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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 – that means, the nuclear charge and the bound electrons – 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.
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 Alfvén 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.
Recent experimental campaigns in the Wendelstein 7-X stellarator, a
plasma-confining device designed to investigate the Magnetic Confinement Fusion
(MCF) approach to generating electrical power, have shown that the injection of
fuelling pellets had an unexpected and considerable impact on the performance of
the plasma. Rather than simply refuelling the device and `diluting' the plasma
energy, pellet injection is followed by a significant increase in the ratio of
the ion temperature to the electron temperature. It has been suggested that this
is not merely due to the improved confinement following the reduction of
turbulent transport after the pellet material has homogenised with the bulk
plasma, but also due to a direct transfer of energy from electrons to ions. The
proposed mechanism for this energy transfer is the ambipolar expansion of the
pellet plasmoid, the localised plasma structure produced by the
ionisation of ablated pellet material, along magnetic field lines.
Early work on pellet plasmoid expansion predicted that half the heating power
deposited in plasmoid electrons by collisions with hot ambient electrons is
transferred to plasmoid ions in the form of flow velocity as the plasmoid
expands. The complicated nature of the system of the pellet plasmoid embedded in
the ambient plasma, particularly the behaviour of electrons, which experience
many collisional and collisionless phenomena on multiple disparate timescales,
means that early models of the expansion were not wholly self-consistent, but
rather made use of strong approximations that apply in some regions of the
plasmoid but not in others. For example, only electrons and ions associated with
the plasmoid were rigorously treated, meaning that the framework was one of
`expansion into vacuum'. Combined with the assumption of Maxwellian electrons,
this led to an electric potential that was unbounded at infinity. Naturally, the
validity of the conclusions of such a model are called into question because the
approximations lose their validity far from the plasmoid and as time advances,
yet predictions about the final state of the plasma are desired. A deeper
investigation is required: careful consideration of the phenomena in question
and the timescales (and lengthscales) on which they act must be made in order to
rigorously construct a model that is valid throughout the entire expansion.
The first two papers presented in this thesis iterate on the model established
in the paper that first predicted the electron-to-ion energy transfer; their aim
was to find out how the character of the expansion changes with a more
sophisticated and accurate description of various phenomena, while remaining
within the existing framework of expansion into vacuum. Ultimately, we find that
the qualitative character is unchanged, and that approximately half the heating
power deposited in plasmoid electrons is transferred to ions.
Two other papers in this thesis address the limitations of the original model.
This is achieved by properly considering the electron kinetic problem in a
plasmoid. One paper considers the electron kinetic problem when electrons are
highly isotropised. In this case the kinetic equation can be integrated to
remove all but two independent variables, which is the maximum possible
reduction considering it is a time-dependent problem. The full nonlinear
integro-differential Landau self-collision operator is integrated exactly and
few approximations are made, leading to a rather general kinetic equation.
However, for fuelling pellets some anisotropy in the electron distribution is
expected. Another paper considers the electron kinetic problem (and the entire
plasmoid expansion) allowing for electron anisotropy. Careful consideration of
the ordering of timescales of electron phenomena in a pellet plasmoid leads to a
steady-state kinetic problem that we call collisional quasi-equilibrium (QE). QE
appears in many ways similar to the collisional steady-state characterising a
true thermal equilibrium. It was found that the time-dependent kinetic problem
of the earlier paper, with isotropic electrons, produces the QE distribution
function, corroborating the existence of the QE state. We then take moments of
the electron kinetic equation that is valid on the expansion timescale, assuming
that the electron distribution is that given as the solution to the QE kinetic
problem. This is completely analogous to what is done to obtain the Braginskii
equations or any Chapman-Enskog theory. The result is a set of equations for the
long-term evolution of the macroscopic quantities that describe the distribution
function existing in a quasi-steady-state at each point in time. It is from this
point that one may feasibly describe the plasmoid expansion with an accurate
picture of the electron kinetics and finally obtain the electron-to-ion energy
transfer so desired in a rigorous model of the expansion.
From a broader point of view, the two frameworks provided by these rigorous
investigations of the electron kinetic problem serve as a basis for the future
study of plasmoids. Such a `first-principles' approach to plasmoid dynamics is
novel and interesting in its own right, but it will be demonstrated that such an
approach is essential for pellet plasmoids owing to the fact that they are
poorly described by the `standard tools' of plasma physics.
Using the QE framework it was found that, once more, about half the heating
power experienced by plasmoid electrons is transferred to plasmoid ions. The
incredible robustness of the prediction of such an energy transfer is, in the
author's opinion, the result of the self-similar nature of the expansion found
as a solution to the original model. As a rule, the profiles of self-similar
solutions tend to be attractors for the `real', more complicated, system, and
the qualitative predictions involving no parameters, of which the
electron-to-ion energy transfer is one, tend to be very sturdy.
Aside from fuelling pellets, composed of hydrogen or deuterium, one paper in
this thesis investigates the physics of high-Z pellets that are designed to
terminate the plasma safely in the event of a `disruption', where much of the
magnetic field energy is channelled into a runaway electron beam with
potentially disastrous consequences if the beam encounters a plasma-facing
component. The paper draws on the work carried out in the paper concerning the
kinetic problem of isotropised electrons in a plasmoid.
This thesis is `cumulative'; the vast majority of the work carried out is
described within a set of Papers, labelled A-E, placed at the back of the text.
There is a preceding `wrapper text' (given in numbered Sections) tasked with
introducing the reader to the topic, guiding the reader through the papers, and
expounding some of their main results. Some amount of material not present in
the papers is also provided in the wrapper text. Naturally, the wrapper text
mainly focusses on the results of the papers which are under my first
authorship. In the course of publishing papers over an extended period of time
the nomenclature is bound to vary. Although it is mostly consistent between the
papers, a few difference do arise, and the section `Common symbols and
subscripts' is provided in the frontmatter to alleviate confusion. Particular
care should be taken with the symbols x and z; both can refer to the
coordinate parallel to the magnetic field line, but in papers where z is used
for this purpose x tends to have another definition. In the wrapper text the
choice of symbols is generally chosen to reflect those in the corresponding
paper.