Abstract
We have derived an approximate solution for the one-dimensional steady equation of electron balanceDa∇2n+υn+βn2=0, in which the coefficients ν and β may vary as to sign. The nonlinear term was approximated by two segments of straight lines by the method of least squares, as a result of which the original equation was reduced to a system of two linear differential equations whose solution is presented in analytical form. We have obtained numerical data for the determination of the electron concentration profile in the range −8≤R2βn0/Da≤20 for a plane, cylindrical, and spherical configuration of the discharge zones.
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