Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow generation

Abstract

Nonlinear magnetohydrodynamic (MHD) effects on Alfvén eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfvén eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, δB/B ∼ 10−3. In contrast, when the TAE saturation level predicted by the linear code is δB/B ∼ 10−2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n ⩾ 8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.

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

“…For TAE with a finite growth rate γ L due to EP resonant drive, we then have, ∂ t | Z = 2γ L . The generation of ZF discussed here is a typical forced driven process, consistent with simulation results [15,16]. This process is different from that of modulational instability [14], which, dubbed as "secondary instability", becomes important as the pump wave reaches a certain amplitude to overcome the threshold condition for reinforcement by nonlinearity of its deviation from periodic behavior; while the forced driven process studied here, occurs while the pump wave is still in the linear growth stage.…”

“…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 describe two nonlinear processes that occur at different stages of the TAE nonlinear dynamics.To derive the fully nonlinear equations describing nonlinear ZFZS generation by TAE, we take δφ and δA as the field variables. Here, δφ and δA are the scalar potential and parallel component of vector potential to the equilibrium magnetic field, respectively.…”

“…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].…”

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

“…[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.…”

Simulation Science at the National Institute for Fusion Science

“…(2) "Energetic particle group" investigates physics issues related to energetic particles in toroidal plasmas such as Alfven eigenmodes, neoclassical transport of alpha particles in burning plasmas, and NBI/ICRF heating. Based on the comparison studies of linear and nonlinear simulation runs of a n = 4 TAE evolution, it is found that the saturation level is reduced by the nonlinear MHD effects [16]. (3) "Integrated transport simulation group" works to develop core transport code in 3D configuration (TASK3D) and to apply it in order to predict the overall time evolution of observable physics quantities in the plasma core.…”