Study of kinetic shear Alfvén instability in tokamak plasmas

Dong, J. Q.; Chen, L.; Zonca, F.; Jian, Gong

doi:10.1063/1.1643919

Cited by 21 publications

(44 citation statements)

References 21 publications

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“…Qualitatively similar results are obtained in the case with higher shear, s = 1.0: here the second MHD stable domain is also destabilized by ITG-driven αTAEs in the entire parameter range scanned. Thus, our results disagree with those presented by Dong et al [7] who observed a destabilization only near the second MHD stability boundary.…”

Section: Resultscontrasting

confidence: 99%

“…Our choice of parameters allowed us to revisit two cases which were examined in earlier numerical studies of Alfvénic ITG (AITG) instabilities; one with lower magnetic shear, s = 0.4 [2], and one with higher shear, s = 1.0 [7]. The results reported by Hirose et al [2] for the case with lower shear, s = 0.4, are reproduced and we are now able to explain the observations in that and subsequent studies [2,7,3,4,5,6] in terms of ITGdriven αTAE ground states [9] and on the basis of the theoretical framework provided by the generalized fishbone-like dispersion relation (see [21] for a review). Apart from clarifying earlier results, this new interpretation has two important implications:…”

Section: Resultsmentioning

confidence: 99%

“…In another recent study, it was demonstrated that, in the second MHD stable domain, discrete ideal MHD Alfvén eigenmodes exist [9], which may be resonantly excited, for instance, through interactions with a sparse energetic ion population [10]. One may now ask the question whether the ITG instabilities reported in [2,3,4,5,6,7] are related to the discrete Alfvén eigenmodes described in [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Pressure-gradient-induced Alfvén eigenmodes: II. Kinetic excitation with ion temperature gradient

Bierwage

Chen

Zonca

2009

Plasma Phys. Control. Fusion

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The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfvén eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as α-induced toroidal Alfvén eigenmodes (αTAE); that is, bound states trapped between pressure-gradientinduced potential barriers of the Schrödinger equation for shear Alfvén waves. Using numerical tools, we examine in detail the effect of kinetic thermal ion compression on αTAEs; both non-resonant coupling to ion sound waves and waveparticle resonances. It is shown that the Alfvénic ITG instability thresholds (e.g., the critical temperature gradient) are determined by two resonant absorption mechanisms: Landau damping and continuum damping. The numerical results are interpreted on the basis of a theoretical framework previously derived from a variational formulation. The present analysis of properties and structures of Alfvénic fluctuations in the presence of steep pressure gradients applies for both positive or negative magnetic shear and can serve as an interpretative framework for experimental observations in (future) high-performance fusion plasmas of reactor relevance. ‡ Present address: Associazione EURATOM-ENEA sulla Fusione, CP 65-00044 Frascati, Rome, Italy. § The factor of 3 is due to the fact that the distribution function is weighted towards high energies by a factor E 5/2 , where E is the kinetic energy of a particle (details are given in section 5.2).

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Section: Resultscontrasting

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pressure-gradient-induced Alfvén eigenmodes: II. Kinetic excitation with ion temperature gradient

Bierwage

Chen

Zonca

2009

Plasma Phys. Control. Fusion

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“…The above simplified calculations also show very similar jump behavior as that by a more comprehensive 1D scanning [37] of parameters for unconventional ITGs using HD7 [38] code. Considering that to obtain the quantitative (especially the global) critical gradient is still challenging due to sensitive of numerical model as mentioned in Sec.I, those discussions are out of the scope of the present study.…”

Section: Eigenstates Jump With Velocity Space Integralsupporting

confidence: 65%

Global theory to understand toroidal drift waves in steep gradient

Xie

2016

Physics of Plasmas

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Toroidal drift waves with unconventional mode structures and non-ground eigenstates, which differ from typical ballooning structure mode, are found to be important recently by large scale global gyrokinetic simulations and especially become dominant at strong gradient edge plasmas [cf., Xie and Xiao, Phys. Plasmas, 22, 090703 (2015)]. The global stability and mode structures of drift wave in this steep edge density and temperature gradients are examined by both direct numerical solutions of a model two-dimensional eigen equation and analytical theory employing WKB-ballooning approach. Theory agrees with numerical solutions quite well. Our results indicate that (i) non-ground eigenstates and unconventional mode structures generally exist and can be roughly described by two parameters 'quantum number' l and ballooning angle ϑ k , (ii) local model can overestimate the growth rate largely, say, > 50%, and (iii) the narrow steep equilibrium profile leads to twisting (triangle-like) radial mode structures. With velocity space integral, semi-local theory predicts that the critical jump gradient of the most unstable ion temperature gradient mode from ground state l = 0 to non-ground state l = 1 is L −1 T R ∼ 50. These features can have important consequences to turbulent transport.

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“…The most unstable solutions in the ballooning space found in the past have usually the ballooning-angle parameter ϑ k = 0 [11], which corresponds to the solution localized at the outside midplane, i.e., θ p = 0 in our notation, where θ p is defined as the local peaking poloidal angle for the mode structure. For this reason, many local eigenvalue codes such as HD7 [12] assume implicitly ϑ k = 0. The unconventional eigen modes with θ p = 0 have been recently discovered in the strong gradient parameter regime.…”

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confidence: 99%

Unconventional ballooning structures for toroidal drift waves

Xie

Xiao

2015

Physics of Plasmas

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With strong gradients in the pedestal of high confinement mode (H-mode) fusion plasmas, gyrokinetic simulations are carried out for the trapped electron and ion temperature gradient modes. A broad class of unconventional mode structures is found to localize at arbitrary poloidal positions or with multiple peaks. It is found that these unconventional ballooning structures are associated with different eigen states for the most unstable mode. At weak gradient (low confinement mode or L-mode), the most unstable mode is usually in the ground eigen state, which corresponds to a conventional ballooning mode structure peaking in the outboard mid-plane of tokamaks. However, at strong gradient (H-mode), the most unstable mode is usually not the ground eigen state and the ballooning mode structure becomes unconventional. This result implies that the pedestal of H-mode could have better confinement than L-mode. Although numerous theoretical models have been suggested [1], a yet unexplained phenomenon in tokamak fusion plasmas, is the transition of low (L) to high (H) confinement states, where H-mode[2] has significant better confinement property than that of the L-mode. Understanding of the H-mode physics is not only important to make controlled fusion more feasible, but also that the existence of and transitions among multi-equilibrium states are important fields of nonlinear physics in laboratory and the Universe. Drift wave turbulence is one of the major causes that leads to the anomalous transport widely observed in fusion and space plasmas [3,4]. In order to control the turbulent transport, it is crucial to understand the underlying transport mechanism, which may vary for different types of instability that drive the turbulence. The correlation time and length are found to be closely related to the mode structure of the turbulence [5]. Therefore, the mode structure of the turbulence has a significant effect on the transport level [6].In this Letter, we show that the linear properties of two major types of electrostatic micro-instabilities [3], namely the trapped electron mode (TEM) and ion temperature gradient (ITG) mode, are completely different in the H-mode (strong gradient) and L-mode (weak gradient) stages. With the conventional weak gradient, the mode structures for drift wave instabilities such as the ITG and TEM are of ballooning type, peaking at the outboard mid-plane of the tokamak (c.f., [7,8]). This type of solution has been intensively studied using the ballooningrepresentation[9, 10] by reducing one two-dimensional (2D) real space eigen mode equation for the drift waves to two one-dimensional (1D) ballooning space eigen mode equations. For the 2D case we solve the eigen equation in the poloidal plane. For the 1D case we solve the eigen equation in the parallel direction. The most unstable solutions in the ballooning space found in the past have usually the ballooning-angle parameter ϑ k = 0 [11], which corresponds to the solution localized at the outside midplane, i.e., θ p = 0 in our notation, where θ p...

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Study of kinetic shear Alfvén instability in tokamak plasmas

Cited by 21 publications

References 21 publications

Pressure-gradient-induced Alfvén eigenmodes: II. Kinetic excitation with ion temperature gradient

Pressure-gradient-induced Alfvén eigenmodes: II. Kinetic excitation with ion temperature gradient

Global theory to understand toroidal drift waves in steep gradient

Unconventional ballooning structures for toroidal drift waves

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