Speedy motions of a body immersed in an infinitely extended medium

TL;DR

This paper analyzes the motion of a body in a Vlasov fluid under a constant force, proving that with sufficiently high initial velocity, the body escapes to infinity with unbounded speed and approaches uniform acceleration.

Contribution

It demonstrates the runaway effect and asymptotic acceleration for a body in a Vlasov medium, including heuristic insights for singular potentials diverging at short distances.

Findings

High initial velocity leads to unbounded acceleration.

The body asymptotically reaches a uniformly accelerated motion.

Runaway effect persists for certain singular potentials.

Abstract

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Psi. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound "runaway effect". Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Psi(r) diverges at short distances like g r^{-a}, g,a>0, by showing that the runaway effect still occurs if a<2.