This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis Nucl. Fusion 39 2137 in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

Linear and nonlinear particle-magnetohydrodynamic ͑MHD͒ simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with the slowing-down distribution are considered and the behavior of nϭ2 toroidal Alfvén eigenmodes ͑TAE modes͒ is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation, two nϭ2 TAE modes are destabilized and alpha particle losses induced thereby are observed. Counterpassing particles are lost when they cross the passing-trapped boundary. They are the major part of lost particles, but trapped particles are also lost appreciably.

Nonlinear magnetohydrodynamic (MHD) effects on Alfvén eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfvén eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, δB/B ∼ 10−3. In contrast, when the TAE saturation level predicted by the linear code is δB/B ∼ 10−2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n ⩾ 8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.

This article is a tutorial review of the interaction between energetic particles and Alfvén eigenmodes (AEs) which is one of the important research issues for fusion burning plasmas. The destabilization mechanism of AEs is a kind of inverse Landau damping through the resonant interaction with energetic particles. The important properties of the AE instability, such as resonance condition, conserved variable during the interaction, and particle trapping by the AE, are explained. The time evolution of AEs is classified into various types, steady state, frequency splitting, frequency chirping, and recurrent bursts. Berk and Breizman presented both a onedimensional weakly nonlinear theory for marginal stability and a reduced simulation model that qualitatively explain the various types of time evolution. Berk-Breizman's theory and reduced simulation model are introduced, and their limitations and the future works are discussed in this article. In addition, energetic particle transport by AEs is illustrated with surface-of-section plots. The particle trapping by the AE creates phase space islands and leads to the local flattening of the energetic particle spatial profile. The resonance overlap of multiple AEs and the overlap of higherorder resonances of a single AE lead to the emergence of stochasticity in phase space and the global transport of energetic particles.

A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a magnetohydrodynamic (MHD) fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic tluctuation of n=2 mode develops and saturates at the level of 1.8X 10m3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. after saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TAE mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite-amplitude wave, causes the saturation. From the linear growth rate the saturation Ievel can be estimated. 0 1995 American Institute of Physics.

Recurring bursts of chirping Alfvén modes that were observed in JT-60U tokamak plasmas driven by negative-ion-based neutral beams (N-NB) are reproduced in first-principle simulations performed with an extended version of the hybrid code MEGA. This code simulates the interactions between gyrokinetic fast ions and magnetohydrodynamic (MHD) modes in the presence of a realistic fast ion source and collisions, so that it self-consistently captures dynamics across a wide range of time scales (0.01-100 ms). The simulation confirms that the experimentally observed phenomena known as "fast frequency sweeping (fast FS) modes" are caused by bursts of energetic particle modes (EPM) with dominant toroidal mode number n = 1. On the long time scale (1-10 ms), the simulation reproduces the chirping range (40-60 kHz), the burst duration (few ms) and intervals (5-10 ms). On the short time scale (0.01-0.1 ms), it reproduces pulsations and phase jumps, which we interpret as the result of beating between multiple resonant wave packets. Having reproduced at multiple levels of detail the dynamics of low-amplitude long-wavelength Alfvén modes driven by N-NB ions, the next goal is to reproduce and explain abrupt large-amplitude events (ALE) that were seen in the same experiments at longer time intervals (10-100 ms).

Properties of energetic-particle continuum modes ͑EPMs͒ destabilized by energetic ions in tokamak plasmas were investigated using a hybrid simulation code for magnetohydrodynamics and energetic particles. The energetic ions are assumed to have beam-like velocity distributions for the purpose of clarifying the dependence on energetic ion velocity. It was found that for beam velocities lower than the Alfvén velocity, the unstable modes are EPMs while the toroidal Alfvén eigenmodes are unstable for the beam velocities well above the Alfvén velocity. The EPMs destabilized by the copassing energetic ions and those destabilized by the counterpassing energetic ions differ in primary poloidal harmonics and spatial locations. The frequencies of the EPMs are located close to the shear Alfvén continuous spectrum when they are compared at the spatial peak locations of the primary poloidal harmonic or compared at the spatial tails if the primary poloidal harmonic is m = 1. The frequencies of the EPMs were carefully compared with the energetic-ion orbital frequencies. It was found that the frequencies of the EPMs are in good agreement with the energetic-ion orbital frequencies with a correction for the toroidal circulation frequency. This demonstrates that the energetic-ion orbital frequency determines the EPM frequency.

We have developed a multi-phase simulation that is a combination of classical and hybrid simulations for energetic particles interacting with an MHD fluid to simulate the nonlinear dynamics on slowing down time scales of the energetic particles [1]. The hybrid simulation code MEGA is extended with realistic beam deposition profiles, collisions, and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111 [2], the stored fast ion energy is saturated due to Alfvén eigenmodes (AE) at a level lower than in the classical simulation. Figure 1 shows the time evolutions of stored fast ion energy and MHD kinetic energy. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. We see in Fig The dominant modes found are toroidal Alfvén eigenmodes (TAE), which is consistent with the experimental observation at the simulated time. The n=1 and 2 modes have also a property like energetic particle mode such that their peak is located on the continuum. The amplitude of the temperature fluctuations brought about by the TAEs is of the order of 1% of the equilibrium temperature which is comparable to electron cyclotron emission measurements in the experiment. In the standard run, the amplitude of the TAE modes is v/v A~δ B/B~3-6 10 -4 for n=1-4, and the fast ion pressure profile is more flattened than that in the experiment. We expect that the half and third energy beam components, which are not included in the present simulations with the beam deposition power 4.95 MW, would increase the beam deposition power to 6.25 MW and make the fast ion pressure closer to the experiment.We carried out two more multi-phase simulations with different dissipation coefficients. Significant flattening of fast ion spatial profile takes place over a range of one order of magnitude for the dissipation coefficients. The kinetic energy of the MHD fluctuations is roughly in proportion to the inverse of the dissipation coefficients. This is consistent with the result that the significant flattening of fast ion spatial profile takes place for all the dissipation coefficients. The physics model in this study does not include kinetic damping of AE modes such as radiative damping and thermal ion Landau damping. The dissipation coefficients enable us to control the damping rate, and we can adjust dissipation coefficients to match the experimental fast ion profile.