Nonlinear Decay and Plasma Heating by a Toroidal Alfvén Eigenmode.
TL;DR: It is demonstrated theoretically that a toroidal Alfvén eigenmode (TAE) can parametrically decay into a geodesic acoustic mode and kinetic TAE in a toroid plasma, which could contribute to the heating as well as regulating the transports of thermal plasmas.
Abstract: We demonstrate theoretically that a toroidal Alfven eigenmode (TAE) can parametrically decay into a geodesic acoustic mode and kinetic TAE in a toroidal plasma. The corresponding threshold condition for the TAE amplitude is estimated to be |δB_{⊥}/B_{0}|∼O(10^{-4}). Here, δB_{⊥} and B_{0} are, respectively, the perturbed magnetic field of the pump TAE and the equilibrium magnetic field. This novel decay process, in addition to contributing to the nonlinear saturation of energetic-particle or α-particle driven TAE instability, could also contribute to the heating as well as regulating the transports of thermal plasmas.
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01 Oct 1981
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.
587 citations
TL;DR: In this paper, a unified theoretical framework of geodesic acoustic modes (GAM) and EPs (EGAM) is presented, with emphasis on kinetic treatment, system non-uniformity and realistic magnetic geometry.
Abstract: Geodesic acoustic modes (GAM) are oscillating zonal structures unique to toroidal plasmas, and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport. This article reviews linear and nonlinear theories of GAM; with emphases on kinetic treatment, system nonuniformity and realistic magnetic geometry, in order to reflect the realistic experimental conditions. Specifically, in the linear physics, the resonant wave-particle interactions are discussed, with the application to resonant excitation by energetic particles (EPs). The theory of EP-induced GAM (EGAM) is applied to realistic devices for the interpretation of experimental observations, and global effects due to coupling to GAM continuum are also discussed. Meanwhile, in the nonlinear physics, the spontaneous GAM excitation by microscale turbulences is reviewed, including the effects of various system nonuniformities. A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings. The first-principle-based GAM/EGAM theories reviewed here, thus, provide the tools needed for the understanding and interpretation of experimental/numerical results.
31 citations
TL;DR: In this article, a unified theoretical framework of geodesic acoustic modes (GAM) and EPs (EGAM) is presented, with emphasis on kinetic treatment, system non-uniformity and realistic magnetic geometry.
Abstract: Geodesic acoustic modes (GAM) are oscillating zonal structures unique to toroidal plasmas, and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport. This article reviews linear and nonlinear theories of GAM; with emphases on kinetic treatment, system nonuniformity and realistic magnetic geometry, in order to reflect the realistic experimental conditions. Specifically, in the linear physics, the resonant wave-particle interactions are discussed, with the application to resonant excitation by energetic particles (EPs). The theory of EP-induced GAM (EGAM) is applied to realistic devices for the interpretation of experimental observations, and global effects due to coupling to GAM continuum are also discussed. Meanwhile, in the nonlinear physics, the spontaneous GAM excitation by microscale turbulences is reviewed, including the effects of various system nonuniformities. A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings. The first-principle-based GAM/EGAM theories reviewed here, thus, provide the tools needed for the understanding and interpretation of experimental/numerical results.
28 citations
20 citations
TL;DR: In this article, the spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfven eigenmode (TAE) was investigated using nonlinear gyrokinetic theory.
Abstract: 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.
18 citations
References
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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 toroidal systems with geodesic curvature, an electrostatic acoustic mode occurs with plasma motion in the magnetic surfaces, perpendicular to the field as discussed by the authors, and this mode should dominate ordinary sound waves associated with motion along the field.
Abstract: In toroidal systems with geodesic curvature an electrostatic acoustic mode occurs with plasma motion in the magnetic surfaces, perpendicular to the field. In typical stellarators this mode should dominate ordinary sound waves associated with motion along the field.
624 citations
01 Oct 1981
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.
587 citations
TL;DR: In this paper, the ideal and resistive MHD equations for the shear Alfven waves are studied in a low-β toroidal model by employing the high-n ballooning formalism.
450 citations