Collisionless microinstabilities in stellarators II - numerical simulations

Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-$J$ geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment (NCSX) and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-$J$ configurations.Comment: 15 pages, 40 figure

Collisionless microinstabilities in stellarators I - analytical theory of trapped-particle modes

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.Comment: 9 pages, 1 figur

Available energy of trapped electrons in Miller tokamak equilibria

Available energy (\AE{}), which quantifies the maximum amount of thermal energy that may be liberated and converted into instabilities and turbulence, has shown to be a useful metric for predicting saturated energy fluxes in trapped-electron-mode-driven turbulence. Here, we calculate and investigate the \AE{} in the analytical tokamak equilibria introduced by \citet{Miller1998NoncircularModel}. The \AE{} of trapped electrons reproduces various trends also observed in experiments; negative shear, increasing Shafranov shift, vertical elongation, and negative triangularity can all be stabilising, as indicated by a reduction in \AE{}, although it is strongly dependent on the chosen equilibrium. Comparing \AE{} with saturated energy flux estimates from the \textsc{tglf} model, we find fairly good correspondence, showcasing that \AE{} can be useful to predict trends. We go on to investigate \AE{} and find that negative triangularity is especially beneficial in vertically elongated configurations with positive shear or low gradients. We furthermore extract a gradient threshold-like quantity from \AE{} and find that it behaves similarly to gyrokinetic gradient thresholds: it tends to increase linearly with magnetic shear, and negative triangularity leads to an especially high threshold. We next optimise the device geometry for minimal \AE{} and find that the optimum is strongly dependent on equilibrium parameters, e.g. magnetic shear or pressure gradient. Investigating the competing effects of increasing the density gradient, the pressure gradient, and decreasing the shear, we find regimes that have steep gradients yet low \AE{}, and that such a regime is inaccessible in negative-triangularity tokamaks.Comment: 31 pages, 16 figure

Bounce-averaged drifts: Equivalent definitions, numerical implementations, and example cases

In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes.Comment: 12 pages, 6 figure

Enhanced transport at high plasma β\beta and sub-threshold kinetic ballooning modes in Wendelstein 7-X

The effect of plasma pressure $\beta$ on ion-temperature-gradient-driven (ITG) turbulence is studied in the Wendelstein 7-X (W7-X) stellarator, showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the quasi-stationary state. By zonal-flow erosion, these highly non-ideal KBMs affect ITG saturation and thereby enable higher heat fluxes. Controlling these KBMs will be essential in order to allow W7-X and future stellarators to achieve maximum performance.Comment: 16 pages, 5 figure

Neurophysiology

Contains research objectives, summary of research and reports on six research objectives.National Institutes of Health (Grant 5 ROl NB-04985-05)National Institutes of Health (Grant NB-07501-02)National Institutes of Health (Grant NB-06251-03)National Institutes of Health (Grant NB-07576-02)U. S. Air Force (Aerospace Medical Division) under Contract AF33(615)-3885Bell Telephone Laboratories IncorporatedNational Institutes of Health (Grant 5 TO1 GM-01555-02