Effect of q-Nonextensively Distributed Plasma Electrons on Double Sheath Characteristics and Virtual Cathode Formation Associated With Electron Emitting Surfaces

Abstract

A double sheath characteristics and virtual cathode formation in a plasma containing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$</tex-math> </inline-formula> -nonextensive distributed electrons, thermally emitted or secondary emitted electrons from the cathode wall, and ions are studied numerically. The distribution of primary (plasma) electrons is taken to be nonextensive, as per Tsallis statistics. The electric field at the cathode, the ratio of ion to electron current density and the velocity of ions are evaluated and the results are compared with the case of electrons having Boltzmann distribution. The variation of the electric potential, space charge density, and sheath thickness are analyzed for the cases of different nonextensivity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$</tex-math> </inline-formula> . The electric field at the cathode becomes zero at a lower value of electron beam current density, and hence the formation of the virtual cathode takes place earlier for the case of super-extensive distributed electrons as compared to that of the Boltzmann-distributed electrons. For super extensively distributed electrons, the electric potential drops slowly to a minimum, the velocity of positive ions increases inside the sheath, and an increase in the sheath thickness is observed.