Structure of collisional magnetized plasma sheath with non-extensive distribution of electrons

Abstract

Many previous researches on the plasma sheath were based on the fact that the electrons satisfy the classical Maxwell velocity distribution function, while the particles in the plasma have long-range electromagnetic interactions. It is more appropriate to use the non-extensive distribution proposed by Tsallis to describe the electrons. In this paper, a collisional magnetized plasma sheath model with non-extensive distribution of electrons is established. Bohm criterion is derived theoretically. With the ion drift motion in the plasma pre-sheath region taken into consideration, the ion Mach number is only related to the angle of the magnetic field, the collision parameters, the electric field at the sheath edge, and non-extensive parameter <inline-formula><tex-math id="M199">\begin{document}$ q $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M199.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M199.png"/></alternatives></inline-formula>. The influence of parameter <inline-formula><tex-math id="M200">\begin{document}$ q $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M200.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M200.png"/></alternatives></inline-formula> on the criterion is discussed in this paper. The lower limit of the ion Mach number changes with the value of parameter <inline-formula><tex-math id="M201">\begin{document}$ q $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M201.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M201.png"/></alternatives></inline-formula>. The lower limit of the ion Mach number increases for <inline-formula><tex-math id="M202">\begin{document}$ q < 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M202.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M202.png"/></alternatives></inline-formula>. And the lower limit of the ion Mach number decreases for <inline-formula><tex-math id="M203">\begin{document}$ q>1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M203.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M203.png"/></alternatives></inline-formula>. With the increase of <inline-formula><tex-math id="M204">\begin{document}$ q $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M204.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M204.png"/></alternatives></inline-formula>, the number of electrons with lower speed increases, ions need less kinetic energy to enter into the sheath and thus enter into the sheath more easily. Through numerical simulation, it is found that compared with the structure of the plasma magnetized sheath with Maxwell distribution (<inline-formula><tex-math id="M205">\begin{document}$ q=1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M205.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M205.png"/></alternatives></inline-formula>), the structure of the plasma magnetized sheath with super-extensive distribution (<inline-formula><tex-math id="M206">\begin{document}$ q < 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M206.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M206.png"/></alternatives></inline-formula>) and that with sub-extensive (<inline-formula><tex-math id="M207">\begin{document}$ q>1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M207.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M207.png"/></alternatives></inline-formula>) are different, including the distribution of the space potential, the ion density, the electron density, and the space charge density. When <inline-formula><tex-math id="M208">\begin{document}$ q < 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M208.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M208.png"/></alternatives></inline-formula>, the space potential, the electron density and the ion density fall more slowly, and the peak of the space charge density curve is closer to the wall. When <inline-formula><tex-math id="M209">\begin{document}$ q>1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M209.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M209.png"/></alternatives></inline-formula>, the space potential and the ion electron density fall faster, especially the electron density drops to zero faster, and the peak of the space charge density curve is far away from the wall. The simulation results show that the non-extensive parameter <inline-formula><tex-math id="M210">\begin{document}$ q $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M210.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20200794_M210.png"/></alternatives></inline-formula> has a significant influence on the structure of collisional plasma magnetized sheath. The influence of the collision on the magnetized plasma sheath with non-extensive distribution is similar to that with the Maxwell distribution. These conclusions may be useful in solving the problems of plasma boundary.