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.

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.

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.

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 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.

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)