The Influence of Non-Extensive Electrons on the Characteristics of the Space-Charge Sheath in Tonks-Langmuir Kinetic Model

Abstract

The purpose of this paper is to investigate the Tonks-Langmuir model by assuming that the electrons obey the q- non-extensive distribution. The plasma equation is analytically solved. It is revealed that the quasi-neutrality length of the glow discharge exceeds with the decrement of the non-extensive parameter q. In the extensive limiting case ($q\to 1$ i.e., Maxwellian case) the previously well-known results are recovered. Moreover, by evaluating the mean inverse kinetic energy of ions, it is illustrated that the kinetic Bohm criterion does not represent an inherent property of the collision- and ionization-free one-dimensional space-charge sheaths in the case of non-extensive electron distribution, contrary to the Maxwellian one. Finally, the plasma-sheath equation is numerically solved in the case of non-extensive electron distribution. It is found that the decrement of q gives rise to the increment of the wall potential value and sheath thickness for super-thermal electron distribution q < 1. On the other hand, it is observed that the wall potential value and the sheath thickness decrease as q increases for sub-thermal electron distribution q > 1. On this basis, it is concluded that the characteristics of the space-charge sheath in the low-pressure plane symmetric discharge depend on the electron non-extensive parameter q. This is in agreement with the prior practical measurements on the ion sheath formed around a non-extensive single electric probe in plasma.