## Doctoral Thesis

Achieving commercial production of electricity by magnetic confinement fusion requires improvements in energy and particle confinement. In order to better understand and optimise confinement, numerical simulations of plasma phenomena are useful. One particularly challenging regime is that in which long wavelength MHD phenomena interact with kinetic phenomena. In such a regime, global electromagnetic gyrokinetic simulations are necessary. In this regime, computational requirements have been excessive for Eulerian methods, while Particle-in-Cell (PIC) methods have been particularly badly affected by the "cancellation problem", a numerical problem resulting from the structure of the electromagnetic gyrokinetic equations. A number of researchers have been working on mitigating this problem with some significant successes. Another alternative to mitigating the problem is to move to a hybrid system of fluid and gyrokinetic equations. At the expense of reducing the physical content of the numerical model, particularly electron kinetic physics, it is possible in this way to perform global electromagnetic PIC simulations retaining ion gyrokinetic effects but eliminating the cancellation problem. The focus of this work has been the implementation of two such hybrid models into the gyrokinetic code EUTERPE. The two models treat electrons and the entire bulk plasma respectively as a fluid. Both models are additionally capable of considering the self-consistent interaction of an energetic ion species, described gyrokinetically, with the perturbed fields. These two models have been successfully benchmarked in linear growth rate and frequency against other codes for a Toroidal AlfvÃ©n Eigenmode (TAE) case. The m=1 internal kink mode, which is particularly challenging in terms of the fully gyrokinetic cancellation problem, has also been successfully benchmarked using the hybrid models with the MHD eigenvalue code CKA. Non-linear simulations in this TAE case have been performed confirming the analytical prediction of a quadratic relationship between the linear growth rate of the TAE and the saturated amplitude of the TAE for a range of moderate values of the linear growth rate. At higher linear growth rate, a slower scaling of saturated amplitude with linear growth rate is observed. This analysis has been extended to include the non-linear wave-wave coupling between multiple TAE modes. It has been shown that wave-wave coupling results in a significant reduction in the saturated amplitude. It has been demonstrated that both plasma elongation and ion kinetic effects can exert a stabilising influence on the internal kink mode. A population of energetic particles can also exert a stabilising influence at low normalised pressure. At high normalised fast particle pressure the stabilised kink mode has been shown to give way to the m=1 EPM, which has been simulated both linearly and non-linearly (the "fishbone" mode). The first self-consistent simulations of global modes in the magnetic geometry of the optimised stellarator Wendelstein 7-X have been performed both linearly and non-linearly. Limitations have been encountered in performing simulations in 3D geometry. A hypothesis for the cause of these problems is outlined and ideas for mitigation are briefly described. In addition to the hybrid model simulations, some of the first utilisations of a new scheme for mitigating the cancellation problem in the fully gyrokinetic regime have been carried out in the framework of this thesis. This scheme, which was developed separately, is concisely described in this work. The new scheme has been benchmarked with existing gyrokinetic and hybrid results. The linear Wendelstein 7-X simulations and linear and single mode non-linear TAE simulations have been repeated with the new model. It is shown that bulk plasma kinetics can suppress the growth rate of global modes in Wendelstein 7-X. The results of fully gyrokinetic TAE simulations, the first to have been performed to our knowledge, are shown to be in close agreement with those results obtained using hybrid models. In the TAE case, the hybrid models are an order of magnitude less computationally demanding than the new gyrokinetic scheme, which is in turn at least an order of magnitude less computationally demanding than the previous gyrokinetic scheme.

The laser-matter interaction is a topic of current research. In this context, the interaction of intensive laser radiation with atomic clusters is of special interest. Du to the small cluster size, the laser field can penetrate the whole cluster volume, which leads to a high absorption of energy in the cluster. As a result, plasmas with high density and high temperature are produced. In the early phase of the laser-cluster interaction, free electrons are initially created in the cluster due to tunnel ionization or photoionization. Via collisions of these electrons with the cluster atoms, the ionization is increased and thus a dense nanoplasma is produced, which is heated by the laser. If free electrons leave the cluster during the laser-cluster interaction (outer ionization), a positive charge buildup is created. The associated charge repulsion finally can lead to the fragmentation of the cluster due to Coulomb explosion. Experimentally, interesting phenomena emerging from laser-excited clusters are observed, e.g., the creation of fast electrons, the production of highly charged ions, and X-ray emission. In this dissertation, the interaction of Gaussian laser pulses in the infrared regime with argon and xenon clusters is simulated by means of a nanoplasma model. Considering laser intensities in the non-relativistic regime, the relevant processes such as ionization, heating and expansion are theoretically described in this model with a set of coupled rate equations and hydrodynamic equations. One focus of the thesis is on the heating of the nanoplasma via inverse bremsstrahlung (IB), which is due to the absorption of laser photons in electron-ion collisions. In particular, the important question is investigated whether the consideration of the ionic structure â€“ that means, the nuclear charge and the bound electrons â€“ modifies the electron-ion collisions and thus the IB heating rate. Starting from a quantum statistical description, effective electron-ion potentials are used which account for both the screening due to the dense plasma and the inner ionic structure. Within the quantum mechanical first Born approximation, the consideration of the ionic structure leads to a drastic increase of the IB heating rate, in particular for high nuclear charges and low ionic charge states. However, for the parameters relevant in experiments, the applicability of the first Born approximation is questionable. Therefore, quantum mechanical calculations going beyond the first-order perturbation theory are performed. In addition, the IB heating rate is investigated with different classical methods. These are based either on transport cross sections for elastic electron-ion scattering or on classical simulations of inelastic scattering processes. Also within the classical approaches, the consideration of the ionic structure leads to an increase of the heating rate. However, this increase is shown to be only moderate. In a further part, the thesis focuses on the question how the dynamics of the laser-cluster interaction is influenced by the consideration of excited states. This is explored exemplarily for argon clusters excited by single or double laser pulses. The consideration of excitation processes in the nanoplasma leads to a decrease of the electron temperature and to an increase of the density of free electrons. Moreover, it is shown that the consideration of excitation processes results in an essential acceleration of the ionization dynamics. As a consequence, the mean ionic charge state in the plasma as well as the number of highly charged ions is significantly increased. For the population of ground states and excited states within an ionic charge state Z, collisional deexcitation processes play an important role. By means of an analytical relation between excitation and deexcitation cross sections, the rates for the respective processes in the presence of the laser field are calculated. The role of deexcitation processes is studied in detail, showing that the inclusion of these processes is essential for the correct theoretical description of the photon emission from laser-excited clusters. Based on these results, the photon yield is calculated for selected radiative transitions resulting from highly charged argon ions in the UV and X-ray regime.