Analytical solution of Boltzmann-Maxwell PDE for plasma Couette flow among two coaxial rotating cylinders: Novel velocity dependent enhanced collision frequency

Abstract

Unfortunately, research on micro-scale computational models in plasma is relatively scarce and related to other mathematical representations. All modern technologies, including quantum computers, nanotechnology, microtechnology, and other essential minuscule-scale applications, are linked to the microscopic domains. The main goal of this study is to use math to look at a small-scale framework of Boltzmann-Maxwell partial differential equations (PDE) that describe plasma flow with a new collision frequency that depends on velocity. This study mostly looks at the Couette flow of Argon plasma that is bound between two rigid circular cylinders that rotate in the same direction. We can resolve the Boltzmann-Maxwell PDE structure by using small parameters along with Lee’s moments’ technique and a two-stream electron velocity distribution function (VDF). An analytical solution is obtained for nonlinear, non-homogeneous PDE in cylindrical coordinates. We are considering laboratory argon plasma as a significant commercial-industrial application. This study examines the impact of electrons’ velocity-dependent growth collision frequency (VDCF) for the first time, a factor overlooked in comparable research for simplification. With the new techniques, research projects will be more successful, especially those that use micro- and nano-electromechanical systems. The relationships among the different plasma variables are examined.

The irreversible thermodynamic properties of the complete system are delineated. The structure seeks to achieve equilibrium within a timescale that aligns with Le Chatelier’s premise. We accomplished that; we precisely determined the system’s equilibrium time, designated as ($t_{equ}\cong 2.01$). We conclude that our pattern is consistent with Boltzmann’s H-theorem, the second rule of NIT, Le Chatelier’s rule, and the Onsager-Casimir reciprocity relation (OCRR). We presented the various contributions to the Internal Energy Change (IEC). We think the change in the system’s IEC related to entropy variability is the most important thing compared to looking at electric and magnetic fields since both electromagnetic fields are self-consistent. We thoroughly compare our new pattern and our previous velocity-independent collision frequency approach. The importance of this search arises from its extensive applications across multiple domains, including plasma physics, electrical engineering, medicine, and biological systems.