Soliton generation and drift wave turbulence spreading via geodesic acoustic mode excitation

Abstract

The two-field equations that govern fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived within the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed using both analytical and numerical approaches. In the ‘linear’ growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability, accounting for the spontaneous resonant excitation of GAM by the DW. The main results of previous works on spontaneous GAM excitation, e.g. the greatly enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of the DW. The soliton structures enhance turbulence spreading from the DW linearly unstable region to the stable region, exhibiting convective propagation instead of a typical linear dispersive process, and are thus expected to induce core-edge interaction and nonlocal transport.

Nonlinear excitation of geodesic acoustic mode by reversed shear Alfvén eigenmodes in non-uniform plasmas

“…In this work, we will investigate the linear growth stage of the excitation of GAM by the pump RSAE, with emphases on the effects of plasma non-uniformities, such as non-uniform KRSAE and GAM continuum frequencies and the finite spatial extent of the pump RSAE (which is also determined by the RSAE continuum), on the parametric decay process. By 'linear growth stage', we mean the feedback of GAM and KRSAE onto the pump RSAE are systematically neglected, which, can become important as the sidebands amplitudes become comparable to the pump RSAE amplitude, and lead to, potentially, complex nonlinear dynamics as well as ballistic mode propagation in the form of solitons (Guo, Chen & Zonca 2009;Chen & Zonca 2016;Chen et al 2022). These effects, however, are beyond the scope of present work and focus on the effects of system non-uniformity, and will be investigated in the future.…”

“…By ‘linear growth stage’, we mean the feedback of GAM and KRSAE onto the pump RSAE are systematically neglected, which, can become important as the sidebands amplitudes become comparable to the pump RSAE amplitude, and lead to, potentially, complex nonlinear dynamics (Wei, Chen & Qiu 2022) as well as ballistic mode propagation in the form of solitons (Guo, Chen & Zonca 2009; Chen & Zonca 2016; Chen et al. 2022). These effects, however, are beyond the scope of present work and focus on the effects of system non-uniformity, and will be investigated in the future.…”

“…Good confinement of energetic particles (EP) including fusion alpha particles is crucial to improve the burning plasma performance and reduce the wall loading of plasma facing materials in the next generation magnetic confinement fusion devices, such as ITER and CFETR (Tomabechi et al 1991;Fasoli et al 2007;Ding et al 2015;Chen & Zonca 2016;Wan et al 2017). Shear Alfvén wave (SAW) instabilities, including Alfvén eigenmodes (Cheng, Chen & Chance 1985) (AEs) and EP continuum modes (Chen 1994), can be resonantly excited by the expansion free energy associated with the non-uniform EP distribution, since EPs have similar characteristic frequencies as those of SAW in typical reactor parameter regimes (Fasoli et al 2007).…”

“…Shear Alfvén wave (SAW) instabilities, including Alfvén eigenmodes (Cheng, Chen & Chance 1985) (AEs) and EP continuum modes (Chen 1994), can be resonantly excited by the expansion free energy associated with the non-uniform EP distribution, since EPs have similar characteristic frequencies as those of SAW in typical reactor parameter regimes (Fasoli et al 2007). Even finite amplitude SAW instabilities may cause significant anomalous EP loss and performance degradation (Zonca et al 2015;Chen & Zonca 2016), it is, thus, necessary to have in-depth understanding of the spectrum of SAW, which depends crucially on the nonlinear dynamics of SAW.…”

“…There are two possible routes for the nonlinear evolution of EP-driven SAW instability: nonlinear wave-particle phase space dynamics (Berk & Breizman 1990;Todo et al 1995;Zhu, Fu & Ma 2013;Zonca et al 2015;Wang et al 2019) and nonlinear wave-wave interactions (Sagdeev & Galeev 1969;Hahm & Chen 1995;Chen & Zonca 2013), among which, three-wave parametric decay instability is one of the most fundamental nonlinear wave-wave interactions (Sagdeev & Galeev 1969). Considering the optimal steady state operation scenario of reactors with full non-inductive current drive (Huang et al 2020), as a specific branch of SAW, the reversed shear Alfvén eigenmode (RSAE) (an alternative name is Alfvén cascades) exists close to the flux surface of q min (Berk et al 2001), and can be preferentially excited by fusion produced alpha particles in the core plasmas (Wang et al 2018).…”