Abstract
Significant efforts are being put into trying to build systematic theory of plasma turbulence.Compared to fluids, the presence of the electromagnetic fields adds an extra layer of complexity to the problem of describing the plasma. Often, one has to describe the physical processes via looking at the dynamics at the phase space, i.e. taking into account not only spatial perturbations of plasma, but also the dynamics happening in velocity space.
Turbulence, in its classical description, creates a fine scale structure in position space, moving perturbations of different physical quantities to smaller and smaller scales, until they are dissipated into heat by some collision mechanism. In the velocity space, the fundamental process which creates a finescale structure is also presented, and is called phase mixing. The balance between the spatial turbulence and velocity space phase mixing represent a fundamental interest, and can help to understand the mechanism of particle heating in a weakly collisional plasma. The simplest textbook example of such mechanism is the linear Landau damping. In a strongly magnetised plasma, the phase mixing can be separated into linear and nonlinear phenomenon. The primary goal of this thesis is to study how linear phase mixing affects turbulence, and vice versa.
For a magnetised plasma, the formalism mapping the sixdimensional particle position space to fivedimensional driftcenter position exists, called gyrokinetic theory. This perturbative theory reduces the description of the phase space dynamics from (x, y, z, vx, vy, vz) dimensions to (X, Y,Z, v⊥, v∥), integrating out the fast gyration particle motions. Using the numerical simulation of gyrokinetic turbulence, obtained with the code GENE, the nonlinear energy transfer across the scales, as well as a distribution of the transport in the position space was studied. The performed analysis shown that the velocity space energy transfer should be taken into account when analysing the energy flux. In particular, the linear phase mixing influence should be investigated further.
To examine the impact of the linear phase mixing on the turbulence in the magnetised plasma turbulence, the driftkinetic formalism, a largescale limit of gyrokinetic equations, was obtained. The resulting formalism allows further simplification of the gyrokinetic theory, reducing the phase space description from five dimensions to four dimensions, (X, Y,Z, v∥). It particularly puts emphasis on two physical effects in the kinetic plasma turbulence and the linear phase mixing.
The resulting new formalism was then modelled using two approaches. The first one, where the nonlinear interactions were modelled using the reduced wavespace shell decomposition, is among the earliest ones to be applied on the kinetic equations of plasma. Such choice of modelling of the nonlinear interactions helps to simplify the computation of the nonlinear term, in exchange of omitting some physical effects. The second one is a direct numerical simulation, in which the nonlinear term is computed with the pseudospectral approach. Using this code, the interplay between the linear phase mixing and turbulence was observed for two and threedimensional cases. Lastly, further possible considerations for the development of the work, which could elucidate the different physical phenomena occurring in the astrophysical plasma, are given.
Date of Award  2023 

Original language  English 
Awarding Institution 

Supervisor  Eunjin Kim (Supervisor) 