## Doctoral Thesis

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.

The confinement of energy has always been a challenge in magnetic confinement fusion devices. Due to their toroidal shape there exist regions of high and low magnetic field, so that the particles are divided into two classes - trapped ones that are periodically reflected in regions of high magnetic field with a characteristic frequency, and passing particles, whose parallel velocity is high enough that they largely follow a magnetic field line around the torus without being reflected. The radial drift that a particle experiences due to the field inhomogeneity depends strongly on its position, and the net drift therefore depends on the path taken by the particle. While the radial drift is close to zero for passing particles, trapped particles experience a finite radial net drift and are therefore lost in classical stellarators. These losses are described by the so-called neoclassical transport theory. Recent optimised stellarator geometries, however, in which the trapped particles precess around the torus poloidally and do not experience any net drift, promise to reduce the neoclassical transport down to the level of tokamaks. In these optimised stellarators, the neoclassical transport becomes small enough so that turbulent transport may limit the confinement instead. The turbulence is driven by small-scale-instabilities, which tap the free energy of density or temperature gradients in the plasma. Some of these instabilities are driven by the trapped particles and therefore depend strongly on the magnetic geometry, so the question arises how the optimisation affects the stability. In this thesis, collisionless electrostatic microinstabilities are studied both analytically and numerically. Magnetic configurations where the action integral of trapped-particle bounce motion, J, only depends on the radial position in the plasma and where its maximum is in the plasma centre, so-called maximum-J configurations, are of special interest. This condition can be achieved approximately in quasi-isodynamic stellarators, for example Wendelstein 7-X. In such configurations the precessional drift of the trapped particles is in the opposite direction from the direction of propagation of drift waves. Instabilities that are driven by the trapped particles usually rely on a resonance between these two frequencies. Here it is shown analytically by analysing the electrostatic energy transfer between the particles and the instability that, thanks to the absence of the resonance, a particle species draws energy from the mode if the frequency of the mode is well below the charateristic bounce frequency. Due to the low electron mass and the fast bounce motion, electrons are almost always found to be stabilising. Most of the trapped-particle instabilities are therefore predicted to be absent in maximum- J configurations in large parts of parameter space. Analytical theory thus predicts enhanced linear stability of trapped-particle modes in quasi-isodynamic stellarators compared with tokamaks. Moreover, since the electrons are expected to be stabilising, or at least less destabilising, for all instabilities whose frequency lies below the trapped-electron bounce frequency, other modes might benefit from the enhanced stability as well. In reality, however, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with another, non-quasiisodynamic stellarator, the National Compact Stellarator Experiment (NCSX) and a typical tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, several microinstabilities, driven by the density as well as both ion and electron temperature gradients, are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilising when the electrostatic energy transfer is analysed. In contrast, if only the ions are treated kinetically but the electrons are taken to be in thermodynamic equilibrium, no such stabilising effect is observed. These results suggest that imperfectly optimised stellarators can retain most of the stabilising properties predicted for perfect maximum-J configurations. Quasi-isodynamic stellarators, in addition to having reduced neoclassical transport, might therefore also show reduced turbulent transport, at least in certain regions of parameter space.