarity variable using the electron density as the parameter and could be imagined as an strong motivation for doing this research
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