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

Abstract

Generation of zonal flow (ZF) by energetic particle (EP) driven toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. 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. 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.There are two routes for the nonlinear saturation of TAEs, i.e., nonlinear wave-particle and nonlinear wavewave interactions [8]. Wave-particle phase space nonlinearity [9], e.g., wave-particle trapping, describes the nonlinear distortion of the EP distribution function; and leads to SAW saturation as the wave-particle trapping frequency, proportional to square root of the mode amplitude, is comparable with linear growth rate [10][11][12][13]. On the other hand, wave-wave coupling accounts for the transfer of TAE wave energy away from the most unstable modes. Among various wave-wave nonlinearities, generation of zonal structures (ZS) is of particular importance. Chen et al [14] investigated the nonlinear excitation of zero frequency zonal structure (ZFZS) by TAE with a prescribed amplitude, and found that finite amplitude TAE can excite ZFZS via modulational instability at a rate proportional to the amplitude of the pump TAE. Meanwhile, zonal current with lower excitation threshold could be preferentially excited in specific plasma equilibria, which, however, do not reflect typical experimental tokamak plasmas [14]. Numerical simulations of nonlinear dynamics of EP driven TAE are carried out by both hybrid code [15] and PIC code [16], and found that zonal flow (ZF) is excited by forced driven process, with the ZF growth rate being twice of TAE growth rate. In this paper, we will clarify the "discrepancies" between analytical theory and simulation, with emphasis on the important role played by EPs [1,17]. Our results indicate that there is no conflict between analytical theory [14] and numerical simulations [15,16]; in fact, they desc...

Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

“…Note that the summation of m in the expression of δφ Z indicates that the fine structure of δφ Z [19,22] locates at the radial position of Φ 0 (nq − m); i.e., |nq − m| ≃ 1/2 for TAE considered here. In fact, it is induced by the fine radial structures of Alfvén modes, which, in turn, is connected with their parallel mode structure because of the dependence of k on r.…”

“…A /ω 2 0 = 0, breaking of Alfvénic state) andF = 0 due to either envelope modulation [13] or wave-particle resonances [22].…”

“…[7], assuming |ω * ,E | ≫ |ω 0 | ordering and circular cross section. EP response to TAE can be derived as [22,33] …”

“…[22] that there is no conflict between analytical theory [13] and numerical simulations [23,24]. The forced driven process [23,24] is dominated by resonant EP contribution in the linear growth stage of the pump TAE; while the modulational instability [13] with a much slower time scale dominates when wave-particle interactions are weak.…”

“…This finding is novel, since it is usually believed that mode-mode coupling is dominated by bulk plasma nonresonant particles, while resonant particles play an important role in wave-particle nonlinearity. In this paper, it will be demonstrated that the forced driven process [22][23][24] and the modulational instability [13], which are respectively due to EP and thermal plasma nonlinear responses, dominate the TAE nonlinear dynamics at different stages, respectively earlier and later.…”