Ion cyclotron resonance heating is a versatile heating method that has been demonstrated to be able to efficiently couple power directly to the ions via the fast magnetosonic wave. However, at temperatures relevant for reactor grade devices such as DEMO, electron damping becomes increasingly important. To reduce electron damping, it is possible to use an antenna with a power spectrum dominated by low parallel wavenumbers. Moreover, using an antenna with a unidirectional spectrum, such as a travelling wave array antenna, the parallel wavenumber can be downshifted by mounting the antenna in an elevated position relative to the equatorial plane. This downshift can potentially enhance ion heating as well as fast wave current drive efficiency. Thus, such a system could benefit ion heating during the ramp-up phase and be used for current drive during flat-top operation. To test this principle, both ion heating and current drive have been simulated in a DEMO-like plasma for a few different mounting positions of the antenna using the FEMIC code. We find that moving the antenna off the equatorial plane makes ion heating more efficient for all considered plasma temperatures at the expense of on-axis heating. Moreover, although current drive efficiency is enhanced, electron damping is reduced for lower mode numbers, thus reducing the driven current in this part of the spectrum.

Ion cyclotron resonance heating (ICRH) has the potential of providing efficient ion heating of reactor grade fusion plasmas especially during the start-up phase. In order to assess such heating scenarios, ICRH modelling is required. However, the physics is complex and certain elements are not universally taken into account in ICRH modelling. In this paper we discuss the importance of including Doppler shift displacements of resonance points away from the cold resonance (i.e. where ω = n Ω c ) in Fokker-Planck calculations of the distribution function of resonating ions. In particular, the resonant interaction time and the wave electric field varies with the local Doppler shifted resonance positions. The importance of accounting for these variations in Fokker-Planck modelling is investigated. Furthermore, it is shown how these effects can be included in a simplified Fokker-Planck treatment that is sufficiently quick for integrated modelling frameworks of fusion plasmas. Because 2D effects in velocity space play a crucial role in determining Doppler shifts, we employ a model of the anisotropy of the non-thermal distribution function. Simulation results show that taking the Doppler effects into account in Fokker-Planck modelling can have a significant impact on the distribution functions of fast ions and important quantities, such as the collisional power transfer to the background plasma. This is especially important in cases where the poloidal variation of the left-hand component of the wave electric field is strong.

Nuclear fusion can provide large amounts of energy from earth-abundant elements,with no carbon emissions and little radioactive waste. For the nuclei to fuse under earth-relevant conditions, temperatures in excess of 100 000 000 °C are needed. At these temperatures, the fuel is in a plasma state. A common method to heat the plasma is ion cyclotron resonance heating (ICRH), where radiofrequency waves are launched from an antenna on the vessel wall into the plasma to resonate with the gyrating ions. Wave propagation and dissipation in hot magnetized plasmas is a nonlocal process, where the plasma response at a given point depends on the particles' cumulative acceleration along their orbits. To quantify how the plasma is heated, numerical simulations are required. This thesis aims to provide a numerical framework that can simulate the coupling of the wave from the antenna to the plasma, the wave propagation and dissipation inside the plasma, as well as the acceleration of individual ions and how they deposit their energy in the plasma. 

To this end, an iterative scheme that adds nonlocal effects to an otherwise local finite element (FE) model is developed. FE models are suitable for modeling irregular geometries and wave coupling through the cold scrape-off layer plasma, but not necessarily the hot core plasma. Examples of nonlocal effects that are added iteratively are mode conversion from the fast magnetosonic wave to the ion Bernstein wave (IBW) and up- and downshift of the parallel wavenumber. Further, the wave solver is coupled to a Fokker-Planck solver that evaluates the effect of ICRH on the ion distribution function. The models presented in this thesis are in 1D or 2D axisymmetry, but are not conceptually different from a generalization to 3D.

Kärnfusion kan producera stora mängder energi från vanligt förekommande grundämnen på jorden utan att släppa ut koldioxid, och ger endast upphov till små mängder radioaktivt avfall. För att atomkärnor ska slås samman under förhållanden som är relevanta för jorden krävs temperaturer som överstiger 100 000 000 °C. Vid dessa temperaturer befinner sig bränslet i ett plasmatillstånd. En vanlig metod för att värma plasman är jon-cyclotronresonans-uppvärmning (ICRH), där radiovågor skickas från en antenn på kärlets vägg in i plasmat för att resonera med de roterande jonerna. Vågutbredning och dissipation i varma magnetiserade plasman är en ickelokal effekt, där plasmats svar i en given punkt beror på partiklarnas ackumulerade acceleration längs deras banor. För att kvantifiera hur ett plasma värms upp krävs numeriska simuleringar. Målet med denna avhandling är att tillhandahålla ett numeriskt ramverk för simulering av koppling av vågen från antennen till plasmat, vågutbredning och dissipation inuti plasmat, samt accelerationen av enskilda partiklar och hur de deponerar sin energi i plasmat.

För att uppnå detta har en iterativ metod som lägger till ickelokala effekter till en i övrigt lokal modell baserad på finita elementmetoden utvecklats. Den finita elementmetoden är lämplig för att modellera oregelbundna geometrier och vågkoppling genom det kalla randplasmat, men inte det varma plasmat i mitten av maskinen. Exempel på ickelokala effekter som läggs till iterativt är modkonvertering från den snabba magnetosoniska vågen till jon-Bernstein-vågen, och upp- och nedskiftet av det parallella vågtalet. Dessutom kopplas våglösaren till en Fokker-Planck-lösare som utvärderar effekten som ICRH har på jonernas fördelningsfunktion. Modellerna som presenteras i avhandlingen är i 1D eller 2D och rotationssymmetriska, men skiljer sig inte konceptuellt från en generalisering till 3D.

During ion cyclotron resonance heating (ICRH) in fusion plasmas the fast magnetosonic wave transports wave energy to the plasma core, where it is transferred to both electrons, thermal ions and fast ions. The modelling of these processes requires a self-consistent treatment of the wave propagation and absorption, as well as the acceleration of fast ions by the wave. Here, a new self-consistent model is presented based on the FEMIC full wave solver [1] and the FOPPLER Fokker-Planck solver [2]. The use of optimised commercial wave solvers in FEMIC and a reduced 1D Fokker-Planck model make the model relatively fast and therefore suitable for e.g. the use in a transport solver.The novelty of this model, compared to other codes with 1D Fokker-Planck models, is the consistent description of Doppler physics in the FEMIC and FOPPLER codes. This description is of particular interest for scenarios with strong absorption around the ion-ion hybrid layer, like in 3-ion scenarios [3] and certain minority scenarios. Here we will present modelling of such scenarios, quantifying the impact of the Doppler shift, as well as characterising the non-linear effects associated with the acceleration of fast ions.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

References:[1] P. Vallejos et al., Nuclear Fusion 59, 076022 (2019)[2] L. Bähner et al., to be submitted (2024) [3] Y.O. Kazakov et al., Nuclear Fusion 55, 032001 (2015)

The current response of a hot magnetized plasma to a radio-frequency wave is non-local, turning the electromagnetic wave equation into an integro-differential equation. Non-local physics gives rise to wave physics and absorption processes not observed in local media. Furthermore, non-local physics alters wave propagation and absorption properties of the plasma. In this work, an iterative method that accounts for parallel non-local effects in 2D axisymmetric tokamak plasmas is developed, implemented, and verified. The iterative method is based on the finite element method and Fourier decomposition, with the advantage that this numerical scheme can describe non-local effects while using a high-fidelity antenna and wall representation, as well as limiting memory usage. The proposed method is implemented in the existing full wave solver FEMIC and applied to a minority heating scenario in ITER to quantify how parallel non-local physics affect wave propagation and dissipation in the ion cyclotron range of frequencies (ICRF). The effects are then compared to a reduced local plane wave model, both verifying the physics implemented in the model, as well as estimating how well a local plane wave approximation performs in scenarios with high single pass damping. Finally, the new version of FEMIC is benchmarked against the ICRF code TORIC.

In 2021 JET exploited its unique capabilities to operate with T and D-T fuel with an ITER-like Be/W wall (JET-ILW). This second major JET D-T campaign (DTE2), after DTE1 in 1997, represented the culmination of a series of JET enhancements-new fusion diagnostics, new T injection capabilities, refurbishment of the T plant, increased auxiliary heating, in-vessel calibration of 14 MeV neutron yield monitors-as well as significant advances in plasma theory and modelling in the fusion community. DTE2 was complemented by a sequence of isotope physics campaigns encompassing operation in pure tritium at high T-NBI power. Carefully conducted for safe operation with tritium, the new T and D-T experiments used 1 kg of T (vs 100 g in DTE1), yielding the most fusion reactor relevant D-T plasmas to date and expanding our understanding of isotopes and D-T mixture physics. Furthermore, since the JET T and DTE2 campaigns occurred almost 25 years after the last major D-T tokamak experiment, it was also a strategic goal of the European fusion programme to refresh operational experience of a nuclear tokamak to prepare staff for ITER operation. The key physics results of the JET T and DTE2 experiments, carried out within the EUROfusion JET1 work package, are reported in this paper. Progress in the technological exploitation of JET D-T operations, development and validation of nuclear codes, neutronic tools and techniques for ITER operations carried out by EUROfusion (started within the Horizon 2020 Framework Programme and continuing under the Horizon Europe FP) are reported in (Litaudon et al Nucl. Fusion accepted), while JET experience on T and D-T operations is presented in (King et al Nucl. Fusion submitted).

Within the 9th European Framework programme, since 2021 EUROfusion is operating five tokamaks under the auspices of a single Task Force called ‘Tokamak Exploitation’. The goal is to benefit from the complementary capabilities of each machine in a coordinated way and help in developing a scientific output scalable to future largre machines. The programme of this Task Force ensures that ASDEX Upgrade, MAST-U, TCV, WEST and JET (since 2022) work together to achieve the objectives of Missions 1 and 2 of the EUROfusion Roadmap: i) demonstrate plasma scenarios that increase the success margin of ITER and satisfy the requirements of DEMO and, ii) demonstrate an integrated approach that can handle the large power leaving ITER and DEMO plasmas. The Tokamak Exploitation task force has therefore organized experiments on these two missions with the goal to strengthen the physics and operational basis for the ITER baseline scenario and for exploiting the recent plasma exhaust enhancements in all four devices (PEX: Plasma EXhaust) for exploring the solution for handling heat and particle exhaust in ITER and develop the conceptual solutions for DEMO. The ITER Baseline scenario has been developed in a similar way in ASDEX Upgrade, TCV and JET. Key risks for ITER such as disruptions and run-aways have been also investigated in TCV, ASDEX Upgrade and JET. Experiments have explored successfully different divertor configurations (standard, super-X, snowflakes) in MAST-U and TCV and studied tungsten melting in WEST and ASDEX Upgrade. The input from the smaller devices to JET has also been proven successful to set-up novel control schemes on disruption avoidance and detachment.

Modelling the propagation and dissipation of RF waves in the ion cyclotron range of frequencies is challenging due to the presence of spatial dispersion. In this work, we are presenting an iterative scheme that includes dispersive effects in all tensor elements in 2D axisymmetry. The proposed method is implemented in the existing full wave solver FEMIC and applied to two fast wave heating scenarios, one with an ITER-like plasma and the other with an AUG-like plasma, in order to evaluate the importance of parallel dispersion in the two different cases. It was found that parallel dispersion is of marginal importance in ITER when using dipole phasing, but has larger impact on the power deposition profiles in AUG, due to up-down asymmetric heating. Furthermore, it is shown that the described iterative method can account for mode conversion to the ion cyclotron wave.

Modeling the propagation and damping of electromagnetic waves in a hot magnetized plasma is difficult due to spatial dispersion. In such media, the dielectric response becomes non-local and the wave equation an integro-differential equation. In the application of RF heating and current drive in tokamak plasmas, the finite Larmor radius (FLR) causes spatial dispersion, which gives rise to physical phenomena such as higher harmonic ion cyclotron damping and mode conversion to electrostatic waves. In this paper, a new numerical method based on an iterative wavelet finite element scheme is presented, which is suitable for adding non-local effects to the wave equation by iterations. To verify the method, we apply it to a case of one-dimensional fast wave heating at the second harmonic ion cyclotron resonance, and study mode conversion to ion Bernstein waves (IBW) in a toroidal plasma. Comparison with a local (truncated FLR) model showed good agreement in general. The observed difference is in the damping of the IBW, where the proposed method predicts stronger damping on the IBW.

The Ion Cyclotron Resonance Heating (ICRH) antenna in WEST has been modelled with the finite element method in 3D. A detailed geometry was used along with a hot plasma model in the plasma region. The convergence of the total absorbed power and the electron power partition was studied by varying different mesh parameters. To obtain a better resolved solution and a wave field without reflections, it is estimated that 1 TB of RAM is required. The coupled power spectrum was also studied using a two-dimensional Fourier decomposition of the electromagnetic fields.