#180
hybrid fluid-kinetic simulations of resistive instabilities in runaway electron beams
Oral
Shi-Jie Liu (Max Planck Institute for Plasma Physics)
Hannes Bergstroem, Tong Liu, Hao-Wei Zhang, Matthias Hoelzl, JOREK Team
Abstract
Runaway electrons (REs) are of particular importance to the safe operation of tokamaks. Understanding the interaction between REs and magnetohydrodynamic (MHD) instabilities is crucial for predicting RE effect on the safe operation of tokamaks. Enabled by the finite plasma resistivity, current driven classical tearing modes lead to magnetic island formation. But while the bulk plasma of a RE beam is cold and highly resistive, the nearly collisionless RE current changes the physical picture and modifies both the linear stability and non-linear dynamics as confirmed by theoretical and simulation studies [1, 2]. In the JOREK code [3] RE physics can be studied in several ways. The first method relies on a fluid treatment of the REs, self-consistently coupled to the background plasmas [4]. This model does not include the energy/pitch-angle distribution of the particles or the accurate kinetic orbits, limiting the accuracy with respect to transport predictions. A novel high-fidelity model was recently developed that overcomes these limitations. It relies on a self-consistent coupling of a full-f relativistic RE particle-in-cell model to the background plasmas, either kinetically with full orbits [5] or with a computationally more efficient drift kinetic approach (this work).
In this work, first, the accurate representation of the major-radial force balance of a RE beam is verified by comparing to analytical results [6]. In a cold plasma with a highly energetic runaway beam, the equilibrium cannot be force-free, and there will be a flux surface shift related to the runaway energy, which is attributed to the curvature drift of REs. Good agreement with analytical predictions is found.
As next step, we perform a comparison to literature [1] regarding the linear growth rate of tearing modes, switching now to full 3D simulations. The growth rates in the presence of REs are found to be larger than in a highly resistive plasma, qualitatively and quantitatively reproducing the theory predictions. Another effect that the presence of the REs has on the tearing modes is a rotation of the mode in the lab frame, i.e., a real frequency. The simulation results from JOREK are compared to literature results from an eigenvalue code and M3D-C1.
Moreover, the nonlinear saturation of tearing modes is significantly influenced by the presence of REs. Previous analytical studies [2] suggested that in case of small Δ', the saturation width of the magnetic island driven by REs is roughly 1.5 times larger than the island width in the otherwise identical Ohmic current scenario. Our simulations (Poincaré plots shown in Figure 2) are quantitatively in line with this prediction, confirming that RE-driven tearing modes can lead to wider islands than those generated in a thermal plasma alone. Besides, REs alter the energy evolution within the magnetic reconnection process and decouple the bulk plasma and magnetic fields. In summary, RE-driven magnetic reconnection leads to larger magnetic islands but weaker reconnection flows.
While the analytical predictions are based on fluid-like assumptions, the drift orbit shifts of highly energetic REs change the picture once more with respect to both an Ohmic plasma and RE beam where such shifts are not accounted for. We will address the effect of orbit width on the linear instability, in comparison with the resistive layer width. Future work will extend efforts towards other instabilities like external kink modes, as they are particularly relevant for achieving benign termination
REFERENCES
[1] Liu, Chang, et al. 2020. Physics of Plasmas 27 (9), 092507.
[2] P. Helander, et al. 2007. Physics of Plasmas 14 (12), 122102.
[3] Hoelzl, M., et al. 2024. Nuclear Fusion 64, 112016.
[4] V. Bandaru, et al. 2019. Phys. Rev. E 99, 063317.
[5] Hannes Bergstroem, et al. 2025. Plasma Phys. Control. Fusion 67, 035004.
[6] Bandaru, V. & Hoelzl, M. 2023. Physics of Plasmas 30 (9), 092508.