Browsing by Author "Groth, Mathias, Prof., Aalto University, Department of Applied Physics, Finland"

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  • Energetic particles in reactor-relevant plasmas: modelling and validation
    (2022) Varje, Jari
     School of Science | Doctoral dissertation (article-based)
    Nuclear fusion is a promising future energy source with few carbon dioxide emissions and nearly limitless source of fuel in heavy isotopes of hydrogen. Energetic particles, such as fusion-born alpha particles and neutral beam injected (NBI) fast ions play a vital role in reactor-relevant fusion plasmas, as they are responsible for heating the plasma, but can simultaneously cause localized heat loads and risk of damage on the plasma facing components. In this work, the Monte Carlo orbit-following code ASCOT has been used to simulate fast ions both to validate simulation results with present-day experiments at the JET tokamak, and to predict fast ion losses in next-generation fusion reactors ITER and DEMO. For validation of ASCOT predictions against JET plasmas, synthetic diagnostics were used to compare the simulated fast ion distributions with the neutral particle analyser (NPA) and fast ion loss detector (FILD) measurements. The NPA simulations qualitatively reproduced the experimentally measured slowing-down distributions and fast ion isotope fraction for NBI-injected hydrogen and deuterium ions, while the FILD simulations for fusion product losses were within 10 % of the experimentally observed losses. For predictions in ITER plasmas, simulations with resonant magnetic perturbations showed that including the response of the plasma to the external perturbations is vital, as the response not only affected the magnitude but also the distribution of fast ion losses. For DEMO plasmas, the sensitivity of fast ion losses due to various magnetic perturbations was studied, including the toroidal field ripple and ferritic inserts in various configurations. The design was found to be robust with respect to fast ion confinement and losses. Finally, over the course of this work, a highly parallelized version of the ASCOT code, called ASCOT5, was developed. The new version substantially increased the performance on modern supercomputer hardware as well as improving its maintainability and extensibility.
  • Fast ion simulations in toroidally asymmetric tokamaks - Model validation with fast ion probes at ASDEX Upgrade and predictive modelling of ITER
    (2016) Äkäslompolo, Simppa
     School of Science | Doctoral dissertation (article-based)
    The world electricity demand is increasing due to the growing global population striving for an ever-improving standard of living. Fusion energy research has the goal of bringing the energy source of the stars to Earth. The leading scheme is to magnetically confine a very hot plasma within a tokamak reactor. This thesis studies the energetic particles produced by the external heating of the plasma and by the fusion reactions themselves. The energetic particles carry a risk of damaging the reactor walls, if they are allowed to escape the plasma. This may occur if the carefully tuned magnetic field is perturbed by, e.g., introducing components made out of ferromagnetic materials to the tokamak. A quantitative study of the confinement of the fast, energetic particles requires careful calculation of the perturbation, followed by detailed simulations of fast ion behaviour with validated tools. In this work, the perturbative effect of the European test blanket modules (TBMs) of ITER were analysed. The TBMs, containing ferromagnetic steel, are needed for testing the technology for breeding tritium fuel from lithium. The magnetisation of the TBMs was computed with the finite element method using a geometry of unprecedented detail. Subsequently, the ASCOT code was used to assess the confinement of neutral beam injected (NBI) deuterons and fusion alpha particles. As the main result, the TBMs were found to be compatible with fast ion confinement requirements, at least in the 15MA Q=10 inductive scenario, the baseline ITER plasma. The fast ion modelling tools were validated with measurements at the ASDEX Upgrade tokamak: the flux of NBI ions was measured with the fast ion loss diagnostics (FILD) and the flux of fusion protons with the activation probe. The ASCOT simulations are in qualitative agreement with FILD measurements. The activation probe facilitated quantitative analysis. This required the development of an adjoint Monte Carlo method for calculating charged particle fluxes to the wall. The new method was used in the fusion proton modelling, the results of which agree quite well with mea- surements even quantitatively. The work presented here affirms the viability of the TBM design. It also validates and expands the fast ion behaviour and diagnostics modelling toolbox.
  • Fast Ions in Fusion Plasmas – Towards Numerical Tokamaks
    (2015) Asunta, Otto
     School of Science | Doctoral dissertation (article-based)
    Constructing a fusion device is a complicated, expensive, and time-consuming enterprise. To avoid costly errors in the design and operation of such a device, sophisticated predictive modelling is needed. To that end, there are several on-going projects striving towards the ambitious goal of building a numerical tokamak; i.e., a set of numerical tools that could be used to simulate the evolution of the fusion plasma through an entire discharge. In a fusion device, fast ions are born in fusion reactions. They also arise from acceleration of thermal particles using electromagnetic waves, and from injection of energetic neutrals that are ionized promptly upon entering the plasma. Fast ions are crucial for heating the plasma but they are also used for driving toroidal rotation and current. In addition, if the fast ions escape the plasma, they can pose a threat to the first walls of the device. Therefore, tools for modelling the fast ions are an integral part of any numerical tokamak. In this work, development and applications of two fast ion modelling tools, the beamlet-based neutral beam injection code BBNBI and the particle-following Monte Carlo code ASCOT, are presented. The former simulates the injection and the ionization of a neutral beam, whereas the latter models the motion and the slowing-down of fast ions in the plasma. The validity of BBNBI and ASCOT is confirmed by benchmarking them against other established neutral beam codes in Joint European Torus (JET) and ASDEX Upgrade (AUG) plasmas. The codes are then utilized to investigate (i) the losses of neutral beam injected (NBI) ions due to in-vessel coil induced magnetic perturbations in AUG, (ii) the distribution function of NBI ions in ITER, and (iii) the behaviour of fusion-born alpha particles in JET advanced scenario plasmas. Finally, the two numerical tokamak constructions into which BBNBI and ASCOT have been incorporated are introduced. While both BBNBI and ASCOT are widely used in JET Integrated Transport Code (JINTRAC), the first results utilizing them within the EFDA Integrated Tokamak Modelling (ITM) framework are presented here. The importance of orbit width effects is highlighted in a benchmark between different fast ion tools on the ITM framework. A study charting the capability of neutral beams to drive current in a future Demonstration Power Plant (DEMO) proves that BBNBI and ASCOT are capable of flexible and sophisticated modelling of NBI on the ITM framework.
  • Global Gyrokinetic Particle Simulations of Circular Limiter Tokamak Plasmas
    (2017) Korpilo, Tuomas
     School of Science | Doctoral dissertation (article-based)
    Magnetic confinement fusion reactors, such as tokamaks, rely on generating fusion power by confining the burning plasma effectively inside the device. Plasma turbulence and associated heat and particle transport out of the plasma, however, degrade the confinement in such devices, thus limiting their performance. Therefore, understanding and controlling of turbulence are of great importance for improving the economics of fusion reactors. The plasma turbulence in tokamaks is studied both experimentally and computationally. The role of computational studies is to elucidate the underlying physical mechanisms for turbulent transport and, eventually, predict and manipulate plasma confinement for future reactors. This modeling effort is increasingly based on numerical tools that solve gyrokinetic Fokker-Planck–Maxwell equations in the plasma. ELMFIRE is one of these gyrokinetic tools designed for first-principles transport simulations. In this thesis, the recent code development work to improve ELMFIRE’s numerical and physical accuracy is presented. The numerical accuracy is improved by a new integration method for the parallel nonlinearity that significantly enhances the energy conservation in the simulation. The physical accuracy, in turn, is increased by a new computational grid that allows a non-uniform resolution. In addition, the simulation domain is extended to cover the entire tokamak plasma volume from the plasma center to the material boundary of a radial wall and poloidal limiter plates. The physical accuracy of ELMFIRE simulations is investigated by testing the code’s ability to reproduce a FT-2 tokamak plasma. A direct comparison of the simulation results and FT-2 data shows that the experimental steady-state profiles are not obtained numerically. In addition to this, the ELMFIRE capability to simulate scrape-off layer plasmas is examined in a toroidal limiter-like configuration. The results of this study show a formation of sheath potential and plasma flows as well as a modification of density and temperature profiles in the scrape-off layer. A numerical plasma perturbation, induced by a large radial E x B flow at the limiter-plasma boundary, is also observed in the scrape-off layer. Finally, grid resolution and boundary conditions are shown to have a significant impact on transport levels.
  • The impact of separatrix conditions on pedestal-SOL coupling: an investigation with integrated transport solvers
    (2025) Simpson, James
     School of Science | Doctoral dissertation (article-based)
    The primary goal of this thesis is to connect the pedestal, the steep gradient region at the edge of the confined plasma defined by its height and width, with the scrape-off layer. The scrape-off layer is a region of unconfined plasma adjacent to the pedestal that connects the main plasma to the material targets, known as the divertor. The pedestal and scrape off layer are intimately linked regions separated by a surface known as the separatrix, which denotes the transition from confined to unconfined plasma. Understanding how these two regions interact is key for the economic viability and net power production of a tokamak power plant. Within this thesis, we first address reduced models for the electron density pedestal (𝑛𝑛𝑒𝑒,𝑝𝑝𝑝𝑝𝑝𝑝) and the electron separatrix temperature (𝑇𝑇eu,sep ) to enable integrated modelling simulations to converge on reasonable timescales (minutes/hours rather than days/weeks). Secondly, we utilise integrated modelling tools which use ideal MHD to limit the pedestal evolution to consider the effect of the electron separatrix temperature and density on the electron pedestal pressure, similar to the IMEP model (T. Luda et al. Nuclear Fusion, 2020, 036023). Considering a reduced model for 𝑇𝑇eu,sep , we demonstrate the importance of measuring the power decay width (𝜆𝜆𝑞𝑞) in impurity seeded and unseeded plasmas to achieve agreement between the scrape-off layer edge transport fluid code - EDGE2D-EIRENE and the analytic two-point model (TPM). These results elucidate the neutral fuelling and pedestal stability as this work considered how neutrals affect 𝑇𝑇eu,sep , which in turn can effect the pedestal stability. A reduced analytic model for the electron density pedestal, the neutral penetration model (NPM) described in reference (R.J. Groebner et al. Plasma Physics and Controlled Fusion, 2002, A265), was tested. A key prediction of the neutral penetration model is that the electron pedestal density is proportional to one over the electron pedestal density width. This relationship was confirmed in the simulations only if the electron density profile was measured at the same poloidal position as the maximum neutral source. However, the predicted scaling was not observed in the measurements performed at the low field side midplane. Combining SOL and core physics using the integrated modelling code JETTO-FRANTIC-MISHKA, which predicts the confined plasma fueling due to hydrogenic atoms, the pedestal width and height, and evolving separatrix boundary conditions (as predicted by EDGE2D-EIRENE), I find that the simulations could not reproduce the degradation of the electron pressure pedestal with electron separatrix density as is observed experimentally in JET. This discrepancy is likely due to resistive MHD effects in the pedestal.
  • Modelling and understanding fast particle transport in non-axisymmetric tokamak plasmas
    (2019) Särkimäki, Konsta
     School of Science | Doctoral dissertation (article-based)
    Understanding fast particle confinement is essential for successful operation of ITER and other advanced fusion experiments. Designing and interpreting experiments require that fast particle transport is studied computationally. The test-particle orbit-following Monte Carlo method is well suited for this purpose as long as the simulations are accompanied with rigorous analysis to ensure the results are valid. This thesis presents a high-performance orbit-following code ASCOT5 for the studies of fast particle transport. The code is verified with respect to known analytical results. Furthermore, this thesis introduces tools to supplement the orbit-following simulations that aid in interpreting the results of the fast particle studies. These tools give credibility to the results and they can also be used to decrease the time required to execute the simulations. ASCOT5 was designed to take full advantage of the modern CPU hardware. The code supports MPI, multithreading, and SIMD instructions resulting in a parallelisation on multiple levels. ASCOT5 uses computational resources more efficiently than its predecessor, but physics-wise they are similar with the exception of the adaptive collision operator. The tools to supplement the orbit-following simulations are demonstrated for ITER. This thesis demonstrates how to construct loss maps which are used to connect fast particle losses to the collisionless transport mechanisms. Constructing loss maps directly from the magnetic field structure provides an alternative way to estimate the fast particle losses without orbit-following simulations. ASCOT5 and the loss-map analysis are used to study fast ion confinement in the presence of various magnetic field perturbations. It was found that the plasma response to the ELM control coils introduces a new loss channel which explains the previously observed shift in fast ion divertor loads. Furthermore, it is shown that the radial transport of runaway electrons and fast ions in an externally perturbed field can be modelled as an advection-diffusion process. This result can be utilized to provide the transport coefficients to the orbit-averaged codes and to perform fast estimates on fast ion losses.
  • Monte Carlo simulation of fast ion losses in ITER in the presence of static 3D magnetic perturbations
    (2014) Koskela, Tuomas
     School of Science | Doctoral dissertation (article-based)
    The confinement of fast ions is of paramount importance for future nuclear fusion reactors, such as ITER. Confined fast ions are needed to heat the plasma into fusion-relevant temperatures, while fast ion losses may compromise the integrity of the vacuum vessel. Fast ions are well confined in an axisymmetric tokamak with a high plasma current, but even small deviations from axisymmetry may lead to localized fast ion losses that may compromise the operation of the machine.  This thesis describes Monte Carlo simulations of fast ion confinement and losses in ITER as well as existing tokamaks. Since fast ions are relatively collisionless, the theory of collisionless orbits of charged particles in tokamak geometry is first discussed. The collisionless orbits are perturbed by the infrequent collisions with the background plasma and by deviations from magnetic axisymmetry, which. To study these orbits in realistic tokamaks, the theory is put into use in the ASCOT code, whose main features are described in the thesis. Finally, as simulations need to be connected with experiments, the most commonly used fast ion diagnostics are described and their connections to simulations discussed.  The results obtained in this thesis are encouraging for the operation of ITER. The ASCOT code has been benchmarked with several fast ion diagnostics as well as other codes, and satisfactory agreement has been found. The predictive modelling of ITER suggests that the toroidal field ripple will induce significant fast ion losses, but it can be effectively mitigated by ferritic inserts. The perturbation due to the magnetization of the ferritic steel in test blanket modules is not seen as a threat to fast ion confinement. The impact of ELM control coils on fast ion losses needs more study, but it seems likely that the plasma will screen the error field inside the pedestal, preventing the high fast ion losses seen in vacuum models.
  • Particle scattering in magnetised plasmas: a theoretical and numerical approach
    (2024) Iorio, Riccardo Nicolò
     School of Science | Doctoral dissertation (article-based)
    The intricate dynamics of charged particles within plasmas are mainly shaped by their collisional interactions. As a result, it is crucial to address these phenomena through both theoretical and numerical approaches. In pursuit of this objective, this work embarks on reviewing the formal derivation of the Vlasov equation, followed by an extensive exploration of Coulomb scattering, elucidating the Landau collision integral and its underlying characteristics. Furthermore, we delve into the nonconventional neoclassical theory for toroidal systems, providing the theoretical framework for the subsequent numerical findings. Utilizing the ELMFIRE code, gyrokinetic simulations employ a discrete Landau collision integral, ensuring the conservation of energy and momentum. Tailored to conservation laws, a specific binary collision model provides valuable insights into variations in impurity density arising from steep gradients in density and temperature profiles. The analysis compares Landreman-Fülöp- Guszejnov model's theory with neoclassical predictions and ELMFIRE data. Remarkably, within the analytical theory's validity, numerical agreement is 5-10%, especially for δ<0.4 with low charge numbers. Yet, within the pedestal region, the Landreman-Fülöp-Guszejnov framework may not be directly applicable due to pronounced gradients. Furthermore, a novel analysis explores the correlation between turbulent transport and the radial electric field. Using Lower Hybrid (LH) heating operator in an FT-2 tokamak at off-axis and onaxis reveals heightened turbulence at r/a=0.55 during a 70μs simulation. Turbulence induces noticeable fluctuations in the radial electric field profile, with strong high-shearing flow in the former and neoclassical dominance in the latter. These findings align with prior research, suggesting a robust shearing phenomenon, reinstating transport equilibrium. In conclusion, to enhance the central theme of this dissertation, we investigate the formal derivation of a collisional bracket from the Landau collision integral using the metriplectic bracket formulation for dissipative systems. This theoretical framework is then applied to the guiding center Vlasov-Maxwell-Landau model, resulting in a specific collisional bracket that ensures energy and momentum conservation. The implications of this finding are explored within broader frameworks, including the electromagnetic gyrokinetic case, offering a theoretical culmination to this dissertation.
  • Power and momentum removal in the Scrape-Off Layer of ASDEX Upgrade
    (2021) Paradela Pérez, Iván
     School of Science | Doctoral dissertation (article-based)
    Dedicated experiments in ASDEX Upgrade (AUG) and interpretative studies of these experiments with the edge fluid code SOLPS have been carried out to investigate the relative importance of underlying physical processes of divertor transport and exhaust of momentum and power in tokamak plasmas in AUG. Analysis of pressure conservation in AUG H-mode plasmas shows that, at low electron target temperatures, the momentum losses in the scrape-off layer (SOL) near the separatrix are up to two orders of magnitude stronger compared to the momentum losses in the far SOL in flux tubes with the same target temperature. In L-mode-like and H-mode-like SOLPS 5.0 simulations, the momentum losses are up to two orders of magnitude weaker than experimentally observed at target temperatures below Te,t < 5 eV, and the dependence of the losses on the distance to the separatrix of the flux tube is only significant in the vicinity the separatrix. The L-mode-like simulations show that the impact of ion-atom charge-exchange on momentum transfer is larger than the impact of ion-molecule elastic scattering for the range of temperatures and plasma conditions observed in the SOL of AUG. Experiments and SOLPS-ITER simulations of the upper open divertor in AUG show that the net effect of increasing the core plasma density or the plasma current on the heat loads onto the targets strongly depends on the toroidal field direction. Within experimental and computational uncertainties, SOLPS-ITER predicted trends of the peak heat flux density at the targets with increasing core plasma density and plasma current are in quantitative agreement with the experimental data. Within the divertor region, these simulations show that the radial energy transport due to cross-field drifts is the primary component of the total radial transport contribution to energy transport. In L-mode-like simulations, the neutral model, the divertor closure, the boundary conditions and the SOLPS version do not significantly impact the target to upstream ratio of the total plasma pressure, ptot, t/ptot, u within the outer divertor, except for low temperatures (Te,t < 3 eV) in the vicinity of the separatrix. In the vicinity of the separatrix, drifts have a stronger impact on plasma momentum losses than the neutral model and divertor closure.
  • Radiative divertor studies in JET high confinement mode plasmas
    (2015) Järvinen, Aaro
     School of Science | Doctoral dissertation (article-based)
    Controlled power exhaust is one of the key challenges in reactor scale fusion devices. These devices must maintain heat loads less than 10 MW/m2 at the plasma-facing materials (PFM), while producing gigawatts of fusion power. Furthermore, sufficiently low erosion of and fuel retention in PFMs are required to reach reactor relevant component duty cycles. The presently preferred solution to these challenges is to utilize tungsten PFMs with injection of extrinsic radiating impurities, such as nitrogen or neon. However, significant gaps do still exist in the technology and scientific understanding needed to fully rely that these devices will perform according to their design specifications. Predictive capability for these devices relies on model validation and physics interpretation studies conducted on existing fusion test reactors.  In this doctoral thesis, radiative divertor studies with nitrogen and neon injection are investigated experimentally and interpreted with the multi-fluid code package EDGE2D-EIRENE for high confinement mode plasmas in the JET tokamak. The studies include comparison of predicted and measured divertor conditions, investigations of the impact of PFMs and divertor geometry on the divertor performance, and comparison of divertor performance with nitrogen and neon injection. Furthermore, predictions for tungsten retention in the divertor chamber with the Monte-Carlo code DIVIMP were conducted.  When imposing the divertor radiation by impurities, the simulations capture the experimentally observed reduction of the low-field side (LFS) divertor peak heat load, radiated power, and their spatial distribution. However, consistent with earlier studies, the simulations underestimate the radiated power by deuterium, indicating a shortfall in the radiation from the fuel species. Due to similar radiative characteristics of nitrogen and carbon, the divertor radiation distributions observed in JET with carbon PFMs can be obtained with nitrogen seeding in JET with the ITER-like wall. Detachment is obtained at similar divertor radiation levels in both PFM configurations. Unexpectedly, divertor geometry is observed to have only a marginal impact on the reduction of the LFS heat load with increasing radiation. It is also observed that similar levels of LFS heat load reduction can be obtained at JET with either nitrogen or neon injection. However, unlike nitrogen radiation, a significant fraction of neon radiation is predicted to occur in the confined plasma, expected to reduce plasma performance. Furthermore, high density, low temperature divertor conditions are predicted to be beneficial for improving tungsten retention in the divertor of JET, and edge-localized modes (ELMs) are predicted to dominate tungsten erosion and leakage out of the divertor chamber in JET.
  • Role of hydrogenic molecules in fusion-relevant divertor plasmas
    (2022) Holm, Andreas
     School of Science | Doctoral dissertation (article-based)
    Power production using magnetic confinement fusion is technically challenging and necessitates operation under detached divertor conditions. Under detached conditions the power loads to the plasma-facing components are reduced within their thermo-mechanical properties. Molecular processes are critical at temperatures relevant to onset of plasma detachment. Therefore, molecules are expected to affect the local plasma conditions and the onset of detachment. This dissertation evaluates the role of molecular effects on the onset of detachment using a fluid model for molecules implemented in the edge-fluid code UEDGE coupled to the collisional-radiative (CR) code CRUMPET. The applicability of the molecular fluid model is assessed using the kinetic neutral Monte-Carlo code EIRENE. To assess the validity of the predictions, and to quantify the role of molecular particle and power sinks on the onset of detachment, the numerical UEDGE predictions are compared to Divertor Thomson Scattering (DTS) and Langmuir probe measurements in DIII–D low-confinement (L-mode) plasmas. Including fluid molecules in UEDGE simulations of deuterium plasmas in L-mode conditions improves the qualitative code-experiment agreement for detachment onset compared to UEDGE simulations considering atoms only. Accounting for molecularly-induced plasma particle and power sinks in the simulations reduces the plasma temperatures sufficiently for detachment onset to occur. The role of electronic and vibrational CR transitions are shown to be more important for the effective CR dissociation rates than the assumption of ion-electron thermal equilibration and non-local transport effect of vibrationally excited molecules. Omitting vibrational and electronic transitions from EIRENE simulations decrease effective dissociation rates by up to 65% compared to when they are included. UEDGE fluid predictions of molecular content and mean energy are shown to lie within 15% and a factor of 2 of EIRENE kinetic predictions, respectively. These findings indicate that a fluid treatment of the molecules in divertor plasmas is applicable for divertor-relevant conditions. Using fluid molecular models in plasma-edge simulations reduces the computational times compared to kinetic molecular models, especially under highly collisional conditions encountered in detached divertor plasmas. The effect of approximating the molecules as a fluid is found to be smaller than that of other processes affecting molecular predictions, such as the CR processes included in the effective rates. The dissertation suggests a number of improvements to the implemented molecular fluid model to further reduce the difference between kinetic and fluid molecular models.
  • Simulations of turbulence-flow interplay in tokamak plasmas - Gyrokinetic studies of isotope effect on turbulent transport and flows in Ohmic discharges
    (2018) Niskala, Paavo
     School of Science | Doctoral dissertation (article-based)
    Performance of tokamak fusion reactors is limited by heat and particle losses. Fusion reactions require extreme temperatures that ionise the fuel and transform it into a plasma, which is confined by strong magnetic fields in tokamaks. Designing future reactors requires the capability to predict the efficiency of the confinement based on known parameters. Generally the design process utilises simple scaling laws based on databases of previous experiments. These scaling laws, however, give little insight into the physical mechanisms that determine the confinement properties.  The heat and particle losses are understood to be governed by the non-linear interplay of turbulence and plasma flows, but uncertainty remains on e.g. sudden transitions between confinement regimes and isotopic scaling of confinement. Experimental studies of these issues are aided by advanced computer models. This thesis investigates the interplay of flows and turbulence in ohmically heated tokamak plasmas via gyrokinetic simulations with the ELMFIRE and GENE codes.  The first part of the thesis presents the verification of ELMFIRE predictions against theoretical estimates of fundamental physics properties with ad-hoc plasma parameters. The simulation predictions agree quantitatively with the analytical estimates for the neoclassical mean plasma flow and electrical conductivity in different collisionality regimes. ELMFIRE predictions for the frequency of oscillating flows are also within a few percent of the analytical estimate.  The second part presents studies of isotope effect on transport and plasma flows in Ohmic tokamak plasmas. Gyrokinetic simulations predict decreased particle transport, when the fuel is switched from hydrogen to deuterium and other parameters remain comparable in the FT-2 tokamak. Experimental measurements of the corresponding plasmas validate the prediction qualitatively. Simulations indicate that the reduction of particle flux results from less intense fluctuations at small spatial scales for the heavier isotope. Linear analysis of turbulence identifies the dominant instability as the trapped electron mode driven by the density gradient. Experiments and simulations show clear evidence of geodesic acoustic mode (GAM) activity; they follow an isotopic scaling of GAM frequency, wavelength, and amplitude. The interplay of GAM and turbulence results in modulation of particle flux, which is more distinct for the deuterium plasma. The deuterium parameters also have a larger GAM amplitude. The simulations predict that both neoclassical effects and turbulence determine the mean flow profile in the plasmas, and that the safety factor profile is important for the organisation of mean flows and turbulence.
  • Theoretical and numerical methods for kinetic simulation of plasmas
    (2023) Zonta, Filippo
     School of Science | Doctoral dissertation (article-based)
    Understanding and simulating the dynamics of plasmas in Tokamak devices is a crucial aspect of the plasma physics research, especially with the upcoming ITER device. The development of numerical schemes that possess conservation laws over the vast time scale that covers the dynamics of charged particles in fusion plasmas is an intimidating yet a very important task. This thesis presents novel numerical and theoretical techniques to tackle this problem. First, an overview of the kinetic theory, in particular the derivations of the Vlasov equation, the Fokker-Planck equation and the Vlasov-Maxwell equation in a variational setting, is given. The Euler-Poincar\'{e} reduction, which is a powerful mathematical tool that allows to derive the the Vlasov-Maxwell equations in a straightforward way, is presented as well. A multi-species, marker based, structure-preserving numerical code for the Landau equation is presented. The code is able to preserve energy and momentum to machine precision and leverages GPU-computing to efficiently scale with the dimension of the system. The scheme was validated against relaxation, isotropization and thermalization theoretical estimates for different mass-ratio of the species, including a real electron-deuteron case, showing good agreement in all performed tests. Finally, the problem of fast ions is tackled by introducing the Backward Monte Carlo (BMC) scheme. The approach aims at increasing the poor statistics of current Forward Monte Carlo simulations by integrating the probability of fast ions backward in time and taking into account deterministically the spread of the Monte Carlo collision operator. The scheme was implemented as a module of the orbit following code ASCOT5, enabling high performance simulations especially with modern supercomputers, and test cases with realistic plasma profiles, magnetic fields and wall geometries. The BMC scheme was applied to a realistic ASDEX Upgrade configuration of beam-ion distributions, with a Fast-Ion Loss Detector (FILD) placed near the divertor. The results shows a substantial increase of wall hits compared to a standard Forward Monte Carlo simulation.
  • Towards realistic orbit-following simulations of fast ions in ITER
    (2014) Snicker, Antti
     School of Science | Doctoral dissertation (article-based)
    One of the main scientific goals of the international ITER experiment is to provide understanding of burning plasmas, including the behavior of fusion-born alpha particles. These particles form both a potential risk for the first wall and a massive source of free energy in the plasma. Such free energy can drive a multitude of MHD modes, most notably the Alfvénic ones, that can lead to increased transport and even losses of fast ions. In this work, the alpha particle physics has been studied using kinetic orbit-following Monte Carlo code ASCOT. The code was enhanced with two new physics models. The first model relaxes the usual guiding center (GC) approximation used to save computation time. In some cases, this approximation is not valid and the full gyro motion (FO) has to be resolved. The second model is for fast ion relevant MHD modes and its implementation allows taking into account electromagnetic fields due to these modes. When the MHD model was used to simulate ITER plasmas, the wall power loads due to fast particles were not found to exceed the design limits of the wall materials even for unrealistically large perturbations. However, redistribution of fast ions was observed to alter the alpha particle heating profile and neutral beam ion (NBI) driven current profile. Fusion alphas were simulated for the ITER 15 MA scenario using different integration methods. Following the full gyro motion gave slightly larger alpha particle wall power loads than the GC method. Since the FO method uses more than 50 times more CPU than GC integration, a third method was introduced as a compromise between the speed and accuracy: the GC method is used in the plasma core and FO integration is activated in the vicinity of the wall. Finally, alpha-driven current and torque in ITER were studied using different magnetic field configurations. It was found that, independent of the magnetic configurations, the alpha-driven current is less than 1% of the total plasma current for both 9 MA and 15 MA baseline scenarios. On the contrary, the alpha-driven torque depends on the magnetic field configuration. While in the axisymmetric case the total torque was found to be close to zero, with realistic 3D effects the alpha particles produced substantial torque, about one tenth of that driven by the NBI particles, but in direction opposite to it.
  • Validation of tungsten erosion and transport simulations in tokamaks
    (2023) Kumpulainen, Henri
     School of Science | Doctoral dissertation (article-based)
    This dissertation evaluates the validity and options for improvement of simulation codes in predicting tungsten erosion and transport in tokamaks, by code-code comparisons and validation against measurements from JET and ASDEX Upgrade experiments. Tungsten is a leading candidate as the plasma-facing material in magnetic confinement fusion power plants. However, W contamination of the fusion plasma is highly detrimental to reactor performance and impedes the attainment of viable power production. The ability to predict the erosion rate of W components and the resulting W density in the plasma is crucial for designing fusion reactors. The simulations studied in this thesis predict the sputtering of W atoms from plasma-facing components, their ionisation in the scrape-off layer, and the transport of W ions parallel and perpendicular to the magnetic field in the scrape-off layer, pedestal, and core plasma regions. In this thesis, the predicted W erosion rate at the JET divertor targets is found to have a negligible impact on the W density in the main plasma due to efficient divertor screening. According to EDGE2D-EIRENE, DIVIMP, and ERO2.0 predictions, the W influx to the main plasma is predominately due to W sputtering near the low-field side divertor entrance due to energetic D atoms created by charge-exchange. EDGE2D-EIRENE consistently predicts 30--40% lower W density in the main plasma compared to DIVIMP in both L-mode and H-mode plasmas. In this work, the difference is demonstrated to be mostly due to the bundling of the 74 W ionised charge states into 6 fluid species in EDGE2D-EIRENE. Integrated core-edge JINTRAC predictions agree with measurements of the main plasma W density in L-mode, indicating that both the DIVIMP and EDGE2D-EIRENE predictions are consistent with the experimentally inferred W density within a factor of 2. Simulations of high-power type-I ELMy H-mode plasmas, using ERO2.0 for W erosion and transport in the edge plasma and JINTRAC with NEO for core W transport, predict the 2D poloidal W density profile in agreement with the inferred W density within the modelling uncertainties. Accurate predictions of the main plasma W density in type-I ELMy H-mode require thorough validation of the simulated ELM and edge transport barrier properties, as well as precise reproduction of the toroidal rotation frequency, and the ion temperature and density gradients in the main plasma.