In the study of thermal equilibrium of the electrons, it is very necessary to use the fluid model method. In this work, effect of the gas density, the electrons initial energy and the electric field on the electron thermal equilibrium is studied. It is found that the steady state can be achieved by increasing the gas density or the inter-electrode distance. If the gas density or the inter-electrode distance are not sufficient, steady state can be achieved by increasing the electric field. The initial energy of the electrons has great effect on the steady state if the electric field is weak and the difference between the initial energy and the electrons mean energy is great, however this problem can be solved by extending the time. It is necessary to make a best combination between the gas density, inter-electrode distance and the electric field to make a modeling by the fluid model method in the best cases of the steady state. A simple formula is given here to find the minimum time required to use the fluid model for E/N ≥ 500 Td.

It has come to the attention of IOP Publishing that this paper contains an error in the formulation of the model addressing the definition of scattering angle θ (page 2, section 2.2.). The equation has been applied in subsequent calculations throughout the paper and so the publisher has chosen to retract the manuscript. We apologize to the author and journal readership for our not detecting the error at the review stage.

It has come to the attention of IOP Publishing that this paper contains an error in the formulation of the model addressing the definition of scattering angle θ (page 2, section 2.2.). The equation has been applied in subsequent calculations throughout the paper and so the publisher has chosen to retract the manuscript. We apologize to the author and journal readership for our not detecting the error at the review stage.