Xin Wang

Accurate modeling of core instabilities in tokamak plasmas is essential to understand the underlying physical mechanisms and their impact on plasma confinement. The ideal stability of the internal kink mode and the m=1 collisionless tearing mode are analyzed numerically both with gyrokinetic and magnetohydrodynamic (MHD) codes. The simulation results show that the stability of the internal kink mode strongly depends on the choice of several setup parameters like the inclusion of parallel magnetic field fluctuations, the tokamak aspect ratio, the drift kinetic or gyrokinetic treatment of the ions, and the electron mass. Furthermore, we demonstrate the stabilization of the instabilities by diamagnetic effects. Our results indicate that gyrokinetic and MHD models can be reconciled in the description of the internal kink mode by careful consideration of the simulation setup and model assumptions, but instabilities like the collisionless tearing mode require a more advanced treatment beyond MHD.

We review the physics of energetic particles (EPs) in magnetically confined burning fusion plasmas with focus on advances since the last update of the ITER Physics Basis (Fasoli et al 2007 Nucl. Fusion 47 S264). Topics include basic EP physics, EP generation, diagnostics of EPs and instabilities, the interaction of EPs and thermal plasma instabilities, EP-driven instabilities, energetic particle modes (EPMs), and turbulence, linear and nonlinear stability and simulation of EP-driven instabilities and EPMs, 3D effects, scenario optimization strategies based on EP phase-space control, EPs in reduced field scenarios in ITER before DT, and the physics of runaway electrons. We describe the simulation and modeling of EPs in fusion plasmas, including instability drive and damping as well as EP transport, with a range of approaches from first-principles to reduced models, including gyrokinetic simulations, kinetic-MHD models, gyrofluid models, reduced models, and semi-analytical approaches.

The nonlinear dynamics of toroidal Alfvén eigenmodes (TAEs) driven unstable by the resonant interaction with trapped energetic particles and, to a lesser extent, with nonstandard copassing particles are analyzed using simulations performed with the HMGC code (Hybrid Magnetohydrodynamic Gyrokinetic Code). The magnetic equilibrium considered is the low-shear configuration from the International Tokamak Physics Activity benchmark. The detailed investigation of the nonlinear mode-particle dynamics is based on the Hamiltonian-mapping approach, where the resonant phase-space structure is sampled by a large number of test particles evolving in the perturbed fields computed in the self-consistent simulations. Several precession-bounce resonances effectively drive the TAE unstable. Around each resonance radius, density mixing occurs as resonant particles form closed-trajectory islands in the (phase, radius) space. It is shown that these islands, whose width increases with the mode amplitude, eventually coalesce, leading to global density mixing. It causes a sudden reduction in the mode-particle power exchange, which is the main saturation mechanism when the energetic-particle density is relatively high. Correspondingly, the scaling of the saturation amplitude with the mode growth rate is slightly weaker than linear, similar to the radial-decoupling scaling observed in previous papers. This result is consistent with the observation that the width of the density-mixing region is limited, at saturation, by the mode width, which is nearly independent of the growth rate. At lower energetic-particle densities, local density mixing around each isolated resonance effectively reduces the power transfer, causing a transition to a stronger scaling, similar to the resonance-detuning regime reported in the literature.

In this work, we use the global electromagnetic and electrostatic gyro kinetic approaches to investigate the effects of zonal flows forced-driven by Alfvén modes due to their excitation by energetic particles on the dynamics of ITG (ion temperature gradient) instabilities. The equilibrium of the 92416 JET tokamak shot is considered. The linear, nonlinear Alfvén modes, and the zonal flow dynamics are investigated, and their respective radial structures and saturation levels are reported. ITG dynamics in the presence of the zonal flows excited by these Alfvén modes are also investigated. The zonal flows forced-driven by Alfvén modes can significantly impact the ITG dynamics. A zonal flow amplitude scan reveals the existence of an inverse relation between the zonal flow amplitude and the ITG growth rate. These results indicate that forced-driven zonal flows can be an important indirect part of turbulence mitigation due to the injection of energetic particles.

Frequency chirping of Alfvén modes, a phenomenon observed in tokamak fusion plasmas driven by energetic particles (EPs), can result in significant losses of EPs. In this study, we use the global gyrokinetic code ORB5 (Lanti et al 2020 Comput. Phys. Commun. 251 107072) to investigate the nonlinear dynamics of non-adiabatic frequency chirping EP modes (EPMs). Our results illuminate non-perturbative features of EPMs caused by the presence of EPs. Additionally, we find that, with a fixed safety factor profile and a single toroidal mode number, the frequency chirping rate is linearly proportional to the mode saturation amplitude, as predicted by the theory (Chen and Zonca 2016 Rev. Mod. Phys. 88 015008).

Energetic particle (EP)-driven instabilities will be of strongly increased relevance in future burning plasmas as the EP pressure will be very large compared to the thermal plasma pressure. Understanding the interaction of EPs and bulk plasma is crucial for developing next-generation fusion devices. In this work, the JOREK magnetohydrodynamic code and its full-f kinetic particle-in-cell module are extended by an anisotropic pressure coupling model to allow for the simulation of EP instabilities at high EP pressures using realistic plasma and EP parameters. Furthermore, a diagnostic is implemented to allow for the visualization of phase-space resonances. The resulting code is first benchmarked linearly for the International Tokamak Physics Activity-toroidal Alfvén eigenmodes as well as the experiment-based ASDEX-Upgrade-NonLinear Energetic particle Dynamics cases, obtaining good agreement with other codes. Then, it is applied to a high energetic particle pressure discharge in the ASDEX Upgrade tokamak using a realistic non-Maxwellian distribution of EPs, reproducing aspects of the experimentally observed instabilities. Non-linear applications are possible based on the implementation, but will require dedicated verification and validation left for future work.

In the present paper, the evolution of the Alfvén modes (AMs) is studied in a realistic ASDEX Upgrade equilibrium by analyzing the results of simulations with the global, electromagnetic, gyrokinetic particle-in-cell code ORB5. The energetic particles (EPs) are modelled both via the newly implemented isotropic slowing-down and with Maxwellian distribution functions. The comparison of the numerical results shows that modelling the EPs with the equivalent Maxwellian rather than with the slowing-down, does not significantly affect the frequency of the driven AM, while its growth rate appears to be underestimated with a quantitative difference as large as almost 30%. Additionally the choice of the isotropic slowing-down allows a better description of the nonlinear modification of the dominant AM frequency, while an equivalent Maxwellian underestimates it. A good comparison with the experimental spectrogram is found.

Chirping Alfvén modes are considered as potentially harmful for the confinement of energetic particles in burning tokamak plasmas. In fact, by changing their frequency, they are able to extract as much power as possible from these particles, possibly increasing their transport. In this paper, the nonlinear evolution of a single-toroidal-number chirping mode is analyzed by numerical particle simulation. The relevant resonant structures are identified by numerical techniques based on the use of a coordinate system including two constants of motion: the magnetic moment and a suitable function of the initial particle coordinates. The analysis is focused on the dynamics of two different resonant structures in the particle phase space: those yielding the largest drive during the linear and the nonlinear phase, respectively. It is shown that, for each resonant structure, a density-flattening region is formed around the respective resonance radius, with a radial width that increases as the mode amplitude grows. It is delimited by two steepened negative density gradients, drifting inwards and outward. If the mode frequency were constant, phase-space density flattening would quench the resonant-structure drive as the steepened gradients leave the original resonance region. The frequency chirping, however, causes the resonance radius and the resonance region to drift inwards. This drift, along with a relevant increase in the resonance width, delays the moment in which the inner density gradient reaches the inner boundary of the resonance region, leaving it. On the other hand, the island evolves consistently with the resonance radius; as a consequence, the steepened density gradient further moves inward. This process continues as long as it allows to keep the steepened gradient within the resonance region. When this is no longer possible, the resonant structure ceases to be effective in driving the mode. To further extract energy from the particles, the mode has to tap a different resonant structure, possibly making use of additional frequency variations.