Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave–wave coupling

Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

“…Meanwhile, various nonideal effects, notably the magnetic geometry, plasma nonuniformity, compressibility and kinetic effects, could break such a 'pure Alfvénic state' [1] and lead to nonlinear spectral energy transfer by coupling with other collective oscillations [2,58,63]. These nonideal effects, which must be accounted for when studying SAW instability nonlinear dynamics and EP transport in burning plasmas, have been intensively investigated using TAE as a paradigm case [51,[120][121][122][123][124][125][126][127], as recently reviewed in [128]. The developed theoretical framework and obtained insights can be straightforwardly applied to other kinds of SAW instabilities, e.g., RSAE, which is the subject of this section, based on the understanding of RSAE linear physics and saturation due to wave-particle interactions as reviewed in section 2.…”

“…For example, considering the high frequency range with and all three SAWs are normal modes satisfying , the frequency matching conditions can be naturally satisfied. E.g., equation ( 11) can be applied for the coupling among TAE, ellipticity induced AE and noncircular triangularity induced AE [127]. If the parallel electric field due to kinetic effect is properly considered [57], equation (11) can also be generalized to describe the resonant decay and spectral cascading of KAWs in, e.g., the solar wind.…”

Effects of plasma nonuniformity on toroidal Alfvén eigenmode nonlinear decay

“…Nonlinear gyrokinetic theory is necessary for the crucial physics of ion-induced scattering in the short wavelength regime [7,43,45]. The governing equations describing the nonlinear interactions among TAMs and DSW can be derived from the quasi-neutrality condition…”

“…Here, k ⊥ is the perpendicular wavenumber, ρ i is the ion Larmor radius, and Ω ci is the ion cyclotron frequency. At short wavelengths, the dominant nonlinear terms are Reynolds and Maxwell stresses in the radially fast varying inertial layer, and nonlinear gyrokinetic theory [44] is mandatory to capture the crucial physics, as addressed in [45]. Reference [33] yields a significantly enhanced nonlinear coupling cross-section, and consequently, much lower TAE saturation level and the induced resonant circulating EP transport rate.…”