Dynamics of reversed shear Alfvén eigenmode and energetic particles during current ramp-up

Abstract

Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and non-linear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizing wave-EP power transfer. In the linear stage, EPs induce evident mode structure and frequency shifts; meanwhile, RSAE saturates by radial decoupling with resonant EPs due to weak magnetic shear, and gives rise to global EP convective transport and fast frequency chirping in the non-adiabatic regime. The spatiotemporal scales of phase space wave-EP interactions are characterized by the perpendicular wavelength and wave-particle trapping time. The simulations provide insights into general as well as specific features of the RSAE spectra and EP transport in experimental observations, and illustrate the fundamental physics of wave-EP resonant interaction with the interplay of the magnetic geometry, plasma non-uniformity and non-perturbative EPs. Possible application for understanding the non-adiabatic frequency chirping as convective and relaxation branches is also discussed.

Nonlinear reversed shear Alfvén eigenmode saturation due to spontaneous zonal current generation

“…In fact, depending on the parameter regimes such as driving/dissipative rate and the initial conditions, the system may exhibit limit cycle oscillation, period doubling as well as route to chaos (Russell, Hanson & Ott 1980). Noting that the modification to local RSAE continuum frequency is ∼ O(nδqv A /(qR)) and that for reactor burning plasma with ρ d /a ∼ O(10 −2 ) most unstable RSAEs are characterized by n O(10) (Wang et al 2018), the modification to local SAW continuum is comparable to the RSAE linear growth rate γ L R or frequency differences between different radial eigenstates (∼ Δ). Thus, one expects the ZC-induced SAW continuum modification in the vicinity of q min to play an important role in RSAE nonlinear saturation, though the self-consistent study analogous to Zonca et al (1995) and Chen et al (1998) is not presented.…”

“…the ITER; Tomabechi et al 1991) are expected to operate at steady state with a substantial non-inductive current fraction (Gormezano et al 2007), which generally renders a reversed shear scenario (Huang et al 2020). In this circumstance, the reversed shear Alfvén eigenmode (RSAE; also known as Alfvén cascade) is frequently observed (Sharapov et al 2001) as driven unstable by energetic particles (EPs) (Zonca et al 2002;Fasoli et al 2007;Chen et al 2014;Chen & Zonca 2016) in present-day tokamaks, and is expected to play significant roles in future reactors (Wang et al 2018), in transporting fusion alpha particles to the tokamak edge (Wang et al 2019), which has deleterious effects on plasma self-heating, and may damage the plasma-facing components (Ding et al 2015). The RSAE is a branch of the shear Alfvén wave (SAW) eigenmode localized radially near the minimum of the safety factor q-profile (Sharapov et al 2002), which is denoted as q min .…”

On the Effect of Beating during Nonlinear Frequency Chirping

“…In both cases, there is a convective interchange of light and dense packets of EP Vlasov fluid, with plumes of dense fluid advancing outward and vice versa. These phase space structures are nonadiabatic and may be regarded as a semi-perturbative manifestation of what Wang Tao et al [44] call "convective branch" 21 .…”

“…The radial structure ω A (ψ P ) of these spectra is known to affect chirping by providing a preferred trajectory for the chirps (e.g., see Refs. [42][43][44]) and by contributing to the field damping [45]. For the time being, we choose to ignore these effects without further justification other than saying that this simplification appears to be acceptable for our purposes.…”

“…5.1, we characterize the beats and their feedback on the phase space dynamics at the beginning of the simulations, where the first hole-clump wave pair forms 21 In Ref. [44], the "convective branch" was only responsible for relatively minor transient chirps, while the dominant signal was associated with an MHD eigenmode that was referred to as "relaxation branch". In our semi-perturbative model, there are no discrete eigenmodes, but the seed wave may be regarded as the counterpart of the "relaxation branch", and the early nonadiabatic chirps may be regarded as manifestations of the "convective branch".…”