Dynamical chaos in the problem of magnetic jet collimation

TL;DR

This paper studies the complex dynamics of magnetically collimated jets, identifying conditions for stable and chaotic behaviors through bifurcation analysis and Poincaré sections.

Contribution

It introduces a reduced differential equation model for jet collimation and analyzes the transition from periodic to chaotic solutions, revealing new insights into jet stability.

Findings

Existence of parameter ranges with stable periodic solutions

Identification of bifurcations leading to chaos

Demonstration of regular and chaotic motion domains

Abstract

We investigate dynamics of a jet collimated by magneto-torsional oscillations. The problem is reduced to an ordinary differential equation containing a singularity and depending on a parameter. We find a parameter range for which this system has stable periodic solutions and study bifurcations of these solutions. We use Poincar\'e sections to demonstrate existence of domains of regular and chaotic motions. We investigate transition from periodic to chaotic solutions through a sequence of period doublings.