Compact optimized stellarators offer novel solutions for confining high-β plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide driftorbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high β limit, and good confinement of advanced tokamaks. Quasiaxisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation ∼1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassicaltearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.

A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.

Abstract. Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The 3D plasma shape can be designed to enhance the MHD stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low-aspect ratio, high beta-limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4 -4.4 and average elongation ~1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β=4% (the rest is from the coils), thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.3

It is found that the thermal fluctuation level of the shear-Alfvén waves in a gyrokinetic plasma is dependent on plasma β(≡cs2/vA2), where cs is the ion acoustic speed and vA is the Alfvén velocity. This unique thermodynamic property based on the fluctuation–dissipation theorem is verified in this paper using a new gyrokinetic particle simulation scheme, which splits the particle distribution function into the equilibrium part as well as the adiabatic and nonadiabatic parts. The numerical implication of this property is discussed.

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Strategies for the improvement of quasi-axisymmetric 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.1

A novel method to calculate the neoclassical radial electric field in stellarator plasmas is described. The method, which does not have the inconvenient of large statistical fluctuations (noise) of standard Monte Carlo technique, is based on the variation of the combined parallel and perpendicular pressures on a magnetic surface. Using a three-dimensional gyro-kinetic δf code, the calculation of the radial electric field (E r ) in the National Compact Stellarator Experiment has been carried out. It is shown that a direct evaluation of E r based on a direct calculation of the radial particle flux is not tractable due to the considerable noise.

The theory of variances of equilibrium reconstruction is presented. It complements existing practices with information regarding what kind of plasma characteristics can be reconstructed, how accurately, and what remains beyond the abilities of diagnostic systems. The σ-curves, introduced by the present theory, give a quantitative assessment of quality of effectiveness of diagnostic systems in constraining equilibrium reconstructions. The theory also suggests a method for aligning the accuracy of measurements of different physical nature and for improvements of numerical algorithms used in reconstruction.