Nonlinear dynamics of Alfvén eigenmodes in toroidal plasmas

Abstract

Nonlinear saturation of toroidal Alfvén eigenmodes (TAE) via mode-mode couplings is investigated both analytically and numerically. It is demonstrated that, as the TAE mode amplitude increases, the corresponding nonlinear ponderomotive force produces a fine-structure density modulation, which then causes enhanced energy dissipation in the short scales and leads eventually to the nonlinear saturation of TAE.

Physics of Alfvén waves and energetic particles in burning plasmas

“…Again, including finite damping of SAW sideband and ISW would lead to a threshold in |Φ 0 |. We note that the current analysis has assumed (Chen andZonca, 2011, 2013)…”

“…Dispersion relations in a form similar to Eq. (3.17) have been derived in many works on the effect of EPs on low frequency MHD modes by precession resonance (Biglari and Chen, 1986;Chen et al, 1984;Coppi and Porcelli, 1986;Rewoldt and Tang, 1984;Spong et al, 1985;Weiland and Chen, 1985;White et al, 1985White et al, , 1990. Meanwhile, the generality of Eq.…”

“…After fishbone observation and theoretical interpretation, MHD modes have been considered on the same footing as SAWs concerning their possible effect on EPs confinement. Essential physics ingredients in these analyses were non-uniform equilibrium profiles of EP sources, of SAW continuous spectrum (Chen, 1988Chen et al, 1984;Cheng et al, 1985), the corresponding continuum damping by phase mixing (Grad, 1969), the specific equilibrium geometries of magnetized plasmas, and the resultant frequency gaps inside the SAW continuum (D'Ippolito and Goedbloed, 1980;Kieras and Tataronis, 1982;Pogutse and Yurchenko, 1978). In the same years, further demonstration of the articulated role played by EPs in tokamak plasmas came with the evidence of "sawtooth" 1 stabilization in plasma discharges with additional heating (Campbell et al, 1988) observed in the Joint European Torus (JET) (Rebut et al, 1985).…”

“…(Breizman and Sharapov, 2011) for a recent review]. The other paradigm may be dubbed as the "fishbone" paradigm Zonca et al, 2015b),; in which the role of magnetic field geometry and plasma nonuniformity is crucial, and wave-particle interaction may be limited due to the finite radial localization of the mode structures; i.e., "radial decoupling" Chen et al, 1984;Zonca et al, 2005). Furthermore, the self-consistent interplay of instabilities and EP transport may lead to secular EP losses due to phase locking of fluctuations and resonant particles via frequency sweeping .…”

“…They are, hence, the relevant equations for the self-consistent evolution of PSZS excited by EPs and related transport. These equations have so far been investigated only in simplified limits; i.e., either dropping the contribution of wave-particle resonances (Chen et al, , 2001Chen and Zonca, 2007b, 2012Guo et al, 2009) (cf. Sec.…”