Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

Zocco, A.; Plunk, G. G.; Xanthopoulos, P.; Helander, P.

doi:10.1063/1.4960993

Cited by 6 publications

(24 citation statements)

References 41 publications

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“…We take the fluid limit of the ITG equation (see (19) of Zocco et al. (2016), or the Fourier transform of (12) of Connor & Taylor (1987), or (B1) of Candy, Waltz & Rosenbluth (2004)), neglect altogether the shear, i.e. , and restore the streaming term, to obtain the Mathieu equation with , and , where is the field-following coordinate and is the parallel connection length.…”

Section: Floquet Solutionsmentioning

confidence: 99%

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Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

et al. 2018

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The threshold for the resonant destabilisation of ion-temperature-gradient (ITG) driven instabilities that render the modes ubiquitous in both tokamaks and stellarators is investigated. We discover remarkably similar results for both confinement concepts if care is taken in the analysis of the effect of the global shearŝ. We revisit, analytically and by means of gyrokinetic simulations, accepted tokamak results and discover inadequacies of some aspects of their theoretical interpretation. In particular, for standard tokamak configurations, we find that global shear effects on the critical gradient cannot be attributed to the wave-particle resonance destabilising mechanism of Hahm & Tang (Phys. Plasmas, vol. 1, 1989, pp. 1185-1192, but are consistent with a stabilising contribution predicted by Biglari et al. (Phys. Plasmas, vol. 1, 1989, pp. 109-118). Extensive analytical and numerical investigations show that virtually no previous tokamak theoretical predictions capture the temperature dependence of the mode frequency at marginality, thus leading to incorrect instability thresholds. In the asymptotic limitŝι 1, where ι is the rotational transform, and such a threshold should be solely determined by the resonant toroidal branch of the ITG mode, we discover a family of unstable solutions below the previously known threshold of instability. This is true for a tokamak case described by a localŝ − α local equilibrium, and for the stellarator Wendelstein 7-X, where these unstable solutions are present even for configurations with a small trapped-particle population. We conjecture they are of the Floquet type and derive their properties from the Fourier analysis of toroidal drift modes of Connor & Taylor (Phys. Fluids, vol. 30, 1987, pp. 3180-3185), and to Hill's theory of the motion of the lunar perigee (Acta Math., vol. 8, 1886, pp. 1-36). The temperature dependence of the newly determined threshold is given for both confinement concepts. In the first case, the new temperature-gradient threshold is found to be rather insensitive to the temperature ratio T i /T e , at least for T i /T e 1, and to be a growing function of the density gradient scale for T i /T e 1. For Wendelstein 7-X, the new critical temperature gradient is a growing function of the temperature ratio. The importance of these findings for the assessment of turbulence in stellarators and low-shear tokamak configurations is discussed.

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Section: Floquet Solutionsmentioning

confidence: 99%

“…2014), or with detailed structure on equilibrium magnetic surfaces (Zocco et al. 2016); of the isolated or general (Dickinson et al. 2014) type, or else ‘passing’ or ‘trapped’ (Dewar 1997); this list may not be complete.…”

Section: Introductionmentioning

confidence: 99%

Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

et al. 2018

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“…In the work of Zocco et al. (2016), the authors performed an asymptotic expansion in . For finite , the authors introduced a discrete Fourier expansion of the ion-temperature-gradient driven (ITG) eigenvalue equation (Zocco, Xanthopoulos & Helander 2018).…”

Section: Lattice-drift Model For Kbmsmentioning

confidence: 99%

“…2016; Zocco et al. 2016) and electron-temperature-gradient-driven modes (Jenko & Kendl 2002). Electromagnetic gyrokinetic instabilities have been explored much less.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, great effort has been devoted to the investigation of gyrokinetic instabilities that can cause turbulent transport in stellarators. In particular, analytical and numerical progress has been made for electrostatic instabilities, such as trapped electron modes (Proll, Xanthopoulos & Helander 2013;Faber et al 2015), ion-temperature-gradient-driven modes (Plunk et al 2014;Helander et al 2015;Xanthopoulos et al 2016;Zocco et al 2016) and electron-temperature-gradient-driven modes (Jenko & Kendl 2002). Electromagnetic gyrokinetic instabilities have been explored much less.…”

Section: Introductionmentioning

confidence: 99%

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Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

2018

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Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugama et al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.

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Nonlinear drift-wave and energetic particle long-time behaviour in stellarators: solution of the kinetic problem

et al. 2023

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We propose a theoretical scheme for the study of the nonlinear interaction of drift-wave-like turbulence and energetic particles in stellarators. The approach is based on gyrokinetics, and features a separation of time and scales, for electromagnetic fluctuations, inspired by linear ballooning theory. Two specific moments of the gyrokinetic equation constitute the main equations of the system, which requires a full kinetic nonlinear solution. This is found iteratively, expanding in the smallness of the bounce-average radial drift frequency, and nonlinear $\boldsymbol {E}\times \boldsymbol {B}$ drift frequency, compared with the inverse time scales of the resonantly interacting energetic particles. Our analysis is therefore valid for neoclassically optimised stellators. The resummation of all iterative and perturbative nonlinear kinetic solutions is discussed in terms of Feynman diagrams. Particular emphasis is put on the role of collisionlessly undamped large-scale structures in phase space, the kinetic equivalent of zonal flows, i.e. phase-space zonal structures, and on wave-like fluctuations generated by energetic particles.

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Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

Cited by 6 publications

References 41 publications

Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

Nonlinear drift-wave and energetic particle long-time behaviour in stellarators: solution of the kinetic problem

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