Self-organized circular flow of classical point particles

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.