Nonlocal particle loss effects on the electron kinetics in a direct current helium diffusion-controlled positive column

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Abstract
The electron energy distribution function (EEDF) in a positive column of low-pressure and discharge current is determined not only by the local collision processes and the axial electric field action, but also by the transport phenomenon, the radial ambipolar diffusion due to the gradient of plasma density. Thus, to completely determine the EEDF, the Boltzmann equation including radial inhomogeneity terms has to be solved. The present work proposes a simplified method to account for the radial inhomogeneity, when the electron kinetics in the central part of the positive column can be reduced to be one energy-dimensional. The radial diffusion of electrons is taken into account via a wall loss term. A greatly simplified kinetic equation is obtained and its numerical solutions agree well with the EEDF determined from Langmuir probe measurements in a helium dc discharge positive column. Also, a comparison of the present method with local and nonlocal approach theories is made. A discrepancy is observed, especially at high energies, where either local or nonlocal approach theories predict too-large values of EEDF.