Physics of Alfvén waves and energetic particles in burning plasmas

Abstract

Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

“…This explains why the mode is observed to shrink radially during the early nonlinear phase. The interaction with the continuum is qualitatively different for EPMs with respect to AEs [2,5,6], and this yields a lower order polynomial dependence of the nonlinear frequency on the linear drive (see Fig. 12).…”

“…Shear Alfvén waves (SAWs) are among the most unstable, because the characteristic Alfvén velocity v A = B/ √ 4π̺ (B is the equilibrium magnetic field and ̺ the mass density of the plasma) is comparable with that of the EPs. In addition, SAW group velocity is directed along the magnetic field line and, therefore, EPs can stay in resonance and effectively exchange energy with the wave [1,2]. SAW in a nonuniform equilibrium experience continuum damping [3,4], because of the formation of singular structures where the SAW continuum is resonantly excited.…”

“…Two types of shear Alfvén modes exist in tokamak plasmas: energetic-particle continuum modes (EPM) [5,6], with frequency determined by the EP characteristic frequencies, and discrete Alfvén eigenmodes (AE), with frequencies inside SAW continuum gaps [7]. EPMs can become unstable if the drive exceeds a threshold determined by the continuum damping absorption; AEs, on the other hand, are practically unaffected by continuum damping [1,2,3,4], and therefore are generally more unstable. A unified approach for weakly and strongly driven AEs and EPMs has been recently derived, based on a generalized fishbone-like dispersion relation (GFLDR), which helps extracting the underlying physics of the numerical simulations [8].…”

Effects of energetic particles on zonal flow generation by toroidal Alfvén eigenmode

“…With frequency comparable to the characteristic frequencies of EPs, and group velocities mainly along magnetic field lines, SAWs are expected to be driven unstable by resonant EPs [2][3][4][5]; leading to EP transport and degradation of overall confinement, as reviewed in Ref. 1. Toroidal Alfvén eigenmode (TAE) [6,7], excited inside the toroidicity-induced SAW continuum gap to minimize continuum damping, is one of most dangerous candidates for effectively scattering EPs.…”

“…The generated ZF has both the usual meso-scale and microscale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.Understanding the nonlinear dynamics of shear Alfvén waves (SAW) is of crucial importance to future burning plasmas with energetic particle (EP) population such as fusion-αs significantly contributing to the overall plasma energy density [1]. With frequency comparable to the characteristic frequencies of EPs, and group velocities mainly along magnetic field lines, SAWs are expected to be driven unstable by resonant EPs [2-5]; leading to EP transport and degradation of overall confinement, as reviewed in Ref.…”