J.N. Talmadge

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...

Evolution of the plasma rotation and the radial electric field for a toroidal plasma in the Pfirsch–Schlüter and plateau regimes subject to a biased electrode

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–Schluter 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 o...

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.

Internal electron transport barrier due to neoclassical ambipolarity in the helically symmetric experiment

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. Plasmas12, 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. Turbulenttransport 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)].

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.

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 helically symmetric stellarator (HSX)

The Helically Symmetric Experiment (HSX) Is a quasi-helically symmetric (QHS) stellarator currently under construction at the Torsatron/Stellarator Laboratory of the University of Wisconsin-Madison. This device is unique in its magnetic design in that the magnetic field spectrum possesses only a single dominant (helical) component. This design avoids the large direct orbit losses associated with conventional stellarators. The restoration of an ignorable coordinate in the confining magnetic field makes this device analogous to an axisymmetric q=1/3 tokamak with respect to neoclassical confinement.

Simulations of edge configurations in quasi-helically symmetric geometry using EMC3–EIRENE

Simulations of the edge of a quasi-helically symmetric (QHS) stellarator with geometry based on the Helically Symmetric eXperiment (HSX) are performed using the coupled codes EMC3–EIRENE. The standard configuration of HSX has an island structure outside the separatrix, corresponding to the 8/7 resonance. In addition to the standard configuration, two other configurations are examined: one with small islands outside the separatrix corresponding to the 16/15 resonance, and one with large islands corresponding to the 4/4 resonance. Using EMC3–EIRENE, density scans are employed, while scaling input power linearly with density, in order to determine the transition point from a low- to a high-recycling regime. The small island and the standard cases show markedly similar behaviour, but the large island configuration transitions to high-recycling and detached regimes at significantly lower plasma densities. Reducing the perpendicular diffusion coefficients creates behaviour more consistent with two-point model predictions by reducing the role of perpendicular transport through edge islands and reducing friction loss from counter-streaming parallel flows. When carbon impurities are added, the large island configuration exhibits a large increase in radiated power, while the two configurations with smaller islands do not.

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.