Interatomic potentials for fusion reactor material simulations

Fusion energy is a clean and safe solution for the intricate question of how to produce non-polluting and sustainable energy for the constantly growing population. The fusion process does not result in any harmful waste or green-house gases, since small amounts of helium is the only bi-product that is produced when using the hydrogen isotopes deuterium and tritium as fuel. Moreover, deuterium is abundant in seawater and tritium can be bred from lithium, a common metal in the Earth's crust, rendering the fuel reservoirs practically bottomless. Due to its enormous mass, the Sun has been able to utilize fusion as its main energy source ever since it was born. But here on Earth, we must find other means to achieve the same. Inertial fusion involving powerful lasers and thermonuclear fusion employing extreme temperatures are examples of successful methods. However, these have yet to produce more energy than they consume. In thermonuclear fusion, the fuel is held inside a tokamak, which is a doughnut-shaped chamber with strong magnets wrapped around it. Once the fuel is heated up, it is controlled with the help of these magnets, since the required temperatures (over 100 million degrees C) will separate the electrons from the nuclei, forming a plasma. Once the fusion reactions occur, excess binding energy is released as energetic neutrons, which are absorbed in water in order to produce steam that runs turbines. Keeping the power losses from the plasma low, thus allowing for a high number of reactions, is a challenge. Another challenge is related to the reactor materials, since the confinement of the plasma particles is not perfect, resulting in particle bombardment of the reactor walls and structures. Material erosion and activation as well as plasma contamination are expected. Adding to this, the high energy neutrons will cause radiation damage in the materials, causing, for instance, swelling and embrittlement. In this thesis, the behaviour of a material situated in a fusion reactor was studied using molecular dynamics simulations. Simulations of processes in the next generation fusion reactor ITER include the reactor materials beryllium, carbon and tungsten as well as the plasma hydrogen isotopes. This means that interaction models, {\it i.e. interatomic potentials}, for this complicated quaternary system are needed. The task of finding such potentials is nonetheless nearly at its end, since models for the beryllium-carbon-hydrogen interactions were constructed in this thesis and as a continuation of that work, a beryllium-tungsten model is under development. These potentials are combinable with the earlier tungsten-carbon-hydrogen ones. The potentials were used to explain the chemical sputtering of beryllium due to deuterium plasma exposure. During experiments, a large fraction of the sputtered beryllium atoms were observed to be released as BeD molecules, and the simulations identified the swift chemical sputtering mechanism, previously not believed to be important in metals, as the underlying mechanism. Radiation damage in the reactor structural materials vanadium, iron and iron chromium, as well as in the wall material tungsten and the mixed alloy tungsten carbide, was also studied in this thesis. Interatomic potentials for vanadium, tungsten and iron were modified to be better suited for simulating collision cascades that are formed during particle irradiation, and the potential features affecting the resulting primary damage were identified. Including the often neglected electronic effects in the simulations was also shown to have an impact on the damage. With proper tuning of the electron-phonon interaction strength, experimentally measured quantities related to ion-beam mixing in iron could be reproduced. The damage in tungsten carbide alloys showed elemental asymmetry, as the major part of the damage consisted of carbon defects. On the other hand, modelling the damage in the iron chromium alloy, essentially representing steel, showed that small additions of chromium do not noticeably affect the primary damage in iron. Since a complete assessment of the response of a material in a future full-scale fusion reactor is not achievable using only experimental techniques, molecular dynamics simulations are of vital help. This thesis has not only provided insight into complicated reactor processes and improved current methods, but also offered tools for further simulations. It is therefore an important step towards making fusion energy more than a future goal.

Shock acceleration in the solar corona

In this thesis acceleration of energetic particles at collisionless shock waves in space plasmas is studied using numerical simulations, with an emphasis on physical conditions applicable to the solar corona. The thesis consists of four research articles and an introductory part that summarises the main findings reached in the articles and discusses them with respect to theory of diffusive shock acceleration and observations. This thesis gives a brief review of observational properties of solar energetic particles and discusses a few open questions that are currently under active research. For example, in a few large gradual solar energetic particle events the heavy ion abundance ratios and average charge states show characteristics at high energies that are typically associated with flare-accelerated particles, i.e. impulsive events. The role of flare-accelerated particles in these and other gradual events has been discussed a lot in the scientific community, and it has been questioned if and how the observed features can be explained in terms of diffusive shock acceleration at shock waves driven by coronal mass ejections. The most extreme solar energetic particle events are the so-called ground level enhancements where particle receive so high energies that they can penetrate all the way through Earth's atmosphere and increase radiation levels at the surface. It is not known what conditions are required for acceleration into GeV/nuc energies, and the presence of both very fast coronal mass ejections and X-class solar flares makes it difficult to determine what is the role of these two accelerators in ground level enhancements. The theory of diffusive shock acceleration is reviewed and its predictions discussed with respect to the observed particle characteristics. We discuss how shock waves can be modeled and describe in detail the numerical model developed by the author. The main part of this thesis consists of the four scientific articles that are based on results of the numerical shock acceleration model developed by the author. The novel feature of this model is that it can handle complex magnetic geometries which are found, for example, near active regions in the solar corona. We show that, according to our simulations, diffusive shock acceleration can explain the observed variations in abundance ratios and average charge states, provided that suitable seed particles and magnetic geometry are available for the acceleration process in the solar corona. We also derive an injection threshold for diffusive shock acceleration that agrees with our simulation results very well, and which is valid under weakly turbulent conditions. Finally, we show that diffusive shock acceleration can produce GeV/nuc energies under suitable coronal conditions, which include the presence of energetic seed particles, a favourable magnetic geometry, and an enhanced level of ambient turbulence.

Multiscale study on hydrogen mobility in metallic fusion divertor material

For achieving efficient fusion energy production, the plasma-facing wall materials of the fusion reactor should ensure long time operation. In the next step fusion device, ITER, the first wall region facing the highest heat and particle load, i.e. the divertor area, will mainly consist of tiles based on tungsten. During the reactor operation, the tungsten material is slowly but inevitably saturated with tritium. Tritium is the relatively short-lived hydrogen isotope used in the fusion reaction. The amount of tritium retained in the wall materials should be minimized and its recycling back to the plasma must be unrestrained, otherwise it cannot be used for fueling the plasma. A very expensive and thus economically not viable solution is to replace the first walls quite often. A better solution is to heat the walls to temperatures where tritium is released. Unfortunately, the exact mechanisms of hydrogen release in tungsten are not known. In this thesis both experimental and computational methods have been used for studying the release and retention of hydrogen in tungsten. The experimental work consists of hydrogen implantations into pure polycrystalline tungsten, the determination of the hydrogen concentrations using ion beam analyses (IBA) and monitoring the out-diffused hydrogen gas with thermodesorption spectrometry (TDS) as the tungsten samples are heated at elevated temperatures. Combining IBA methods with TDS, the retained amount of hydrogen is obtained as well as the temperatures needed for the hydrogen release. With computational methods the hydrogen-defect interactions and implantation-induced irradiation damage can be examined at the atomic level. The method of multiscale modelling combines the results obtained from computational methodologies applicable at different length and time scales. Electron density functional theory calculations were used for determining the energetics of the elementary processes of hydrogen in tungsten, such as diffusivity and trapping to vacancies and surfaces. Results from the energetics of pure tungsten defects were used in the development of an classical bond-order potential for describing the tungsten defects to be used in molecular dynamics simulations. The developed potential was utilized in determination of the defect clustering and annihilation properties. These results were further employed in binary collision and rate theory calculations to determine the evolution of large defect clusters that trap hydrogen in the course of implantation. The computational results for the defect and trapped hydrogen concentrations were successfully compared with the experimental results. With the aforedescribed multiscale analysis the experimental results within this thesis and found in the literature were explained both quantitatively and qualitatively.

Hybrid Modelling of Titan's Interaction with the Magnetosphere of Saturn

In this dissertation we study the interaction between Saturn's moon Titan and the magnetospheric plasma and magnetic field. The method of research is a three-dimensional computer simulation model, that is used to simulate this interaction. The simulation model used is a hybrid model. Hybrid models enable individual tracking or tracing of ions and also take into account the particle motion in the propagation of the electromagnetic fields. The hybrid model has been developed at the Finnish Meteorological Institute. This thesis gives a general description of the effects that the solar wind has on Earth and other planets of our solar system. Planetary satellites can also have similar interactions with the solar wind but also with the plasma flows of planetary magnetospheres. Titan is clearly the largest among the satellites of Saturn and also the only known satellite with a dense atmosphere. It is the atmosphere that makes Titan's plasma interaction with the magnetosphere of Saturn so unique. Nevertheless, comparisons with the plasma interactions of other solar system bodies are valuable. Detecting charged plasma particles requires in situ measurements obtainable through scientific spacecraft. The Cassini mission has been one of the most remarkable international efforts in space science. Since 2004 the measurements and images obtained from instruments onboard the Cassini spacecraft have increased the scientific knowledge of Saturn as well as its satellites and magnetosphere in a way no one was probably able to predict. The current level of science on Titan is practically unthinkable without the Cassini mission. Many of the observations by Cassini instrument teams have influenced this research both the direct measurements of Titan as well as observations of its plasma environment. The theoretical principles of the hybrid modelling approach are presented in connection to the broader context of plasma simulations. The developed hybrid model is described in detail: e.g. the way the equations of the hybrid model are solved is shown explicitly. Several simulation techniques, such as the grid structure and various boundary conditions, are discussed in detail as well. The testing and monitoring of simulation runs is presented as an essential routine when running sophisticated and complex models. Several significant improvements of the model, that are in preparation, are also discussed. A main part of this dissertation are four scientific articles based on the results of the Titan model. The Titan model developed during the course of the Ph.D. research has been shown to be an important tool to understand Titan's plasma interaction. One reason for this is that the structures of the magnetic field around Titan are very much three-dimensional. The simulation results give a general picture of the magnetic fields in the vicinity of Titan. The magnetic fine structure of Titan's wake as seen in the simulations seems connected to Alfvén waves an important wave mode in space plasmas. The particle escape from Titan is also a major part of these studies. Our simulations show a bending or turning of Titan's ionotail that we have shown to be a direct result of the basic principles in plasma physics. Furthermore, the ion flux from the magnetosphere of Saturn into Titan's upper atmosphere has been studied. The modelled ion flux has asymmetries that would likely have a large impact in the heating in different parts of Titan's upper atmosphere.