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Register a new userSuppression of turbulence by trapped electrons in optimised stellarators
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Josefine Henriette Elise Proll
Publication date
2020
fields
Physics
and research's language is
English
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In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the trapped electron mode (TEM) is stabilised if specific optimisation criteria are satisfied, as in the Wendelstein 7-X experiment (W7-X). Here we find, by numerical simulation, that W7-X indeed has low TEM-driven transport, and also benefits from stabilisation of the ion-temperature-gradient mode, giving theoretical support for the existence of enhanced confinement regimes at finite density gradients.
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With the advent of neoclassically optimised stellarators, optimising stellarators for turbulent transport is an important next step. The reduction of ion-temperature-gradient-driven turbulence has been achieved via shaping of the magnetic field, and the reduction of trapped-electron mode (TEM) turbulence is adressed in the present paper. Recent analytical and numerical findings suggest TEMs are stabilised when a large fraction of trapped particles experiences favourable bounce-averaged curvature. This is the case for example in Wendelstein 7-X [C.D. Beidler $textit{et al}$ Fusion Technology $bf{17}$, 148 (1990)] and other Helias-type stellarators. Using this knowledge, a proxy function was designed to estimate the TEM dynamics, allowing optimal configurations for TEM stability to be determined with the STELLOPT [D.A. Spong $textit{et al}$ Nucl. Fusion $bf{41}$, 711 (2001)] code without extensive turbulence simulations. A first proof-of-principle optimised equilibrium stemming from the TEM-dominated stellarator experiment HSX [F.S.B. Anderson $textit{et al}$, Fusion Technol. $bf{27}$, 273 (1995)] is presented for which a reduction of the linear growth rates is achieved over a broad range of the operational parameter space. As an important consequence of this property, the turbulent heat flux levels are reduced compared with the initial configuration.
In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations, and explained by a simple turbulence theory. The first regime is marked by strong zonal flows, and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small- scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.
It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless trapped-particle instability is therefore stable as well as the ordinary electron-density-gradient-driven trapped-electron mode. This result follows from the energy balance of electrostatic instabilities and is thus independent of all other details of the magnetic geometry.
This is the first of two papers about collisionless, electrostatic micro-instabilities in stellarators, with an emphasis on trapped-particle modes. It is found that, in so-called maximum-$J$ configurations, trapped-particle instabilities are absent in large regions of parameter space. Quasi-isodynamic stellarators have this property (approximately), and the theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounce-averaged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding wave-particle resonance. These considerations only depend on the electrostatic energy balance, and are independent of all geometric properties of the magnetic field other than the maximum-$J$ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trapped-electron modes should therefore be more stable in quasi-isodynamic stellarators than in tokamaks.
In recent years, a strong reduction of plasma turbulence in the presence of energetic particles has been reported in a number of magnetic confinement experiments and corresponding gyrokinetic simulations. While highly relevant to performance predictions for burning plasmas, an explanation for this primarily nonlinear effect has remained elusive so far. A thorough analysis finds that linearly marginally stable energetic particle driven modes are excited nonlinearly, depleting the energy content of the turbulence and acting as an additional catalyst for energy transfer to zonal modes (the dominant turbulence saturation channel). Respective signatures are found in a number of simulations for different JET and ASDEX Upgrade discharges with reduced transport levels attributed to energetic ion effects.
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