Investigation of guiding center dynamics in turbulent plasmas

Transport of particles inside thermonuclear magnetic fusion devices is of great interest. The greatest limit on confinement time is indeed associated with the transport of particles across the plane perpendicular to magnetic field lines, the experimental data reveal much larger values of diffusion coefficients with respect to the expected ones. A phenomenon considered one of the main ones responsible for this behaviour is turbulence-induced transport. In this manuscript, a guiding centre model is exploited to study the motion of particles inside a turbulent electrostatic field in simplified slab geometry. It is showed how to obtain the gyrokinetic Hamiltonian expression at the second order in the small parameter (related to the amplitude of the fluctuations in the electrostatic potential) and the related governing equations for guiding centres in the transverse plane. It is then outlined how to obtain the same kind of governing equations for a full kinetic approach. The numerical Python code is presented in its main parts. A time-step analysis is then presented for both the guiding centre and full orbits approach. The main analysis of results is focused on the investigation of the influence of physical parameters ρ and η, respectively Larmor radius and real parameter, on the dynamics of the system, together with the investigation of an unveiled anomalous ballistic behaviour for certain regimes of motion. The computation of rotational number with weighted Birkhoff average leading to interesting results is included in this last analysis. A possible explanation for this super-diffusive regime through the existence of meandering invariant tori is then provided. The last part of numerical analysis is focused on the comparison of results from the guiding centre model with the full kinetic one, the presence of the anomalous super-diffusive behaviour in a non-approximated and more reliable model would mean that the phenomenon may be really present in turbulent plasmas.