Andrew Simon Ware

Physics issues of compact drift optimized stellarators

Physics issues are discussed for compact stellarator configurations which achieve good confinement by the fact that the magnetic field modulus |B| in magnetic co-ordinates is dominated by poloidally symmetric components. Two distinct configuration types are considered: (1) those which achieve their drift optimization and rotational transform at low β and low bootstrap current by appropriate plasma shaping; and (2) those which have a greater reliance on plasma β and bootstrap currents for supplying the transform and obtaining quasi-poloidal symmetry. Stability analysis of the latter group of devices against ballooning, kink and vertical displacement modes has indicated that stable β values on the order of 15% are possible. The first class of devices is being considered for a low β near term experiment that could explore some of the confinement features of the high β configurations.

Suppression of Transport Cross Phase by Strongly Sheared Flow

flow with a linearly varying mean shows thatthe cross phase factor in the transport flux is strongly reduced in the strong shear regime (shearingrate . eddy turnover rate), leading to significant transport suppression. The cross phase scales muchmore strongly with shear strength than do fluctuation amplitudes, allowing significant transport reductioneven if fluctuations increase, or decrease only slightly. Cross-phase suppression thus can be the dominanttransport-reduction mechanism in transport barriers.

Turbulent heat and particle flux response to electric field shear

Turbulent heat and particle fluxes are shown to have different responses to E×B shear flow in edge plasmas. Recent work has shown that E×B shear can affect the cross phase between electrostatic potential and pressure fluctuations as well as fluctuation levels, thus affecting the heat and particle fluxes. Resistive pressure gradient driven turbulence (RPGDT) is considered including a collisional electron temperature equation. While the particle flux is sensitive to moderate amounts of shear in the radial electric field, the heat flux is insensitive to moderate shear. In the collisional regime, the difference in the sensitivity of the heat and particle fluxes to E×B shear is due to the large parallel heat conductivity. The large parallel heat conductivity dominates the temperature response to electrostatic perturbations. In lower collisionality regimes, the difference in the dissipation rates between density and temperature is negligible, but other effects can still produce different responses in the heat a...

DEVELOPMENT OF A ROBUST QUASI-POLOIDAL COMPACT STELLARATOR

Abstract A compact quasi-poloidally symmetric stellarator (QPS) plasma and coil configuration is described that has desirable physics properties and engineering feasibility with a very low aspect ratio plasma bounded by good magnetic flux surfaces both in vacuum and at β = 2%. The plasma is robust with respect to variations of pressure and the resulting bootstrap current, which leave the bounding flux surface approximately unchanged and thus reduce active positional control requirements. This configuration was developed by reconfiguring the QPS modular coils and applying a new computational method that maximizes the volume of good (integrable) vacuum flux surfaces as a measure of robustness. The stellarator plasma and coil design code STELLOPT is used to vary the coil geometry to determine the plasma geometry and profiles that optimize plasma performance with respect to neoclassical transport, infinite-n ballooning stability up to β = 2%, and coil engineering parameters. The normal component of the vacuum magnetic field is simultaneously minimized at the full-beta plasma boundary.

Shear flow generation in stellarators—configurational variations

Plasma momentum transport within magnetic surfaces plays a fundamental role in a number of toroidal plasma physics issues, such as turbulence suppression, impurity transport, bootstrap current generation and the shielding of resonant magnetic error field perturbations. Stellarators provide opportunities for improved understanding of plasma flow effects because (a) new forms of quasi-symmetry (e.g. helical, poloidal) can be produced that differ significantly from the tokamak and (b) symmetry-breaking effects (always present to some degree) reduce the close coupling between parallel and cross-field transport characteristics of symmetric systems. External control coils can also be used to further enhance or suppress such effects. A method has been developed to evaluate the variation of neoclassical self-generated plasma flows in stellarators both within and across magnetic surfaces. This introduces a new dimension into both the optimization of stellarators and to the improved understanding of the existing confinement database. Application of this model to a range of configurations indicates that flow directionality and shearing rates are significantly influenced by the magnetic structure. In addition, it is demonstrated that flows in stellarators are sensitive to profile effects and the presence of external momentum sources, such as neutral beams.

Ballooning stability optimization of low-aspect-ratio stellarators

The implementation of ideal ballooning stability within an optimization code is used to determine stable, moderate-β compact stellarator configurations. Due to the large computational requirements of existing ballooning codes, such calculations within the optimization process were previously impractical. The recently developed COBRA code can efficiently compute ideal ballooning growth rates on various magnetic surfaces, using the VMEC code to supply equilibrium data. The optimization code has been used to minimize these growth rates, giving rise to new stellarator configurations at low aspect ratios with good ballooning stability properties, which also maintain previously determined desirable physics properties. This particular implementation is robust due to the enhanced convergence features included in COBRA, while incurring only a small overhead on the total computational time.

Local particle flux reversal under strongly sheared flow

The advection of electron density by turbulent E×B flow with linearly varying mean yields a particle flux that can reverse sign at certain locations along the direction of magnetic shear. The effect, calculated for strong flow shear, resides in the density-potential cross phase. It is produced by the interplay between the inhomogeneities of magnetic shear and flow shear, but subject to a variety of conditions and constraints. The regions of reversed flux tend to wash out if the turbulence consists of closely spaced modes of different helicities, but survive if modes of a single helicity are relatively isolated. The reversed flux becomes negligible if the electron density response is governed by electron scales while the eigenmode is governed by ion scales. The relationship of these results to experimentally observe flux reversals is discussed.

Marginal stability diagrams for infinite-n ballooning modes in quasi-symmetric stellarators

By varying the pressure-gradient and average shear at a selected surface in a given arbitrary stellarator equilibrium and by inducing a coordinate variation such that the perturbed state remains in equilibrium, a family of magnetohydrodynamic equilibria local to the surface is constructed. The equilibria are parameterized by the pressure-gradient and averaged magnetic shear. The geometry of the surface is not changed. The perturbed equilibria are analysed for infinite-n ballooning stability and marginal stability diagrams are constructed that are analogous to the (s, α) diagrams constructed for axisymmetric configurations.The method describes how pressure and rotational-transform gradients influence the local shear, which in turn influences the ballooning stability. Stability diagrams for the quasi-axially symmetric NCSX, a quasi-poloidally symmetric configuration and the quasi-helically symmetric HSX are compared. Regions of second-stability are observed in both NCSX and the quasi-poloidal configuration, whereas no second-stable region is observed for the quasi-helically symmetric device.To explain the different regions of stability, the curvature and local shear of the quasi-poloidal configuration are analysed. The results are seemingly consistent with the following simple explanation: ballooning instability results when the local shear is small in regions of bad curvature with sufficient pressure-gradient. Examples will be given that show that the structure and stability of the ballooning mode is determined by the structure of the potential function arising in the Schrodinger form of the ballooning equation.

Design studies of low aspect ratio quasi-omnigenous stellarators

Significant progress has been made in the development of new modest-size compact stellarator devices that could test optimization principles for the design of a more attractive reactor. These are 3 and 4 field period low-aspect-ratio quasi-omnigenous (QO) stellarators based on an optimization method that targets improved confinement, stability, ease of coil design, low-aspect-ratio, and low bootstrap current.

Bootstrap current in quasi-symmetric stellarators

Abstract This work examines bootstrap current in quasi-symmetric stellarators with a focus on the impact of bootstrap current on the equilibrium properties of stellarator configurations. In the design of the Quasi-Poloidal Stellarator (QPS), a code was used to predict the bootstrap current based on a calculation in an asymptotically collisionless limit. This calculation is believed to be a good approximation of the bootstrap current for low-collisionality plasmas but is expected to be higher than the actual bootstrap current for more collisional plasmas. A fluid moments approach has been developed to self-consistently calculate viscosities and neoclassical transport coefficients. The viscosities and transport coefficients can be used to calculate the bootstrap current for arbitrary collisionality and magnetic geometry. The bootstrap current calculations from the two codes were done for low-density, electron cyclotron–heated (ECH) plasmas and high-density, ion cyclotron–heated (ICH) plasmas for a range of configurations, and provide a benchmark for the moments code and a test of the range of validity of the collisionless code. In the configurations examined here, namely, QPS, the National Compact Stellarator Experiment, the Helically Symmetric Experiment, the Large Helical Device, and the Wendelstein-7X Stellarator, the bootstrap currents predicted from the two codes agree qualitatively for both ICH and ECH profiles.