This paper presents a theoretical study of the electron multiplication in Townsend dis charge in the case of large values of E/p. An equation for the electron current density at different discharge points is found. An analytical expression for the first Townsend's ionization coefficient u/p has been obtained from the solution of this equation for a uniform electric field. The slopes a and k of the curves of ionization and total inelastic collision cross sections as functions of energy for some

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... ases are obtained from the analysis of experimental data for a/p. Using the values of a and k one can solve the equation for the electron current density also for the case of non-uniform electric field. As an example, electron current densities in the discharge in nitrogen between two concentric cylinders as functions of voltages are calculated.