# Radiating Electron Interaction with Multiple Colliding Electromagnetic Waves: Random Walk Trajectories, Levy Flights, Limit Circles, and Attractors (Survey of the Structurally Determinate Patterns)

## TL;DR

This paper surveys the complex dynamics of electrons interacting with multiple colliding laser pulses, highlighting phenomena like Levy flights, attractors, and stable patterns caused by high-intensity electromagnetic fields and radiation friction effects.

## Contribution

It introduces a comprehensive overview of the structured patterns and dynamic behaviors of electrons in high-intensity laser fields, emphasizing the role of nonlinear dissipation and radiation effects.

## Key findings

- Electrons exhibit random walk trajectories and Levy flights in colliding laser fields.
- High intensity fields lead to stable, narrow-region particle trajectories and regular pattern formations.
- Nonlinear dissipation stabilizes particle motion, resulting in attractors and limit cycles.

## Abstract

The multiple colliding laser pulse concept formulated in Ref. [1] is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields oscillating in time of multiple colliding laser pulses is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Levy flights. Under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motion resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.