W.A. Cooper

Configuration flexibility and extended regimes in Large Helical Device

Recent experimental results in the Large Helical Device have indicated that a large pressure gradient can be formed beyond the stability criterion for the Mercier (high-n) mode. While the stability against an interchange mode is violated in the inward-shifted configuration due to an enhancement of the magnetic hill, the neoclassical transport and confinement of high-energy particle are, in contrast, improved by this inward shift. Mitigation of the unfavourable effects of MHD instability has led to a significant extension of the operational regime. Achievements of the stored energy of I MJ and the volume-averaged beta of 3% are representative results from this finding. A confinement enhancement factor above the international stellarator scaling ISS95 is also maintained around 1.5 towards a volume-averaged beta, (beta), of 3%. Configuration studies on confinement and MHD characteristics emphasize the superiority of the inward-shifted geometry to other geometries. The emergence of coherent modes appears to be consistent with the linear ideal MHD theory; however, the inward-shifted configuration has reduced heat transport in spite of a larger amplitude of magnetic fluctuation than the outward-shifted configuration. While neoclassical helical ripple transport becomes visible for the outward-shifted configuration in the collisionless regime, the inward-shifted configuration does not show any degradation of confinement deep in the collisionless regime (nu* < 0.1). The distinguished characteristics observed in the inward-shifted configuration help in creating a new perspective of MHD stability and related transport in net current-free plasmas. The first result of the pellet launching at different locations is also reported.

Ballooning instabilities in tokamaks with sheared toroidal flows

The ballooning-mode eikonal representation is applied to the linearized incompressible magnetohydrodynamic (MHD) equations in axisymmetric systems with toroidal mass flows to obtain a set of initial value partial differential equations in which the time t and the poloidal angle theta are the independent variables. To derive these equations, the eikonal function S is assumed to satisfy the usual condition B.gradS=0 to guarantee that the modes vary slowly along the magnetic field. In addition, to resolve the V.grad operator acting on perturbed quantities, the eikonal must also satisfy the condition dS/dt=0. this induces a Doppler shift in S. This description of the instability, however, is incompatible with normal mode solutions of the MHD equations because the wave vector gradS becomes time dependent when the velocity shear is finite. Nevertheless, the author is able to investigate the effects of the sheared toroidal flows on localized ballooning instabilities because the initial value formulation of the problem developed does not constrain the solutions to evolve as exp (i omega t). Fixed boundary MHD equilibria with isothermal toroidal flows that model the JET device are generated numerically with a variational inverse moments code. As the initial value evaluations are evolved in time, periodic burst of ballooning activity are observed which are correlated with the formation of a ballooning structure at the outside edge of the torus that becomes displaced by 2 pi in the extended poloidal angle domain from one burst to the next. The velocity shear has a stabilizing influence on plasma ballooning.

Effects of global MHD instability on operational high beta-regime in LHD

In the Large Helical Device (LHD), the highest operational averaged beta value has been expanded from 3.2% to 4% in the last 2 years by increasing the heating capability and exploring a new magnetic configuration with a high aspect ratio. Although the magneto-hydrodynamic (MHD) stability properties are considered to be unfavourable in the new high aspect configuration, the heating efficiency due to neutral beams and the transport properties are expected to be favourable in a high-beta range. In order to clarify the effect of the global ideal MHD unstable mode on the operational regimes in helical systems, especially the beta gradients in the peripheral region and the beta value, the MHD analysis and the transport analysis are performed in a high-beta range of up to 4% in LHD. In a high-beta range of more than 3%, the maxima of the observed thermal pressure gradients at a low order rational magnetic surface in the peripheral region are marginally unstable to the low-mode-number ideal MHD instability. Though a gradual degradation of the local transport in the region has been observed as beta increases, a disruptive degradation of the local transport does not appear in the beta range up to 4%.

Methods for the efficient calculation of the magnetohydrodynamic (MHD) stability properties of magnetically confined fusion

A magnetohydrodynamic (MHD) model is applied to the problem of the stability of magnetically confined ther monuclear plasmas of interest in the pursuit of fusion power. Previous studies limited to two-dimensional con figurations are here generalized to three-dimensional toroidal plasmas. Using finite Fourier representations in the angle coordinates and finite hybrid elements in the radial direction, we solve the discretized Euler-Lagrange equations to determine the linear stability properties of the plasma.

Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbationsa)

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10−3 relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated non...

Physics issues in the design of high-beta, low-aspect-ratio stellarator experiments

High-beta, low-aspect-ratio ~‘‘compact’’ ! stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks ~2‐4!. They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A b54% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment ~NCSX!. It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at b54% have been evaluated for the Quasi-Omnigeneous Stellarator ~QOS! experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described.

Three-dimensional corrugation of the plasma edge when magnetic perturbations are applied for edge-localized mode control in MAST

The distortion of the plasma boundary when three-dimensional resonant magnetic perturbations (RMPs) are applied has been measured in MAST H-mode plasmas. When the n = 3 RMPs are applied to control edge-localized modes (ELMs), the plasma experiences a strong toroidal corrugation. The displacement of the plasma boundary is measured at various toroidal locations and found to be of the order of 5% of the minor radius for an applied field magnitude which mitigates ELMs. The empirically observed corrugation of the plasma edge position agrees well with three-dimensional ideal plasma equilibrium reconstruction.

Recent advances in the design of quasiaxisymmetric stellarator plasma configurations

Strategies for the improvement of quasiaxisymmetric stellarator configurations are explored. Calculations of equilibrium flux surfaces for candidate configurations are also presented. One optimization strategy is found to generate configurations with improved neoclassical confinement, simpler coils with lower current density, and improved flux surface quality relative to previous designs. The flux surface calculations find significant differences in the extent of islands and stochastic regions between candidate configurations. (These calculations do not incorporate the predicted beneficial effects of perturbed bootstrap currents.) A method is demonstrated for removing low order islands from candidate configurations by relatively small modifications of the configuration. One configuration is identified as having particularly desirable properties for a proposed experiment.

Global Linear Gyrokinetic Simulations in Quasi-Symmetric Configurations

First global linear study of electrostatic drift waves in two realistic quasisymmetric configurations, namely the Quasi-Axially symmetric Stellarator with three fields periods (QAS3) [P. Garabian and L. P. Ku, Phys. Plasma 6, 645 (1999)] and the Helically Symmetric eXperiment (HSX) [F. S. B. Anderson , Trans. Fusion Technol. 27, 273 (1995)], are presented. Effects of the shape of the plasma on the growth rate and frequency of the ion temperature gradient (ITG) driven mode are investigated by varying the quasi-symmetric configurations to an equivalent symmetric system. The calculations have been performed using a three-dimensional (3D) global gyrokinetic code in the magnetic configurations provided by the magnetohydrodynamic (MHD) equilibrium code VMEC [S. P. Hirshman and D. K. Lee, Comput. Phys. Commun. 39, 161 (1986)]. The plasma is modeled by gyrokinetic ions and adiabatic electrons. In QAS3, results are very close to those obtained for a tokamak. The drift waves are only slightly affected by the shape of the plasma or the local magnetic shear. On the other hand, results for the HSX configuration show a clear 3D effect, namely a strong toroidal variation of the drift wave mode structure. This variation is a clear structure of the 3D plasma shape. However, first results show that the growth rate of the ITG driven mode is largely unaffected by this effect

A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations

The GENE/GIST code package is developed for the investigation of plasma microturbulence, suitable for both stellarator and tokamak configurations. The geometry module is able to process typical equilibrium files and create the interface for the gyrokinetic solver. The analytical description of the method for constructing the geometric elements is documented, together with several numerical evaluation tests. As a concrete application of this product, a cross-machine comparison of the anomalous ion heat diffusivity is presented.