Chaotic behaviour of charged particles in electromagnetic fields

Ani, Chinenye Jane

Chaotic behaviour of charged particles in electromagnetic fields

Master Thesis

2018

Abstract

In order to understand the motion of charged particles we numerically investigate the chaoticity of magnetic field lines of tokamak fields, as charged particles move along field lines. In particular, the symmetric tokamap was studied to determine the physical quantities that influence the system’s chaotic behaviour. We implement several chaos detection techniques: the construction of Poincaré maps, the computation of the maximum Lyapunouv characteristic exponent (mLCE), as well as the Smaller Alignment Index (SALI). The analyses performed showed that the mLCE and SALI methods accurately quantified magnetic field lines’ chaotic behaviour and that the relative perturbation strength influences the system’s chaoticity. In addition, we illustrate the diffusive properties of magnetic field lines, using statistical measures like the mean square displacement (MSD) and calculating diffusion coefficients. Lastly, we present the construction of explicit near-symplectic mappings of the symmetric tokamap with Lie-generating functions.

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