Alternate islands of multiple isochronous chains in wave-particle interactions

TL;DR

This paper investigates how standing electrostatic waves influence the formation of multiple isochronous island chains in phase space during relativistic particle dynamics, providing analytical tools for optimizing particle acceleration.

Contribution

It introduces an analytical framework to determine the number and position of island chains caused by pulsed waves in wave-particle interactions.

Findings

Number of island chains varies with wave parameters.

Analytical expressions for positions of periodic points.

Wave amplitude influences the number of resonant island chains.

Abstract

We analyze the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a standing electrostatic wave. We show that a pulsed wave produces an infinite number of perturbative terms with the same winding number, which may generate islands in the same region of phase space. As a consequence, the number of isochronous island chains varies as a function of the wave parameters. We observe that in all the resonances, the number of chains is related to the amplitude of the various resonant terms. We determine analytically the position of the periodic points and the number of island chains as a function of the wave number and wave period. Such information is very important when one is concerned with regular particle acceleration, since it is necessary to adjust the initial conditions of the particle to obtain the maximum acceleration.