Direct path from microscopic mechanics to Debye shielding, Landau damping, and wave-particle interaction

TL;DR

This paper derives fundamental plasma phenomena like Debye shielding and Landau damping directly from Newtonian mechanics without probabilistic assumptions, providing a clear, elementary approach that links microscopic particle interactions to macroscopic plasma behavior.

Contribution

It introduces a straightforward, Newtonian derivation of plasma effects, extending the theory to include trapping and chaos, and clarifies the relation between shielding and collisional transport.

Findings

Debye shielding and Landau damping are derived from N-body Newtonian mechanics.

The approach is valid in one dimension with large particle numbers in a Debye sphere.

Shielding and collisional transport are interconnected through electron deflections.

Abstract

The derivation of Debye shielding and Landau damping from the $N$-body description of plasmas is performed directly by using Newton's second law for the $N$-body system. This is done in a few steps with elementary calculations using standard tools of calculus, and no probabilistic setting. Unexpectedly, Debye shielding is encountered together with Landau damping. This approach is shown to be justified in the one-dimensional case when the number of particles in a Debye sphere becomes large. The theory is extended to accommodate a correct description of trapping and chaos due to Langmuir waves. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons, in such a way that each particle is shielded by all other ones while keeping in uninterrupted motion.