Controlling chaos in wave-particle interactions

TL;DR

This paper demonstrates how adding a small control term to a relativistic particle system under magnetic and electrostatic influences can significantly reduce chaos, leading to more regular trajectories and improved particle acceleration.

Contribution

It introduces a novel control method for near-integrable Hamiltonian systems that creates invariant tori to suppress chaos in wave-particle interactions.

Findings

Control term effectively reduces chaos with minimal energy cost.

Invariant tori prevent chaos from spreading in phase space.

Enhanced regularity improves particle acceleration efficiency.

Abstract

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists in the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions and make the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.