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Register a new userThe intermittent excitation of geodesic acoustic mode by nonlinear Instanton of electron drift wave envelope in L-mode discharge near tokamak edge
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There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. For drift wave turbulence driven by ion temperature gradient mode (ITG), these two stages of dynamics were displayed in [Zhang Y Z, Liu Z Y, Xie T, Mahajan S M and Liu J 2017 Physics of Plasmas 24 122304]. In this paper we show that the dynamical attributes of ITG turbulence are readily replicated when the turbulence rotates in the electron direction; our model calculation deals specifically with the toroidal electron drift waves (EDW) in the well-known delta_e model. While the basic calculations are presented in parallel to the ITG counterpart, more emphasis is laid here on the motion of Instanton; several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The calculation brings out the defining characteristics of the Instanton: it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.
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Through a systematically developed theory, we demonstrate that the motion of instanton identified in [Y. Z. Zhang, Z. Y. Liu, T. Xie, S. M. Mahajan, and J. Liu, Physics of Plasmas 24, 122304 (2017)] is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode (GAM) that are observed in tokamaks. While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient (ITG) mode, and slab-based phenomenological model of zonal flow. When full toroidal effect are introduced into the system, two branches of zonal flow emerge: the torus-modified low frequency zonal flow (TLFZF), and GAM, necessitating a unified exploration of GAM and TLFZF. Indeed, we observe that the transition (decay) from the caviton to instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset. Many features peculiar to intermittent GAMs, observed in real machines, are thus identified in the numerical experiment. The results will be displayed in figures and in a movie; first for single central rational surface, and then with coupled multiple central rational surfaces. The periodic bursting first shown disappears as being replaced by irregular one, more similar to the intermittent characteristics observed in GAM experiments.
The two-field equations governing fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) in the toroidal geometry are derived in nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed. In the linear growth stage, the set of nonlinear equations can be reduced to the intensively studied parametric decay instability (PDI), accounting for the spontaneous resonant excitation of GAM by DW. The main results of previous works on spontaneous GAM excitation, e.g., the much enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from 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 DW. The soliton structures enhance turbulence spreading from DW linearly unstable to stable region, exhibiting convective propagation instead of typical linear dispersive process, and is thus, expected to induce core-edge interaction and nonlocal transport.
Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfven eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, the nonlinear decay process depends on thermal ion beta value. Here, beta is the plasma thermal to magnetic pressure ratio. In the low-beta limit, TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfven wave continuous spectrum gap; while in the high-beta limit, TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear saturation levels of both GAM and daughter wave are derived. The corresponding power balance and wave particle power transfer to thermal plasma are computed. Implications on thermal plasma heating are also discussed.
Interaction of an intense electron beam with a finite-length, inhomogeneous plasma is investigated numerically. The plasma density profile is maximal in the middle and decays towards the plasma edges. Two regimes of the two-stream instability are observed. In one regime, the frequency of the instability is the plasma frequency at the density maximum and plasma waves are excited in the middle of the plasma. In the other regime, the frequency of the instability matches the local plasma frequency near the edges of the plasma and the intense plasma oscillations occur near plasma boundaries. The latter regime appears sporadically and only for strong electron beam currents. This instability generates copious amount of suprathermal electrons. The energy transfer to suprathermal electrons is the saturation mechanism of the instability.
Secondary low frequency mode generation by energetic particle induced geodesic acoustic mode (EGAM) observed in LHD experiment is studied using nonlinear gyrokinetic theory. It is found that the EGAM frequency can be significantly higher than local geodesic acoustic mode (GAM) frequency in low collisionality plasmas, and it can decay into two GAMs as its frequency approaches twice GAM frequency, in a process analogous to the well-known two plasmon decay instability. The condition for this process to occur is also discussed.
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