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The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices. [ABSTRACT FROM AUTHOR]

This study shows the feasibility of a beam emission spectroscopy (BES) diagnostic in the Helically Symmetric eXperiment (HSX) stellarator for obtaining the spatiotemporal structure of density fluctuation. A beam emission simulation was applied to HSX plasmas to design and optimize viewing chords and to estimate the beam emission spectrum. A Doppler-shifted beam emission spectrum was measured from a 30 kV, 4 A diagnostic neutral beam injected into HSX plasmas. The beam emission was measured with a high-time-resolution avalanche photodiode (APD) assembly to determine the feasibility of BES in HSX. For HSX plasmas heated by 28 GHz electron cyclotron heating, a mode around f = 15 kHz was observed in the BES signal. The coherence between the BES signal and the density fluctuation measured by an interferometer system was significant. A plan for improving the BES system to enable the measurement of higher frequency related to turbulent transport is presented. The array of sightlines proposed in this study can be used to measure beam emission with a Doppler shift larger than 3 nm (blue shift), which enables the use of a wide passband interference filter to obtain higher throughput. The adoption of a large objective optics and a chilled APD assembly will improve the signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate kx, but the oscillation and damping time scales are longer in local representations, particularly for small kx approaching the system size. [ABSTRACT FROM AUTHOR]

Gyrokinetic simulations of plasma microturbulence in the Helically Symmetric eXperiment are presented. Using plasma profiles relevant to experimental operation, four dominant drift wave regimes are observed in the ion wavenumber range, which are identified as different flavors of density-gradient-driven trapped electron modes. For the most part, the heat transport exhibits properties associated with turbulence driven by these types of modes. Additionally, longwavelength, radially localized, nonlinearly excited coherent structures near the resonant central flux surface, not predicted by linear simulations, can further enhance flux levels. Integrated heat fluxes are compatible with experimental observations in the corresponding density gradient range. Despite low shearing rates, zonal flows are observed to regulate turbulence but can be overwhelmed at higher density gradients by the long-wavelength coherent structures. [ABSTRACT FROM AUTHOR]

Stiffness measurements are presented in the quasi-helically symmetric experiment (HSX), in which the neoclassical transport is comparable to that in a tokamak and turbulent transport dominates throughout the plasma. Electron cyclotron emission is used to measure the local electron temperature response to modulated electron cyclotron resonant heating. The amplitude and phase of the heat wave through the steep electron temperature gradient (ETG) region of the plasma are used to determine a transient electron thermal diffusivity that is close to the steady-state diffusivity. The low stiffness in the region between 0.2 ≤r/a≤0.4 agrees with the scaling of the steady-state heat flux with temperature gradient in this region. These experimental results are compared to gyrokinetic calculations in a flux-tube geometry using the gyrokinetic electromagnetic numerical experiment code with two kinetic species. Linear simulations show that the ETG mode may be experimentally relevant within r/a≤0.2, while the Trapped Electron Mode (TEM) is the dominant long-wavelength microturbulence instability across most of the plasma. The TEM is primarily driven by the density gradient. Non-linear calculations of the saturated heat flux driven by the TEM and ETG bracket the experimental heat flux. [ABSTRACT FROM AUTHOR]

The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the reconstruction is constrained by the measured data from a diagnostic array that is internal to the vacuum chamber. [ABSTRACT FROM AUTHOR]

Electron cyclotron heated plasmas in the Helically Symmetric Experiment (HSX) feature strongly peaked electron temperature profiles; central temperatures are 2.5 keV with 100 kW injected power. These measurements, coupled with neoclassical predictions of large “electron root” radial electric fields with strong radial shear, are evidence of a neoclassically driven thermal transport barrier. Neoclassical transport quantities are calculated using the PENTA code [D. A. Spong, Phys. Plasmas 12, 056114 (2005)], in which momentum is conserved and parallel flow is included. Unlike a conventional stellarator, which exhibits strong flow damping in all directions on a flux surface, quasisymmetric stellarators are free to rotate in the direction of symmetry, and the effect of momentum conservation in neoclassical calculations may therefore be significant. Momentum conservation is shown to modify the neoclassical ion flux and ambipolar ion root radial electric fields in the quasisymmetric configuration. The effect is much smaller in a HSX configuration where the symmetry is spoiled. In addition to neoclassical transport, a model of trapped electron mode turbulence is used to calculate the turbulent-driven electron thermal diffusivity. Turbulent transport quenching due to the neoclassically predicted radial electric field profile is needed in predictive transport simulations to reproduce the peaking of the measured electron temperature profile [Guttenfelder et al., Phys. Rev. Lett. 101, 215002 (2008)]. [ABSTRACT FROM AUTHOR]

This paper presents edge measurements utilizing Langmuir probes to characterize plasma turbulence in the Helically Symmetric Experiment (HSX) [F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995)]. Normalized density and potential fluctuations exhibit strong intensities but are comparable to mixing length estimates using measured correlation lengths. The correlation lengths are isotropic with respect to radial and poloidal directions and follow local (gyro-Bohm) drift wave expectations. These observations are common to measurements in both the optimized quasihelically symmetric (QHS) configuration, as well as a configuration where the symmetry is degraded intentionally. The resulting turbulent particle flux in higher density QHS discharges is in good quantitative agreement with transport analysis using three-dimensional neutral gas simulations. The measured turbulence characteristics are compared to a quasilinear trapped electron mode (TEM) drift wave model [H. Nordman, J. Weiland, and A. Jarmén, Nucl. Fusion 30, 983 (1990)] that has been used to predict the anomalous transport in HSX. While quantitative differences exist (factors of 2–3), there is a general consistency between the turbulence measurements and the TEM drift wave model. [ABSTRACT FROM AUTHOR]

Measurements of particle and heat transport have been made in the Helically Symmetric Experiment [F. S. B. Anderson et al., Fusion Technology 27, 273 (1995)]. Experimental differences in the density and temperature profiles are reported between plasmas produced in a quasihelically symmetric (QHS) magnetic field and a configuration with the symmetry broken. The electron temperature is higher in the QHS configuration, due to a reduction in electron thermal diffusivity that is comparable to the neoclassical prediction. The density profile in plasmas with the symmetry broken is measured to be hollow, while in QHS plasmas the profile is centrally peaked. Calculations of the radial particle flux using the DEGAS code [D. Heifetz et al., J. Comput. Phys. 46, 309 (1982)] show that the hollow profile observed with the symmetry broken is due to neoclassical thermodiffusion. Thermodiffusion is reduced in the QHS configuration, resulting in a peaked density profile. [ABSTRACT FROM AUTHOR]

The moment equation approach to neoclassical transport is used to calculate neoclassical particle and heat fluxes, impurity transport, the ambipolar electric field, and momentum damping rates. These equations are often written in Hamada coordinates which makes it easier to obtain analytic solutions. However, previous simplifying assumptions used to evaluate the basis vectors analytically are often invalid for advanced stellarator configurations. In this paper, a numerical method is presented by which the Hamada basis set can be determined for an arbitrary three dimensional toroidal confinement device by integrating along a magnetic field line. The method is applied to the magnetic configuration in the Helically Symmetric Experiment [F. S. B. Anderson, A. F. Almagri, D. T. Anderson, P. G. Matthews, J. N. Talmadge, and J. L. Shohet, Fusion Technol. 27, 273 (1995)] and compared to the large-aspect-ratio tokamak approximation to the basis set. The results indicate that the numerical technique is a more accurate method to specify the basis vectors, especially in a device with negligible toroidal curvature. [ABSTRACT FROM AUTHOR]

Measurements of plasma flow damping have been made in the Helically Symmetric eXperiment [F. S. B. Anderson, A. F. Almagri, D. T. Anderson, P. G. Mathews, J. N. Talmadge, and J. L. Shohet, Fusion Technology 27, 273 (1995)] using a biased electrode to impulsively spin the plasma and Mach probes to measure the rotation. There is a distinct asymmetry between the spin-up when the bias is initiated and relaxation when the electrode current is broken. In each case, two time-scales are observed in the evolution of the plasma flow. These observations motivate the development of new neoclassical modeling techniques, including a new model where the fast increment of the electric field initiates the spin-up process. The flow in the quasisymmetric configuration rises more slowly and to a higher value than in a configuration with the quasisymmetry broken, and the rise time-scale is in reasonable agreement with the neoclassical spin-up model. The flows decay more slowly in the quasisymmetry configuration than in the configuration with the quasisymmetry broken, although the decay rates are significantly faster than the neoclassical prediction. [ABSTRACT FROM AUTHOR]

Neoclassical viscous damping rates have been calculated for the helically symmetric experiment [F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995)], concentrating on the effects of magnetic surface shape changes due to magnetic islands. The interaction between the main helical spectral component and magnetic surface shape changes caused by an island chain introduces symmetry breaking spectral components on closed surfaces near the island chain. Results indicate that small islands present in the quasihelically symmetric configuration can give rise to an observable but not problematic deviation from quasisymmetry on surfaces near the islands. These islands can be eliminated via a small reduction in the rotational transform. Large islands can be produced by the introduction of the ι[slanted_horizontal_slash]=4/4 resonance inside the last closed magnetic surface. These islands result in not only a significant reduction in the volume of closed nested magnetic surfaces, but also an elevated level of viscous damping on magnetic surfaces adjacent to the islands. [ABSTRACT FROM AUTHOR]

A system of electrodes and Langmuir probes has been developed for the measurement of plasma flow damping in the Helically Symmetric Experiment (HSX) stellarator. A biased electrode is used to apply a J×B torque to the plasma. The fast switching electrode power supply allows the electrode voltage to be applied in ∼1 μs, which is much faster than any of the plasma time scales; the electrode current is terminated on a similar time scale at the end of the electrode pulse. A pair of multitipped Mach probes have been designed to measure the plasma flows in a magnetic surface with good spatial and time resolution (Δt>20 μs). The unmagnetized model by Hutchinson is used to analyze the Mach probe data, and radial force balance is found to be well satisfied during electrode bias. These probes allow for measurements of the transient response of the plasma flows and floating potential when the electrode is energized. An example of using the system for the estimation of viscous damping times in HSX is provided. [ABSTRACT FROM AUTHOR]

Measuring the equilibrium electron density distribution and its response to perturbations provides important information to magnetically confined plasma research. A multichannel interferometer system is now routinely operating on the new quasihelically symmetric stellator (HSX) to measure the equilibrium profile and electron density dynamics. The interferometer system has nine viewing chords with 1.5 cm spacing. The source is a bias-tuned Gunn diode at 96 GHz with passive solid-state tripler providing output at 288 GHz (8 mW). The HSX plasma is produced by 28 GHz electron cyclotron resonance heating and first results of the interferometer measurement are reported. The density spatial distribution is reconstructed from the measured line-integrated density. At high density [&nmacr;[sub e]>2 × 10[sup 12] cm[sup -3]], an m = 1 density oscillation with frequency of 1-2 kHz is observed. Plans to determine the radial particle flux and transport coefficients will be discussed. [ABSTRACT FROM AUTHOR]

The leading terms of the magnetic field spectrum for the Helically Symmetric Experiment [Fusion Technol. 27, 273 (1995)] at low magnetic field are determined by analyzing the orbits of passing particles. The images produced by the intersection of electron orbits with a fluorescent mesh are recorded with a charge coupled device and transformed into magnetic coordinates using a neural network. To obtain the spectral components, the transformed orbits are then fit to an analytic expression that models the drift orbits of the electrons. The results confirm for the first time that quasihelical stellarators have a large effective transform that results in small excursions of particles from a magnetic surface. The drift orbits are also consistent with a very small toroidal curvature component in the spectrum. An external magnetic perturbation, nearly resonant with the transform, is shown to induce a large excursion of the particle orbit off a flux surface. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, the fluid equation approach is used to analyze the time evolution of the plasma rotation and the ambipolar electric field in a nonsymmetric toroidal plasma subject to an external biasing voltage induced by a probe. Under consideration is a plasma with low rotation speed in the Pfirsch–Schlüter or the plateau regime that includes the effects of a background neutral gas. A time-dependent charge conservation equation is used to determine the ambipolar electric field as a function of time. It is found that, after the application of the biasing voltage, the electric field and the plasma rotation change quickly and reach steady-state after a time inversely proportional to the sum of the momentum damping rates due to parallel viscosity and ion–neutral collisions. The steady state is characterized by a radial electric field and a plasma rotation that are proportional to the electric current flowing through the biasing probe. The direction of the plasma flow is determined by the relative magnitude of the momentum damping rates on the flux surface. From the steady-state solution, an expression for the radial electric conductivity is obtained, which includes the effect of collisions with neutrals as well as viscosity. Axisymmetric systems without neutrals are also discussed, which is a special case since there is no momentum damping in the toroidal direction. Here, the toroidal velocity increases continuously in time with the bias and never reaches steady state. Finally, a model for nonsymmetric magnetic fields is presented and the viscous damping rate, the radial conductivity and the spin-up rate for a plasma in the Pfirsch–Schlüter regime are calculated. As examples, the cases of the rippled tokamak and the classical and helically symmetric stellarators are evaluated. [ABSTRACT FROM AUTHOR]

A Mach probe is used to measure poloidal and toroidal flows induced by a biased electrode in IMS. Mach probe theories are reviewed and classified as either magnetized or unmagnetized. A simple geometric model of the IMS Mach probe shows that the variation of the effective probe area as a function of the probe orientation with respect to the magnetic field is 20%-25%, predicting the probe to be only slightly magnetized. Measurements of the variation in the total ion saturation current collected by the probe, as the angle with respect to the magnetic field is varied, demonstrate this level of magnetization only at low neutral pressure at large minor radius, while in other cases the variation in the total collected current is negligible. Based on this result an unmagnetized model [M. Hudis and L. M. Lidsky, J. Appl. Phys. 41, 5011 (1970)] is chosen to analyze the IMS Mach probe data. Comparison of Mach probe poloidal flow measurements as a function of minor radius to calculations of the Ex B drift velocity and the ion diamagnetic drift velocity from radial profiles of floating potential and ion saturation current, respectively, shows agreement to within 15%. [ABSTRACT FROM AUTHOR]

The numerically predicted magnetic surface structure within the separatrix of the interchangeable module stellarator (IMS) [IEEE Trans. Plasma Sci. PS-9, 212 (1981)] has been measured experimentally with the use of an electron beam. The results show nested, wellformed surfaces with a rotational transform profile corresponding to the predicted profile. In the area outside the separatrix, regions of localized magnetic flux emergence from the coil volume (modular divertors) have been seen using an electron beam as well as during plasma operation, and correspond to regions of localized particle flux emergence from between the modular coils. [ABSTRACT FROM AUTHOR]

Probe measurements over the two-dimensional plasma cross section of the average and fluctuating density, electron temperature, and potential, as well as the Reynolds stress, have been made in the Interchangeable Module Stellarator (IMS) [D. T. Anderson, J. A. Derr, and J. L. Shohet, IEEE Trans. Plasma Sci. PS-9, 212 (1981)]. These measurements were performed at two magnetic field strengths, and also when a positively biased electrode induces a poloidal plasma flow. The data shows the fluctuation-induced transport to be poloidally asymmetric and dependent upon the location of the electron cyclotron resonance position, and upon the electrode biasing. The induced poloidal plasma flow changes the nominally outward fluctuation-induced particle transport to be inward (negative radial transport) by changing the phase relationship of the density and potential oscillations. The amplitude of the density and potential fluctuations are, in general, not reduced by the sheared poloidal flow. Calculations are presented comparing the computed Reynolds stress induced poloidal plasma flows with the flow calculated from momentum balance. [ABSTRACT FROM AUTHOR]

The magneto-optical Kerr effect (MOKE) has been observed and characterized in 1–80 nm thick Fe21Ni79 films deposited onto Si(100), for an external magnetic field (variable in strength up to 400 G) oriented parallel or orthogonal to the magnetization axis of the film. A measurable response is observed for film thicknesses (d) as small as 2 nm and, if the external magnetic field lies in the plane of the film, two-dimensional quantum behavior is evident for d≲6 nm. A precipitous decline in the magnitude of the MOKE response is accompanied by an increase in the coercivity and, when the external field is perpendicular to the film magnetization axis, a rapid rise in the saturation field. Experiments also confirm the existence of a component of the film magnetization oriented out of the plane of the film, a result consistent with the prediction of computational studies [T. Trunk et al., J. Appl. Phys. 89, 7606 (2001)] that the transition between Bloch and Néel wall domain structure occurs in FeNi films for film thicknesses of ≈30 nm. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]