The role of the electron diffusion on the stability of a Townsend discharge was investigated with the linear stability theory for the one-dimensional fluid equation with drift-diffusion approximation. It was proved that the discovered instability occurs as a result of the coupled action of electron diffusion and the perturbed electric field by space charge. The larger electron diffusion results in the faster growth rate at the regime of small perturbation of the electric field by space charges.

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... There has been considerable interest in non-thermal atmospheric pressure glow discharges over last time due to the increased variety of their industrial applications Fridman and Lee [1,2]. The basic feature of the non-thermal discharges is that majority of the energy of the applied electric field goes into electrons, instead of heating the entire gas in the discharge cell. Numerous experiments show that depending on the parameters of the discharge, atmospheric pressure glow discharge is realized in two forms: a Townsend and glow discharges. A Townsend discharge is the simplest type of glow discharges. It is characterized by the absence of quasi-neutral plasma--the absolute value of the ion density exceeds much that of the electron density. The applied electric field is weakly disturbed by spatial charge, and the discharge current is governed mainly by the processes of the electron emission from the cathode. The current of a Townsend discharge is only limited by the external circuit. The transition to a glow discharge occurs when the space charge in a Townsend discharge becomes large enough to cause a significant disturbance of the applied field. The physics of space charge driven transitions of a Townsend discharge to subnormal, normal, and further to abnormal glow has attracted considerable attention of the discharge research community Melekin, Phelps, Kolobov, Kaganovich, Koch, Bruhn, Amiranashvili, et al [3-9] Numerous experimental, analytical, and numerical investigations provide deep insight into amazing variety of spatio-temporal processes, which are responsible for such transitions. Usually, it is assumed that electron diffusion is ignorable effect in the operation of the Townsend discharge, and a possible instabilities are connected with space charge of the ionized species alone [10] . In this paper, we present the results of the investigations of the dc glow discharges in the framework