Standard map in magnetized relativistic systems: fixed points and regular acceleration

TL;DR

This paper introduces a nonlinear standard map for relativistic particles interacting with electrostatic waves and magnetic fields, revealing unique properties and fixed point relations relevant for accelerator regimes.

Contribution

It develops a novel nonlinear standard map for relativistic systems, enabling exact analytical results and exploring fixed points and acceleration phenomena.

Findings

The map is nonlinear in wave amplitude.

Fixed points relate to accelerator regimes.

Analytical results are exactly obtained.

Abstract

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.