On Mathematical Analysis of a Micro-Scale Boltzmann-Maxwell’s PDEs Model for a Plasma Flow Influence by Non-linear Sinusoidal External Electric Field: Novel Irreversibility Analysis of Plasma Kinetic Theory

Abstract

Unfortunately, the scientific research concerned with the micro-scale mathematical models in plasma has very few numbers compared with the other mathematical models. However, the microscopic fields are related to all modern technology like nano and micro technology, quantum computers, and many other essential applications. This study focuses on the mathematical analysis of a micro-scale Boltzmann-Maxwell partial differential equations (PDE) system for a gaseous plasma flow influenced by a non-linear, non-uniform external electric field, specifically in the context of a novel irreversibility micro-scale analysis of the kinetic theory of plasma. We did that using the analytical solution of the PDE system. The governing equations were developed using the moment and traveling-wave techniques in a new irreversible non-equilibrium thermodynamics (INT) methodology. To our knowledge, this was applied for the first time. We are investigating the distinct behavior of the electron velocity distribution functions (VDF) and the non-equilibrium velocity functions, representing an essential INT novel study. As a result, critical micro-scale INT variables would employ the generated non-equilibrium VDF to get the equilibrium time for each species. We aim to show how the impacts of various thermodynamic forces on internal energy change (IEC) are maintained. The research generates visual representations of physical variables in 3D. Extensive physics, electric manufacturing, and nano-electro-mechanical systems applications in various manufacturing contexts attest to the research’s standing. We aim to calculate the percentages between the numerous contributions of IEC in diamagnetic and paramagnetic plasma based on the total derivatives of the extensive parameters. We apply the results to a typical model of laboratory helium plasma because of the helium’s various excellent applications.