Basic microscopic plasma physics unified and simplified by N-body classical mechanics

TL;DR

This paper offers a unified, microscopic classical mechanics approach to fundamental plasma phenomena like shielding, damping, and transport, deriving key equations directly from Newton's laws without fluid or kinetic models.

Contribution

It introduces a rigorous, N-body classical mechanics framework that unifies and simplifies plasma physics phenomena traditionally treated separately, including shielding, damping, and collisional transport.

Findings

Derived a rigorous equation for electrostatic potential from N-body mechanics

Unified description of shielding, damping, and spontaneous emission phenomena

Computed the collisional diffusion coefficient with a convergent, impact parameter-inclusive expression

Abstract

Debye shielding, collisional transport, Landau damping of Langmuir waves, and spontaneous emission of these waves are introduced, in typical plasma physics textbooks, in different chapters. This paper provides a compact unified introduction to these phenomena without appealing to fluid or kinetic models, but by using Newton's second law for a system of $N$ electrons in a periodic box with a neutralizing ionic background. A rigorous equation is derived for the electrostatic potential. Its linearization and a first smoothing reveal this potential to be the sum of the shielded Coulomb potentials of the individual particles. Smoothing this sum yields the classical Vlasovian expression including initial conditions in Landau contour calculations of Langmuir wave growth or damping. The theory is extended to accommodate a correct description of trapping or chaos due to Langmuir waves. In the linear regime, the amplitude of such a wave is found to be ruled by Landau growth or damping and by spontaneous emission. Using the shielded potential, the collisional diffusion coefficient is computed for the first time by a convergent expression including the correct calculation of deflections for all impact parameters. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons.