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

Zocco, A.; Aleynikova, K.; Xanthopoulos, P.

doi:10.1017/s0022377818000648

Cited by 6 publications

(6 citation statements)

References 41 publications

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“…The enhancement of ITG turbulence with the T e /T i ratio is present in both tokamaks and stellarators [55] and appears to be present in all the magnetic configurations shown in figure 1. However, it appears that in tokamaks, linear gyro-kinetic simulations which focus on the strongest growing mode can quantitatively describe the degree of ion transport stiffness enhancement due to T e /T i .…”

Section: Conclusion and Discussionmentioning

confidence: 85%

“…In tokamaks, this causes a high degree of ion profile stiffness [49][50][51][52][53][54], such that their energy confinement is largely controlled by the achievable edge (ion) temperature, or the so-called pedestal temperature. In [55] the destabilization of the ITG modes in stellarators is compared to that in tokamaks by means of linear gyro-kinetic calculations using the GENE code [23]. The authors of that paper discovered remarkably similar results for both confinement concepts.…”

Section: Modelling Of Ion Turbulent Heat Transportmentioning

confidence: 97%

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Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

et al. 2021

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The neoclassical transport optimization of the Wendelstein 7-X stellarator has not resulted in the predicted high energy confinement of gas fueled electron-cyclotron-resonance-heated (ECRH) plasmas as modelled in (Turkin et al 2011 Phys. Plasmas 18 022505) due to high levels of turbulent heat transport observed in the experiments. The electron-turbulent-heat transport appears non-stiff and is of the electron temperature gradient (ETG)/ion temperature gradient (ITG) type (Weir et al 2021 Nucl. Fusion 61 056001). As a result, the electron temperature T e can be varied freely from 1 keV-10 keV within the range of P ECRH = 1-7 MW, with electron density n e values from 0.1-1.5 × 10 20 m −3 . By contrast, in combination with the broad electron-to-ion energy-exchange heating profile in ECRH plasmas, ion-turbulent-heat transport leads to clamping of the central ion temperature at T i ∼ 1.5 keV ± 0.2 keV. In a dedicated ECRH power scan at a constant density of n e = 7 × 10 19 m −3 , an apparent 'negative ion temperature profile stiffness' was found in the central plasma for (r/a < 0.5), in which the normalized gradient ∇T i /T i decreases with increasing ion heat flux. The experiment was conducted in helium, which has a higher radiative density limit compared to hydrogen, allowing a broader power scan. This 'negative stiffness' is due to a strong exacerbation of turbulent transport with an increasing ratio of T e /T i in this electron-heated plasma. This finding is consistent with electrostatic microinstabilities, such as ITG-driven turbulence. Theoretical calculations made by both linear and nonlinear gyro-kinetic simulations performed by the GENE code in the W7-X three-dimensional geometry show a strong enhancement of turbulence with an increasing ratio of T e /T i . The exacerbation of turbulence with increasing T e /T i is also found in tokamaks and inherently enhances ion heat transport in electron-heated

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Section: Conclusion and Discussionmentioning

confidence: 85%

Section: Modelling Of Ion Turbulent Heat Transportmentioning

confidence: 97%

Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

et al. 2021

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“…A configuration is necessarily unstable if D Merc < 0 (but D Merc > 0 does not guarantee stability, as it does not negate ballooning instability; Connor, Hastie & Taylor 1978;Correa-Restrepo 1978;Dewar & Glasser 1983;Nührenberg & Zille 1988a;Freidberg 2014). The scalar D Merc involves multiple integrals over the fields and geometry of the configuration and can be found in the literature (Greene & Johnson 1962;Correa-Restrepo 1978;Nührenberg & Zille 1988a;Bauer et al 2012;Zocco, Aleynikova & Xanthopoulos 2018) (we include it in Appendix A for completeness). The magnetic well criterion (Greene 1997) is nothing but the small-plasma-β, zero-magnetic-shear limit of the Mercier criterion.…”

Section: Mercier Criterion and Near-axis Frameworkmentioning

confidence: 99%

“…The scalar involves multiple integrals over the fields and geometry of the configuration and can be found in the literature (Greene & Johnson 1962; Correa-Restrepo 1978; Nührenberg & Zille 1988 a ; Bauer et al. 2012; Zocco, Aleynikova & Xanthopoulos 2018) (we include it in Appendix A for completeness). The magnetic well criterion (Greene 1997) is nothing but the small-plasma-, zero-magnetic-shear limit of the Mercier criterion.…”

Section: Mercier Criterion and Near-axis Frameworkmentioning

confidence: 99%

Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

Rodríguez

2023

J. Plasma Phys.

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How much does the cross-section of a toroidal magnetic field configuration tell us about its magnetohydrodynamic (MHD) stability? It is generally believed that positive triangularity (typically leading to bean-shaped cross-sections with their indentation on the inboard side in stellarators) contributes positively to MHD stability. In this paper, we explore the basis of this statement within a near-axis description for axisymmetric and quasisymmetric magnetic configurations. In agreement with the existing literature, we show that positive triangularity stabilises vertically elongated tokamaks. In quasisymmetric stellarators, the toroidal asymmetry of flux surfaces modifies this relation. The behaviour of stellarator-symmetric, quasisymmetric stellarators can still be described in terms of the shape of one of their up–down symmetric cross-sections. However, we show that for a sample of quasisymmetric configurations, the positive-bean-shaped cross-sections do not contribute positively to stability. Unlike in the axisymmetric case, we also learn that finite $\beta$ can improve stability even without magnetic shear.

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“…A generalisation to stellarators is not straightforward mainly for two reasons. The first being that within a multiscale gyrokinetic approach in stellarators, the strong variation of the strength of the equilibrium magnetic field on flux surfaces is very likely more important than the radial variation of thermodynamic equilibrium quantities (Zocco et al 2016;Zocco, Aleynikova & Xanthopoulos 2018a;Zocco, Plunk & Xanthopoulos 2020), the latter being the most important mesoscale effect encountered in asymmetry, and taken into account when evaluating the fluctuation radial envelope. The second problem encountered when extending the work of Falessi & Zonca (2019) to stellarators is the absence of a conserved toroidal canonical momentum, which complicates considerably the analysis.…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 6 publications

References 41 publications

Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

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

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