Resonant cyclotron acceleration of particles by a time periodic singular flux tube

TL;DR

This paper investigates how a time-periodic singular flux tube can resonantly accelerate charged particles in a magnetic field, leading to unbounded energy growth, supported by analytical asymptotic formulas.

Contribution

It introduces a novel mechanism of particle acceleration via resonant flux and cyclotron frequency interaction, with analytical support for the asymptotic behavior.

Findings

Particles can reach arbitrarily high energies due to resonance.

Analytical asymptotic formulas accurately describe the accelerated motion.

The effect occurs even with small flux fields not encircling the cyclotron orbit.

Abstract

We study the dynamics of a classical nonrelativistic charged particle moving on a punctured plane under the influence of a homogeneous magnetic field and driven by a periodically time-dependent singular flux tube through the hole. We observe an effect of resonance of the flux and cyclotron frequencies. The particle is accelerated to arbitrarily high energies even by a flux of small field strength which is not necessarily encircled by the cyclotron orbit; the cyclotron orbits blow up and the particle oscillates between the hole and infinity. We support this observation by an analytic study of an approximation for small amplitudes of the flux which is obtained with the aid of averaging methods. This way we derive asymptotic formulas that are afterwards shown to represent a good description of the accelerated motion even for fluxes which are not necessarily small. More precisely, we argue that the leading asymptotic terms may be regarded as approximate solutions of the original system in the asymptotic domain as the time tends to infinity.