D.T. Anderson

Measurement of ion flows using an ‘‘unmagnetized’’ Mach probe in the interchangeable module stellarator

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 E×B drift velocity an...

Experimental determination of the magnetic field spectrum in the Helically Symmetric Experiment using passing particle orbits

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.

Reduced particle and heat transport with quasisymmetry in the Helically Symmetric Experiment

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.

Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks

Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad?Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.

Comparison of the flows and radial electric field in the HSX stellarator to neoclassical calculations

Intrinsic flow velocities of up to ?20?km?s?1 have been measured using charge exchange recombination spectroscopy (CHERS) in the quasi-helically symmetric HSX stellarator and are compared with the neoclassical values calculated using an updated version (Lore 2010 Measurement and Transport Modeling with Momentum Conservation of an Electron Internal Transport Barrier in HSX (Madison, WI: University of Wisconsin); Lore et al 2010 Phys. Plasmas 17 056101) of the PENTA code (Spong 2005 Phys. Plasmas. 12 056114). PENTA uses the monoenergetic transport coefficients calculated by the drift kinetic equation solver code (Hirshman et al 1986 Phys. Fluids 29 2951; van Rij and Hirshman 1989 Phys. Fluids B 1 563), but corrects for momentum conservation. In the outer half of the plasma good agreement is seen between the measured parallel flow profile and the calculated neoclassical values when momentum correction is included. The flow velocity in HSX is underpredicted by an order of magnitude when this momentum correction is not applied. The parallel flow is calculated to be approximately equal for the majority hydrogen ions and the C6+ ions used for the CHERS measurements. The pressure gradient of the protons is the primary drive of the calculated parallel flow for a significant portion of the outer half of the plasma. The values of the radial electric field calculated with and without momentum correction were similar, but both were smaller than the measured values in the outer half of the plasma. Differences between the measured and predicted radial electric field are possibly a result of uncertainty in the composition of the ion population and sensitivity of the ion flux calculation to resonances in the radial electric field.

Measurements and modeling of plasma flow damping in the Helically Symmetric eXperimenta)

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 co...

A stellarator configuration for reactor studies

A helical coil winding law has been found for a stellarator with many of the desirable properties of the Helias. High performance computer codes make it possible to optimize the configuration over a parameter space of large dimension. For reactor applications an ample gap is provided between the coils and the plasma. Line tracing shows that the magnetic surfaces are robust. Non-linear stability at high beta is verified by equilibrium calculations in three dimensions. A neoclassical theory of transport taking quasi-neutrality into account predicts that energy confinement times sufficient for ignition can be achieved economically. For power plant studies a more attractive modular version of this concept called the MHH stellarator is under investigation

First results from the multichannel interferometer system on HSX

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 [ne>2×1012 cm−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.

Multichannel interferometer system for the helically symmetric experiment

A multichannel millimeter-wave interferometer system has been designed, fabricated and installed on the helically symmetric experiment (HSX), located at the University of Wisconsin, Madison. The interferometer system will view the plasma cross section along nine adjacent chords with 1.5 cm spacing. With this arrangement, coverage will span from the low-field side plasma scrape-off layer to well past the magnetic axis. For the plasma densities anticipated on HSX, a solid-state source operating at 288 GHz will be utilized. At this frequency refraction will be manageable, being less than the channel spacing. The source will be bias-tuned and modulated with a sawtooth wave form at 750 kHz in order to generate the intermediate frequency necessary for the heterodyne detection scheme. The signals will be measured using Schottky-diode corner-cube mixers. The interferometer will have sensitivity nedl≈8×1011 cm−2, being able to measure density changes <1%. Initially, the phase will be evaluated using analog electro...

OVERVIEW OF RECENT RESULTS FROM HSX

Abstract Recent results are summarized for the Helically Symmetric Experiment (HSX), which has the capability of running as a quasi-helically symmetric stellarator or as a more conventional, nonsymmetric stellarator. From X-ray measurements, we have demonstrated improved confinement of energetic particles. With central electron cyclotron heating, the density profiles in the quasi-symmetric configuration are peaked, in contrast to the hollow or flat profiles when the symmetry is broken. The difference in profiles is attributed to the lowering of the neoclassical thermodiffusive flux when the symmetry is present. The central electron temperature is ~200 eV higher for the quasi-symmetric configuration over the nonsymmetric case. The power deposition profiles are similar for the two cases, implying that the neoclassical electron thermal conductivity is reduced with quasi-symmetry. Related to the good confinement characteristics in the quasi-symmetric mode of operation, fluctuations in the density and magnetic field, consistent with that of a global Alfvén eigenmode (GAE), are observed. While the neoclassical characteristics of the quasi-symmetric and nonsymmetric configurations are very different, we have yet to find, under present operating conditions, any significant difference (other than the possible GAE mode) in turbulence characteristics or blob formation at the plasma edge.