<p>The work presented in this thesis involves experimental and theoretical studies related to plasma properties in high power impulse magnetron sputtering (HiPIMS), and more specifically plasma transport. HiPIMS is an ionized PVD method based on conventional direct current magnetron sputtering (dcMS). In dcMS very little of the sputtered material is ionized since the plasma power density is not high enough. This is not the case for HiPIMS, where a substantial part is ionized, and thus presents many new opportunities for thin film growth. Understanding the dynamics of the charged species in the HiPIMS discharge is therefore of essential value when producing high-quality thin film coatings.</p><p>In the first part of the work a new type of anomalous electron transport was found. Investigations of the transport resulted in the discovery that this phenomenon could quantitatively be described as being related and mediated by highly nonlinear waves, likely due to the modified two-stream instability (MTSI), resulting in electric field oscillations in the MHz-range (the so-called lower hybrid frequency). Measurements in the plasma confirmed these oscillations as well as trends predicted by the theory of these types of waves. The degree of anomalous transport in the plasma could also be determined by measuring the current density ratio between the azimuthal current density (of which the Hall current density is one contribution) and the discharge current density, <em>J</em><em>φ</em><em> / J</em><em>D</em>. The results provided important insights into understanding the mechanism behind the anomalous transport.</p><p>It was furthermore found that the current ratio <em>J</em><em>φ</em><em> / J</em><em>D</em> is inversely proportional to the transverse resistivity, eta_perpendicular , which governs how well momentum is transferred from the electrons to the ions in the plasma. By looking at the forces involved in the charged particle transport it was expected that the azimuthally rotating electrons would exert a volume force on the ions tangentially outwards from the circular race track region. The effect of having an anomalous transport would therefore be a large fraction of highly energetic ions being transported sideways and lost to the walls. In a series of experiments, deposition rates as well as incoming ion energy distributions were measured directly at the side of the magnetron. It was found that a substantial fraction of sputtered material is transported radially away from the cathode and lost to the walls in HiPIMS as well as dcMS, but more so for HiPIMS giving one possible explanation to why the deposition rate for substrates placed in front of the target is lower for HiPIMS compared to dcMS. Furthermore, the recorded, incoming ion energy distributions confirmed theoretical estimations on this type of transport regarding energy and direction.</p>

The role of cross field transport and volume recombination are of vital importance for a satisfactory understanding of the plasma edge in magnetically confined devices such as a Tokamak. Plasma fluctuations may travel cross field with significant velocities and play a central role in plasma transport. Cross field transport has been seen to be anomalous in most devices under a very broad range of experimental conditions. In recent years a clear indication of the relation between fluctuation, cross field particle transport and recombination has been reported.The University of Manchester Linear System (the ULS) has been used to observe the Balmer emission of the recombining plasma interacting with a dense neutral Hydrogen gas. The ULS is a device made of a cylindrical vacuum vessel 1.5 m long and 15 cm in radius. The plasma is formed in a separate chamber by a duoplasmatron source in the Demirkhanov configuration; the arc current was limited to 15 A and the potential drop was 100 V. The device is surrounded by a linear solenoid which was used to magnetize the plasma. The highest magnetic field was .1 T. Typical electron temperature in the device spans .1 to 10 eV, and the density 1. E+16 to 5. E+19.Diagnostic includes Langmuir probe and visible spectrometers. In addition, the DivCam imaging system originally designed and built to obtain 2D images of the MAST spherical Tokamak Scrape Off Layer, was used. The DivCam imaging system has enabled to obtain high resolution images of the plasma emission when interacting with the neutral gas. It appears evident that the Electron-Ion Recombination is strongly dependent upon radial transport of plasma particles: light emission attributed to EIR is only observed at a large cross field distance from the plasma source. Moreover, fast imaging of the plasma has also shown the presence of a plasma filament forming and propagating crossfield at the same region of the plasma where the EIR light is observed.To interpret the experimental observations obtained with DivCam, the OSM 1D fluid plasma solver and the EIRENE neutral Monte Carlo solver have been implemented in the linear geometry of the ULS linear system. Both the OSM and the EIRENE solvers were originally intended for tokamak and large magnetic confinement devices. Modelling of the EIR emissivity in the ULS device has demonstrated the importance of the inclusion of turbulent and blob transport in the model to obtain reasonable agreement between the observations and the theoretical predictions. The central density of the plasma filament has been estimated to be approximately .7 E+19 m-3 using EIRENE results.The emission attributed to hydrogenic ions (negative atomic H- and positive molecular ions H2+) and related to Molecular Assisted Recombinations can be estimated within EIRENE using the AMJUEL database. The database provides ion population estimations for three different collisional regimes: in the first regime a large population of vibrational excited hydrogen molecules are assumed to exist within the plasma volume; the second assumes strong Charge Exchange reactions and not vibrational excited molecule; the third assumes electron impact collisions with ground states molecule to be the only ion source. A reasonable agreement between the observations and the EIRENE prediction is only found when using the third estimation suggesting that molecular excitation and charge exchange processes are relatively unimportant under the experimental conditions considered.

The work presented in this thesis involves experimental and theoretical studies related to plasma properties in high power impulse magnetron sputtering (HiPIMS), and more specifically plasma transport. HiPIMS is an ionized PVD method based on conventional direct current magnetron sputtering (dcMS). In dcMS very little of the sputtered material is ionized since the plasma power density is not high enough. This is not the case for HiPIMS, where a substantial part is ionized, and thus presents many new opportunities for thin film growth. Understanding the dynamics of the charged species in the HiPIMS discharge is therefore of essential value when producing high-quality thin film coatings. In the first part of the work a new type of anomalous electron transport was found. Investigations of the transport resulted in the discovery that this phenomenon could quantitatively be described as being related and mediated by highly nonlinear waves, likely due to the modified two-stream instability (MTSI), resulting in electric field oscillations in the MHz-range (the so-called lower hybrid frequency). Measurements in the plasma confirmed these oscillations as well as trends predicted by the theory of these types of waves. The degree of anomalous transport in the plasma could also be determined by measuring the current density ratio between the azimuthal current density (of which the Hall current density is one contribution) and the discharge current density, Jφ / JD. The results provided important insights into understanding the mechanism behind the anomalous transport. It was furthermore found that the current ratio Jφ / JD is inversely proportional to the transverse resistivity, eta_perpendicular , which governs how well momentum is transferred from the electrons to the ions in the plasma. By looking at the forces involved in the charged particle transport it was expected that the azimuthally rotating electrons would exert a volume force on the ions tangentially outwards from the circular race track region. The effect of having an anomalous transport would therefore be a large fraction of highly energetic ions being transported sideways and lost to the walls. In a series of experiments, deposition rates as well as incoming ion energy distributions were measured directly at the side of the magnetron. It was found that a substantial fraction of sputtered material is transported radially away from the cathode and lost to the walls in HiPIMS as well as dcMS, but more so for HiPIMS giving one possible explanation to why the deposition rate for substrates placed in front of the target is lower for HiPIMS compared to dcMS. Furthermore, the recorded, incoming ion energy distributions confirmed theoretical estimations on this type of transport regarding energy and direction.

When plasmas come in contact with the boundaries that confine them, various complex processes occur between the plasma and the materials in the boundary. These processes, called plasma-material interactions (PMI) lead to physical and chemical modifications in the materials and in the plasma. In the case of a tokamak, a magnetic confinement fusion reactor, the interactions between the plasma and the material in the bounding walls can negatively impact the performance and service life of the reactor. Furthermore, PMI are also found in other areas of significant engineering interest, such as plasma-based spacecraft propulsion engines, where interactions affect the transport properties of the plasma and consequently the performance of the engine. Therefore, gaining a fundamental understanding of the various plasma-material interactions is necessary for the development and improvement of these devices. PMI are dictated by the plasma sheath, a layer of net positive charge that forms at the plasma-boundary interface. The sheath regulates the energy and particle fluxes to the boundary, mediating the interactions. Sheaths, however, are only stable and well-developed when the ions enter the sheath with a speed equal to or greater than the `Bohm speed'. The Bohm speed is a landmark result in sheath theory and various mathematical expressions for it have been derived from fluid and kinetic treatment of plasmas. Although these models are widely used, they are only accurate in cases where the thickness of the sheath is negligible when compared to the scale length of the plasma in consideration. These cases are said to satisfy the `asymptotic limit'. To resolve this, a new Bohm speed model that considers the effects of transport terms such as the electron heat flux, thermal force, and temperature isotropization has been recently proposed [Y. Li et al., Physical Review Letters (2022)]. The model is verified using particle-in-cell (PIC) kinetic simulations and is shown to accurately predict the Bohm speed in cases away from the asymptotic limit. This thesis investigates the new model using the continuum kinetic approach on the Gkeyll software framework. The continuum kinetic approach numerically solves the Vlasov-Maxwell equations using the discontinuous Galerkin method and captures the kinetic phenomena of the plasma without needing to track individual particles. Multiple collisional cases ranging from a Knudsen number of 20 to 5000 are considered in a 1X3V simulation domain using the Lenard-Bernstein collisional operator. The results of the continuum kinetic simulations are benchmarked to the PIC simulation results. It is concluded that across a wide range of collisionalities, the continuum kinetic method captures much of the same physics as the PIC method while offering noise-free results. However, there is a discrepancy between the Bohm speed prediction and the simulation results in the continuum kinetic case. This discrepancy is explored and significant error in the collisional integral derived transport terms between the continuum kinetic method and PIC method is found, suggesting that the difference in collisional operator may be the source of the discrepancy. Nevertheless, the sheath profiles developed in the PIC simulations and the continuum kinetic simulations are in reasonable agreement. / Master of Science / Nuclear fusion is a process in which two light atomic nuclei (like hydrogen) fuse to form a heavier nucleus (like helium) and release tremendous amounts of energy. The resultant energy from these reactions powers the sun and has the potential to provide clean energy for our terrestrial needs. Harnessing fusion energy has been one of the biggest scientific and engineering challenges of our time due to various reasons. One of these reasons is the interaction of plasma, which is the fuel for the fusion reaction, and the materials of the walls that bound the plasma. These interactions are called plasma-material interactions (PMI) and can affect the longevity and performance of fusion reactors. The main governing phenomenon behind these interactions is the plasma sheath, a layer of plasma that is formed when the plasma encounters a boundary. For a sheath to form it is also necessary that ions in the plasma possess a speed greater than the so-called `Bohm speed'. While many expressions have been derived for the Bohm speed, these expressions are only valid when there is a clear sheath entrance that divides the bulk plasma and the sheath. This condition is not satisfied in many cases of interest. Instead, a sheath-transition region is found to exist between the bulk plasma and the sheath. A recently proposed Bohm speed model [Y. Li et al., Physical Review Letters (2022)] resolves this. This model is accurate in cases where the sheath-transition region exists and is derived by considering previously overlooked transport physics. In this work, this new model is studied using a different computational approach known as `continuum kinetics' using an open-source solver called Gkeyll. The results of the continuum kinetic simulations are compared to the results used to verify the model.

Le domaine de la physique des plasmas froids a émergé avec les premières découvertes fondamentales en physique atomique et en physique des plasmas il y a plus d’un siècle. Toutefois, ce domaine a été rapidement orienté vers les applications. L’une des plus importantes dans la première moitié du XXème est le "Calutron" (California University Cyclotron), inventé par E. Lawrence à Berkeley, qui faisait partie du projet Manhattan, et utilisé comme un spectromètre de masse pour séparer les isotopes de l’uranium. Dans un rapport du projet Manhattan daté de 1949, D. Bohm fait deux observations qui sont fondamentales pour la physique des plasmas froids :(i) Les ions doivent avoir une énergie cinétique minimales lorsqu’ils entrent dans la gaine du plasma, estimée à Te/2, Te étant la température électronique.(ii) Le transport du plasma à travers un champ magnétique est augmenté par des instabilités.La propulsion électrique par plasma est utilisée pour des satellites militaires et des sondes spatiales depuis les années 1960 et a suscité un intérêt grandissant ces vingt dernières années avec le développement des applications commerciales des technologies spatiales. Néanmoins, les mêmes questions que celles auxquelles D. Bohm était confronté, c’est-à-dire le transport multidimensionnel, l’interaction plasma-gaine, et les instabilités, se posent toujours. La théorie et les simulations sont d’autant plus importantes pour la conception des systèmes de propulsion électrique que les tests en conditions réelles nécessitent le lancement d’un satellite dans l’espace.Dans ce travail, nous établissons les équations du transport multidimensionnel dans un plasma isotherme, nous proposons un critère de gaine qui permet de rendre compte de la saturation du champ magnétique dans un plasma froid et faiblement ionisé, et nous modélisons le refroidissement des électrons à travers le filtre magnétique du propulseur PEGASES (Plasma Propulsion with Electronegative Gases). Toutes les théories sont motivées et validées par un grand nombre de simulations particulaires PIC bi-dimensionnelles, en utilisant le code LPPic qui a été partiellement développé dans le cadre du projet. Enfin, les cas de simulation sont étendus à une décharge inductive à plasma dans l’iode, avec un nouvel ensemble de section efficaces de réaction. / The field of low temperature plasma physics has emerged from the first fundamental discoveries in atom and plasma physics more than a century ago. However, it has soon become very much driven by applications. One of the most important of them in the first half of the XXth century is the "Calutron" (California University Cyclotron) invented by E.~Lawrence in Berkeley, that was part of the Manhattan project, and operated as a mass spectrometer to separate uranium isotopes. In a 1949 report of the Manhattan project, D.~Bohm makes two observations that are fundamental for low-temperature plasma physics.(i) The ions must have minimum kinetic energy when they enter the plasma sheath estimated to T_e/2 , Te being the electron temperature in eV ;(ii) Plasma transport across a magnetic field is enhanced by instabilities.Plasma electric propulsion is used on military satellites and space probes since the 1960s and has gained more and more interest for the last twenty years as space commercial applications were developing. However, the same questions as the ones D.~Bohm was faced with, namely multi-dimensional transport, plasma sheath interaction, and instabilities, arise. Theory and simulation are even more important for electric space propulsion systems design since testing in real conditions involves to launch a satellite into space.In this work, we derive the equations of the multi-dimensional isothermal plasma transport, we establish a sheath criterion that causes the magnetic confinement to saturate in low-temperature, weakly ionized plasmas, and we model the electron cooling through the magnetic filter of the PEGASES (Plasma Propulsion with Electronegative Gases) thruster. All the theories are driven and validated with extensive two-dimensional particle-in-cell (PIC) simulations, using the LPPic code that was partially developed in the frame of this project. Finally, the simulation cases are extended to an iodine inductively coupled plasma (ICP) discharge with a new set of reaction cross sections.

Es wurden die Transportphänomene magnetisierter Plasmen in der Umgebung materieller Limiter am linearen Plasmagenerator PSI-2 unter Verwendung von elektrischen und optischen Diagnostiken untersucht. Der Senkrechtdiffusionskoeffizient wurde mit D= 5 m^2/s und einer 1/B-Abhängigkeit bestimmt. Der dominierende Prozess des Radialtransportes ist turbulenter Natur. Unter Berücksichtigung der Volumenionisation kann das radiale Dichteprofil konsistent beschrieben werden. Der Schaft einer Langmuirsonde reduziert in einem magnetisierten Plasma die Elektronendichte. Dieses wurde mit zwei Sonden untersucht. Es wird eine globale Teilchenbilanz vorgestellt, die diese Reduktion beschreibt. Bringt man einen Limiter in ein strömendes magnetisiertes Plasma ein, so bildet sich hinter diesem ein Schatten aus. Vor dem Limiter zeigt sich für einige Plasmaregime ein inverser Schatten. Beide sind durch die starke Abhängigkeit der Emissivität von der Elektronentemperatur zu erklären. Ortsaufgelöste Messungen mit Langmuirsonden und optischer Spektroskopie bestätigen dieses experimentell und zeigen kurze Skalenlängen der Dichte für den Abfall vor und den Anstieg hinter einem Limiter. Die Längen zeigen keine klare Skalierung mit dem Ionengyrationsradius. Es werden ortsaufgelöste Messungen der Plasmaparameter mit einer Langmuirsonde vor einem Limiter unter schrägem Einfall vorgestellt. In Wasserstoffplasmen lässt sich der Dichteverlauf mit dem Modell von Chodura [Cho:82] gut beschreiben. In einer stationären Bogenentladung sind Fluktuationen in der Entladungsspannung zu finden. Diese Fluktuationen erzeugen suprathermische Elektronen, die von Limitern geblockt werden. Durch das Einbringen von Limitern werden turbulente räumliche Strukturen erzeugt, die in das Schattengebiet eindringen. Diese sind sowohl optisch mit Photomultipliern als auch als Fluktuation des Ionensättigungsstromes einer Langmuirsonde nachweisbar. Die Strukturen können den Quertransport in den Plasmaschatten verstärken. / The transport phenomena of magnetized plasmas in the vicinity of a material limiter have been investigated. The investigations were carried out at the linear plasma generator PSI-2 with electrical and optical diagnostics. The perpendicular diffusion coefficient was determined as D= 5 m^2/s with a magnetic field dependence of 1/B. The dominant process of the radial transport is therefore anomalous. By consideration of volume ionization the radial density profile can be consistently described. The shaft of a Langmuir probe acts as a particle sink and reduces electron density. This was investigated using two probes. The reduction can be explained in terms of a global particle model. On immersing a limiter into a streaming, magnetized plasma a distinct shadow region is observed downstream of the target. In addition, for some plasma conditions the region upstream of the target forms an inverse shadow. Both observations can be explained by the strong dependence of the emissivity on electron temperature. This is confirmed experimentally by Langmuir probes and optical spectroscopy. Spatially resolved measurements reveal short scale lengths for a decrease of density in front of and an increase behind a limiter. These lengths do not clearly scale with the ion gyroradius. Spatially resolved Langmuir probe measurements taken in front of a limiter at oblique incidence are presented. For hydrogen plasmas the model of Chodura [Cho:82] describes the density profile quite well. In a stationary arc discharge fluctuations in the discharge voltage are found. The fluctuations produce suprathermal electrons. These electrons are blocked by limiters. A limited plasma produces turbulent spatial structures which penetrate into the shadow region. These structures can be detected with photomultipliers and also as a fluctuation in the ion saturation current of a Langmuir probe. They can enhance perpendicular transport into the plasma shadow.

Magnetic nozzles, like Laval nozzles, are observed in several natural systems and have application in areas such as electric propulsion and plasma processing. Plasma flowing through these nozzles is inherently tied to the field lines and must separate for momentum redirection or particle transport to occur. Plasma detachment and associated mechanisms from a magnetic nozzle are investigated. Experimental results are presented from the plume of the VASIMR® VX-200 device flowing along an axisymmetric magnetic nozzle and operated at two ion energies to explore momentum dependent detachment. The argon plume expanded into a 150m3 vacuum chamber where the background pressure was low enough that charge-exchange mean-free-paths were longer than experiment scale lengths. This magnetic nozzle system is demonstrated to hydrodynamically scale up to astrophysical plasmas, particularly the solar chromosphere, implying general relevance to all systems. Plasma parameters were mapped over a large spatial range using measurements from multiple plasma diagnostics. The data show that the plume does not follow the magnetic field lines. A mapped integration of the ion flux shows the plume may be divided into three regions where 1) the plume briefly follows the magnetic flux, 2) diverges quadratically before 3) expanding with linear trajectories. Transitioning from region 1→2, the ion flux departs from the magnetic flux suggesting ion detachment. An instability forms in region 2 driving an oscillating electric field that causes ions to expand before enhancing electron cross-field transport through anomalous resistivity. Transitioning from region 2→3 the electric field dissipates, the trajectories linearize, and the plume effectively detaches. A delineation of sub-to-super Alfvénic flow aligns well with the inflection points of the linearization without a change in magnetic topology. The detachment process is best described as a two part process: First, ions detach by a breakdown of the magnetic moment when the quantity |v/fcLB| becomes of order unity. Second, the turbulent electric field enhances electron transport up to a factor of 4±1 above collisional diffusion; electron cross-field velocities approximate that of the ions and depart on more centralized field lines. Electrons are believed to detach by breakdown of magnetic moment further downstream in the weaker magnetic field.

Il est maintenant accepté expérimentalement que les filaments de plasma alignés sur le champ magnétique, appelés “blobs”, jouent un rôle important dans le transport dans le plasma de bord. Dans cette thèse, les phénomènes fondamentaux du transport dans le plasma de bord sont étudiés en mettant l'accent sur le phénomène de filaments plasma. Dans un premier temps, les mécanismes de propagation de blobs uniques sont envisagés. Puis la génération de blobs par la turbulence de bord est étudiée, et le transport turbulent est discuté entant que phénomène collectif. Des particularités du transport turbulent, incluant les blobs auto-organisés, sont reliées à un transport de type Bohm (c'est à dire des perturbations avec des corrélations radiales longues, et un coefficient de transport effectif quisuit la dépendance Bohm). De plus, en prolongement de ce travail, un effort initial vers une transposition du transport non-local au plasmade bord est décrite. / Recently, it has been accepted that magnetic field aligned plasma filaments, referred to as "blobs" play important roles in the transport of Scrape-off Layer (SoL) plasmas. In this thesis, putting an emphasis on the plasma blob phenomenon, we study fundamental processes of SoL transport using numerical simulation. At first, weinvestigate the propagation mechanisms of single and isolated blobs.Next, we study the generation of blobs from edge turbulence, and discuss the SoL turbulent transport as a collective phenomenon. Features of turbulent transport, which includes the self-organized blobs in SoL, are identified as Bohm-like transport (i.e., the perturbation with long radial correlations and the effective transport coefficient that follows the dependence of Bohm-like transport). Additionally, as an advancement of study, we describe an initial effort to extend the view of non local transport to edge plasmas.