Nonlinear reversed shear Alfven eigenmode saturation due to spontaneous zonal current generation
TL;DR: In this article, general nonlinear equations describing reversed shear Alfven eigenmode (RSAE) self-modulation via zero frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZs excitation as well as RSAE nonlinear saturation.
Abstract: General nonlinear equations describing reversed shear Alfven eigenmode (RSAE) self-modulation via zero frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow (ZF) and electromagnetic zonal current (ZC) can be preferentially excited by finite amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfven wave continuum is evaluated using the derived saturation level of ZC, which is shown to play a comparable role in saturating RSAE with the ZFZS scattering.
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TL;DR: In this article , the effects of plasma non-uniformities and kinetic dispersiveness on the spontaneous excitation of geodesic acoustic mode (GAM) by reversed shear Alfvén eigenmode (RSAE) are investigated numerically.
Abstract: Effects of plasma non-uniformities and kinetic dispersiveness on the spontaneous excitation of geodesic acoustic mode (GAM) by reversed shear Alfvén eigenmode (RSAE) are investigated numerically. It is found that, due to the turning points induced by the shear Alfvén continuum structure, the nonlinear excitation of GAM is a quasiexponentially growing absolute instability. As the radial dependence of GAM frequency and pump RSAE mode structure are accounted for, the radially inward propagating GAM is preferentially excited, leading to core localized thermal plasma heating by GAM collisionless damping. Our work, thus, suggests that GAM excitation plays a crucial role in not only RSAE nonlinear saturation, but also anomalous fuel ion heating in future reactors.
27 Jun 2023
TL;DR: In this paper , the authors employ nonlinear gyrokinetic approach in order to account for the breaking of the "pure Alfv\'enic state" in the short-wavelength kinetic regime, due to the short wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas.
Abstract: Nonlinear wave-wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry breaking shear Alfv\'en wave (SAW) instabilities are expected to be excited by energetic fusion alpha particles, and self-consistently determine the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave-wave coupling processes. More specifically, one needs to employ the gyrokinetic approach in order to account for the breaking of the ``pure Alfv\'enic state"in the short wavelength kinetic regime, due to the short wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfv\'en eigenmode (TAE) as a paradigm case, three nonlinear wave-wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1. the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion induced scattering and the resulting saturated TAE spectrum; and 3. the cross-scale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating.
TL;DR: A strong nonlinear saturation mechanism of the reverse shear Alfvén eigenmode (RSAE) induced by thermal electrons is observed in gyrokinetic δf particle-in-cell simulation as discussed by the authors .
Abstract: A strong nonlinear saturation mechanism of the reverse shear Alfvén eigenmode (RSAE) induced by thermal electrons is observed in gyrokinetic δf particle-in-cell simulation. This nonlinear effect occurs at moderate mode amplitude, δB⊥/B<10−3 , and is associated with the electron parallel streaming along the perturbed magnetic field lines, the term v∥δB⊥B⋅∇δf , in the electron drift-kinetic equation. In the case of an n = 4 RSAE, where n is the toroidal mode number, this magnetic fluttering nonlinearity leads to strong mode coupling and broadening of the saturation spectrum. The nonlinear components, which are highly damped through the interaction between thermal electrons and the parallel electric field, modifies the RSAE mode structure and suppresses energetic particle drive significantly. The split-weight scheme (Chen and Parker 2007 J. Comput. Phys. 220 839–55) is used to simulate kinetic electrons.
References
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TL;DR: A comprehensive review of zonal flow phenomena in plasmas is presented in this article, where the focus is on zonal flows generated by drift waves and the back-interaction of ZF on the drift waves, and various feedback loops by which the system regulates and organizes itself.
Abstract: A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.
1,739 citations
TL;DR: Three-dimensional gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas with massively parallel computers showed that, with linear flow damping, an asymptotic residual flow develops in agreement with analytic calculations.
Abstract: Three-dimensional gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas with massively parallel computers showed that, with linear flow damping, an asymptotic residual flow develops in agreement with analytic calculations. Nonlinear global simulations of instabilities driven by temperature gradients in the ion component of the plasma support the view that turbulence-driven fluctuating zonal flows can substantially reduce turbulent transport. Finally, the outstanding differences in the flow dynamics observed in global and local simulations are found to be due to profile variations.
921 citations
TL;DR: A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed in this paper.
Abstract: A nonlinear gyrokinetic formalism for low‐frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed The nonlinear equations thus derived are valid in the strong‐turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves Also, applying the formalism to the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear‐Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects In particular, wave energy is found to cascade in wavenumber instead of frequency
763 citations
TL;DR: In this article, a procedure which reconciles long parallel wavelength, characteristic of plasma instabilities, with periodicity in a sheared toroidal magnetic field is described and applied to the problem of high-n$ ballooning modes in tokamaks.
Abstract: A procedure which reconciles long parallel wavelength, characteristic of plasma instabilities, with periodicity in a sheared toroidal magnetic field is described. Applied to the problem of high-$n$ ballooning modes in tokamaks it makes possible a full minimization of the potential energy functional $\ensuremath{\delta}W$ and shows that previous calculations overestimated stability.
693 citations
TL;DR: In this paper, it was shown that linear collisionless processes do not damp poloidal flows driven by ion-temperature-gradient (ITG) turbulence, since these flows play an important role in saturating the level of the turbulence.
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607 citations