A formalism of the self-consistent solution of the kinetic equation and the field equation is described for the positive plasma column in an inert gas discharge. The model considers the presence of electrons trapped in the potential well transfering the discharge current and of free electrons which reach the walls in a free diffusion regime supporting the required ionization level in the discharge. The calculations have been carried out for neon. In the model application range the comparison is made with experimental data of axial fields, wall potentials, wall currents and in some cases with distribution functions. A good correspondence takes place.
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