Energetic electron effects on an energetic-ion driven toroidal Alfvén eigenmode (TAE) are investigated via hybrid simulations of an MHD fluid interacting with energetic particles. Both energetic electrons and energetic ions described by drift-kinetic equations are included in the present work. It is found that the TAE can be effectively stabilized by off-axis peaked energetic electrons which are located near the mode center, while the centrally peaked energetic electrons fail to stabilize the mode. It is confirmed that the spatially localized pressure profile of energetic electrons causes the stabilization of TAE. The stabilized TAE has a more localized mode structure accompanied by a significant reduction in the energetic ion driving rate. The small change of mode frequency and dissipation rate indicate the stabilization mechanism is different from the so-called pressure gradient stabilization that drives the TAE into continuum. The results suggest that the strong plasma non-uniformity induced by the energetic electron beta profile may be responsible for the change of mode structure. It is also found that this stabilizing effect is more effective for a high-n TAE. Moreover, it is numerically verified that the positive (negative) pressure gradient at the TAE center will increase (decrease) the mode frequency. The wave-particle interactions are also analysed for a case with energetic electrons peaked at the inner side of the TAE center. It is found that the power transfer to a resonant barely trapped energetic electron, which taps energy from the wave, can be comparable to the power transfer from a resonant energetic ion. This suggests that if a sufficient number of resonant barely trapped electrons are present, they might stabilize energetic-ion driven TAE through the wave-particle interaction.

A new kinetic-magnetohydrodynamic hybrid simulation model where the gyrokinetic particle-in-cell simulation is applied to both thermal ions and energetic particles is presented. Toroidal Alfvén eigenmodes (TAEs) destabilized by energetic ions in tokamak plasmas are simulated with the new simulation model. Energy channeling from energetic ions to thermal ions through Alfvén eigenmodes (AEs) is demonstrated by the simulation. The distribution function fluctuations and the resonance condition are analyzed for both thermal ions and energetic ions. The strong energy transfer between the particles and the AE and the strong particle transport occur when the following conditions are satisfied at the resonance location in phase space: (1) the poloidal resonance number is close to the poloidal mode number of the AE, (2) the AE has a substantial amplitude, (3) the distribution function has a substantial gradient along the E ′ = const. line, where E ′ is a conserved variable for the wave-particle interaction. While the distribution function fluctuations for energetic ions are consistent with the resonance condition with the TAEs, the distribution function fluctuations for thermal ions do not satisfy the resonance condition when the bulk plasma beta is 1%. This indicates that the resonance does not play an important role in the interaction between thermal ions and the TAE for the relatively low bulk plasma temperature. On the other hand, when the bulk plasma beta is 4%, the resonance between thermal ions and the TAEs become important leading to Landau damping.

The precessional fishbone instability is an m = n = 1 internal kink mode destabilized by a population of trapped energetic particles. The linear phase of this instability is studied here, analytically and numerically, with a simplified model. This model uses the reduced magneto-hydrodynamics (MHD) equations for the bulk plasma and the Vlasov equation for a population of energetic particles with a radially decreasing density. A threshold condition for the instability is found, as well as a linear growth rate and frequency. It is shown that the mode frequency is given by the precession frequency of the deeply trapped energetic particles at the position of strongest radial gradient. The growth rate is shown to scale with the energetic particle density and particles energy while it is decreased by continuum damping.

The effect of the presence of an impurity species on the trapped particle turbulence is studied using the gyro-bounce kinetic code TERESA, which allows the study of Trapped Electron Modes and Trapped Ion Modes. The impurity species is treated self-consistently and its influence on the nature of the turbulence, ion driven or electron driven, is investigated. It is found that the presence of heavy impurities with a flat density profile tends to stabilize the both electron and ion modes, whereas a peaked or hollow impurity density profile can change the turbulence from an electron driven turbulence to an ion driven turbulence. The effect of the turbulence regime on impurity transport is studied.

In gyrokinetic simulations of turbulent impurity transport, trace impurity species are often treated as passive species, in the sense that they are not included in Maxwell equations. This is consistent with the assumption that impurities with low enough concentrations are impacted by turbulence generated by electrons and main ions, but do not impact it significantly in return. In this work, we relax this assumption, and investigate the active impacts of impurity on impurity transport as a function of its concentration, in the presence of trapped-particle-driven turbulence. We focus on W 40+ tungsten, which is relevant for modern tokamaks, and adopt a reduced gyrokinetic bounce-averaged model for trapped particles in a simplified tokamak geometry. The impacts depend on the relationship between equilibrium density gradient and temperature gradient. When these gradients are equal, we observe that tungsten can be treated as a passive species for concentrations below 2 × 10 −4. Above this concentration, the impurity significantly impacts both density and heat transport, essentially quenching them for concentrations above 10 −3. This quenching occurs as electric potential fluctuations become in phase with impurity density fluctuations.

The diffusive impurity transport as a function of the charge and mass numbers is investigated in an ion driven or an electron driven turbulence, in the limit of zero impurity temperature gradient. It is found that the impurity transport decreases slightly with increasing mass number, and depends much strongly on the charge number. Moreover, this transport depends on the nature of the instability that drives turbulence. The impurity flux due to Trapped Electron Mode (TEM) turbulence increases with the charge number Z. In contrast, it is found to decrease with Z in the Trapped Ion Mode (TIM) dominated. In order to explain these observations, the quasilinear flux is derived and is compared with results obtained from the nonlinear simulations. Quasi-linear theory qualitatively reproduces the gyro-kinetic numerical observations.

In the context of temperature gradient-driven, collisionless trapped-ion modes in magnetic confinement fusion, we perform and analyse numerical simulations to explore the turbulent transport of density and heat, with a focus on the velocity dimension (without compromising the details in the real space). We adopt the bounce-averaged gyrokinetic code TERESA, which focuses on trapped particles dynamics and allows one to study low frequency phenomena at a reduced computational cost. We focus on a time in the simulation where the trapped-ion modes have just saturated in amplitude. We present the structure in velocity space of the fluxes. Both density and heat fluxes present a narrow (temperature-normalized energy width DE/T % 0.15) resonance peak with an amplitude high enough for resonant particles to contribute for 90% of the heat flux. We then compare these results obtained from a nonlinear simulation to the prediction from the quasi-linear theory and we find a qualitative agreement throughout the whole energy dimension: from thermal particles to high-energy particles. Quasi-linear theory over-predicts the fluxes by about 15%; however, this reasonable agreement is the result of a compensation between two larger errors of about 50%, both at the resonant energy and at the thermal energy.

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.