Comparative Analysis of Plasma Sheath Characteristics in One-Dimensional and Three-Dimensional Velocity Spaces Governing Nonextensive Electron Density

Abstract

In this study, we developed a model to explore the characteristics of a magnetized plasma sheath, containing positive ions, electrons, and neutral particles. The ions are described using a fluid model based on the continuity and momentum equations, while the electron distribution is analyzed using three cases: the Maxwell–Boltzmann distribution and the Tsallis distribution in both 1-D and 3-D velocity spaces. Applying the Sagdeev method, we established the modified Bohm sheath criterion to obtain the required ion velocity at the sheath entrance for all three cases. The lower Mach number limit for Bohm velocity modification depends on factors such as ion temperature, ionization frequency, collision frequency, magnetic field angle, nonextensive parameter $q$, and the velocity space governing the density of nonextensive electrons, independent of magnetic field magnitude. Additionally, the electron velocity distribution was analyzed for various q-values, revealing that in 3-D velocity space, the energy range is broad and extensive, while in 1-D velocity spaces, it is narrower and confined within the broader 3-D interval. We examined the influence of key parameters on sheath characteristics under the Maxwellian distribution, as well as in 1-D and 3-D velocity spaces for the Tsallis distribution. The results demonstrated significant differences between the three cases, showing that in the 3-D case, the sheath thickness expands more compared to the 1-D and the Maxwell–Boltzmann distribution. This underscores the significance of accounting for the dimensionality of velocity space when investigating plasma sheath phenomena. Such understanding is crucial for optimizing plasma-surface interactions in various applications.