Self-organized circular flow of classical point particles

TL;DR

This paper models the collective motion of charged particles on a circle with local interactions and external forces, providing insights into the behavior of direct electric current through a mathematical framework.

Contribution

It introduces a new homogeneous solution model for particles with Coulomb interactions and external forces, capturing features of direct electric current.

Findings

Homogeneous solutions with approximately equal velocities and uniform density are constructed.

The model aligns with Feynman's suggestion regarding features of direct electric current.

Provides a qualitative mathematical framework for understanding classical particle flow on a circle.

Abstract

We consider newtonian dynamics of $N$ charged particles on the circle with nearest neigbour interaction with Coulomb repulsive potential $r^{-1}$ . Also there is an external accelerating force which is nonzero only on a small part of the circle. We construct homogeneous solutions where the velocities of all particles are approximately equal and their density is approximately uniform. This gives a qualitative mathematical model for some features of the direct electric current (DC), in agreement with a suggestion by R. Feynman.