Multi-energy reconstructions, central electron temperature measurements, and early detection of the birth and growth of runaway electrons using a versatile soft x-ray pinhole camera at MST.

A multi-energy soft x-ray pinhole camera has been designed, built, and deployed at the Madison Symmetric Torus to aid the study of particle and thermal transport, as well as MHD stability physics. This novel imaging diagnostic technique employs a pixelated x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. The detector of choice is a PILATUS3 100 K with a 450 µm thick silicon sensor and nearly 100 000 pixels sensitive to photon energies between 1.6 and 30 keV. An ensemble of cubic spline smoothing functions has been applied to the line-integrated data for each time-frame and energy-range, obtaining a reduced standard-deviation when compared to that dominated by photon-noise. The multi-energy local emissivity profiles are obtained from a 1D matrix-based Abel-inversion procedure. Central values of Te can be obtained by modeling the slope of the continuum radiation from ratios of the inverted radial emissivity profiles over multiple energy ranges with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. In tokamak plasmas, a novel application has recently been tested for early detection, 1D imaging, and study of the birth, exponential growth, and saturation of runaway electrons at energies comparable to 100 × Te,0; thus, early results are also presented.

Direct Measurement of a Toroidally Directed Zonal Flow in a Toroidal Plasma.

Zonal flow appears in toroidal, magnetically confined plasmas as part of the self-regulated interaction of turbulence and transport processes. For toroidal plasmas having a strong toroidal magnetic field, the zonal flow is predominately poloidally directed. This Letter reports the first observation of a zonal flow that is toroidally directed. The measurements are made just inside the last closed flux surface of reversed field pinch plasmas that have a dominant poloidal magnetic field. A limit cycle oscillation between the strength of the zonal flow and the amplitude of plasma potential fluctuations is observed, which provides evidence for the self-regulation characteristic of drift-wave-type plasma turbulence. The measurements help advance understanding and gyrokinetic modeling of toroidal plasmas in the pursuit of fusion energy.

Simulation, design, and first test of a multi-energy soft x-ray (SXR) pinhole camera in the Madison Symmetric Torus (MST).

A multi-energy soft x-ray pinhole camera has been designed and built for the Madison Symmetric Torus reversed field pinch to aid the study of particle and thermal-transport, as well as MHD stability physics. This novel imaging diagnostic technique combines the best features from both pulse-height-analysis and multi-foil methods employing a PILATUS3 x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. Further improvements implemented on the new cooled systems allow a maximum count rate of 10 MHz per pixel and sensitivity to the strong Al and Ar emission between 1.5 and 4 keV. The local x-ray emissivity will be measured in multiple energy ranges simultaneously, from which it is possible to infer 1D and 2D simultaneous profile measurements of core electron temperature and impurity density profiles with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. The expected time and space resolutions will be 2 ms and <1 cm, respectively.

Development of a multi-channel capacitive probe for electric field measurements with fine spatial and high time resolution.

A capacitive probe [Tan et al., Rev. Sci. Instrum. 88, 023502 (2017)] is one of a few diagnostics that is directly sensitive to the plasma potential. Using this diagnostic technique, a Multi-channel Linear Capacitive Probe (MLCP) is developed for turbulence measurements. The MLCP has 10 spatial channels and provides 9 points of radial electric field measurements simultaneously with a spatial step of 7 mm. A new readout circuit and a correction technique for low frequency attenuation are also developed to achieve the required spatial and time resolution. A performance test of the MLCP using a reversed field pinch plasma confirms that the MLCP resolves sub-centimeter structures of the equilibrium radial electric field profile and fluctuations up to 680 kHz.

Measurements of Impurity Transport Due to Drift-Wave Turbulence in a Toroidal Plasma.

The first direct measurements of an impurity particle flux driven by drift-wave turbulence in a toroidal magnetized plasma are reported. The correlation between the impurity density and radial velocity fluctuations is measured using ion Doppler spectroscopy. The small, very fast radial velocity fluctuation is resolved with the aid of a new linearized spectrum correlation analysis method that rejects uncorrelated noise as the sample size increases. The measured C^{2+} turbulent impurity flux in the edge of the plasma is directed inward and is consistent with impurity density measurements. This is also the first direct evidence for fluctuation-induced transport due to trapped-electron-mode turbulence in reversed field pinch plasmas.

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology.

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ∼ tenfold variation in the fluctuation amplitude, the viscosity increases ∼100-fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Linearized spectrum correlation analysis for line emission measurements.

A new spectral analysis method, Linearized Spectrum Correlation Analysis (LSCA), for charge exchange and passive ion Doppler spectroscopy is introduced to provide a means of measuring fast spectral line shape changes associated with ion-scale micro-instabilities. This analysis method is designed to resolve the fluctuations in the emission line shape from a stationary ion-scale wave. The method linearizes the fluctuations around a time-averaged line shape (e.g., Gaussian) and subdivides the spectral output channels into two sets to reduce contributions from uncorrelated fluctuations without averaging over the fast time dynamics. In principle, small fluctuations in the parameters used for a line shape model can be measured by evaluating the cross spectrum between different channel groupings to isolate a particular fluctuating quantity. High-frequency ion velocity measurements (100-200 kHz) were made by using this method. We also conducted simulations to compare LSCA with a moment analysis technique under a low photon count condition. Both experimental and synthetic measurements demonstrate the effectiveness of LSCA.

A comparison between soft x-ray and magnetic phase data on the Madison symmetric torus.

The Soft X-Ray (SXR) tomography system on the Madison Symmetric Torus uses four cameras to determine the emissivity structure of the plasma. This structure should directly correspond to the structure of the magnetic field; however, there is an apparent phase difference between the emissivity reconstructions and magnetic field reconstructions when using a cylindrical approximation. The difference between the phase of the dominant rotating helical mode of the magnetic field and the motion of the brightest line of sight for each SXR camera is dependent on both the camera viewing angle and the plasma conditions. Holding these parameters fixed, this phase difference is shown to be consistent over multiple measurements when only toroidal or poloidal magnetic field components are considered. These differences emerge from physical effects of the toroidal geometry which are not captured in the cylindrical approximation.

Kinetic stress and intrinsic flow in a toroidal plasma.

A new mechanism for intrinsic plasma flow has been experimentally identified in a toroidal plasma. For reversed field pinch plasmas with a few percent ß (ratio of plasma pressure to magnetic pressure), measurements show that parallel pressure fluctuations correlated with magnetic fluctuations create a kinetic stress that can affect momentum balance and the evolution of intrinsic plasma flow. This implies kinetic effects are important for flow generation and sustainment.

Density fluctuation measurements by far-forward collective scattering in the MST reversed-field pinch.

The multichannel polarimeter-interferometer system on the MST reversed-field pinch can be utilized to measure far-forward collective scattering from electron density fluctuations. The collective scattering system has 11 viewing chords with ∼8 cm spacing. The source is a 432 µm (694 GHz) far infrared laser and the scattered power is measured using a heterodyne detection scheme. Collective scattering provides a line-integrated measurement of fluctuations within the divergence of the probe beam covering wavenumber range: k(⊥) < 1.3 cm(-1), corresponding k(⊥)ρ(s) < 1.3 (ρ(s) is the ion-sound Larmor radius), the region of primary interest for turbulent fluctuation-induced transport. The perpendicular wavenumber consists of toroidal, poloidal, and radial contributions, which vary with chord position. Coherent modes associated with tearing instabilities and neutral-beam driven fast particles are observed along with broadband turbulence at frequencies up to 500 kHz. Changes in frequency are consistent with a Doppler shift due to parallel plasma flow.

Fast-particle-driven Alfvénic modes in a reversed field pinch.

Alfvénic modes are observed due to neutral beam injection for the first time in a reversed field pinch plasma. Modeling of the beam deposition and slowing down shows that the velocity and radial localization are high. This allows instability drive from inverse Landau damping of a bump-on-tail in the parallel distribution function or from free energy in the fast ion density gradient. Mode switching from a lower frequency toroidal mode number n=5 mode that scales with beam injection velocity to a higher frequency n=4 mode with Alfvénic scaling is observed.

Role of nonlinear coupling and density fluctuations in magnetic-fluctuation-induced particle transport.

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnetic fluctuations, leading to strong particle transport.

Classical impurity ion confinement in a toroidal magnetized fusion plasma.

High-resolution measurements of impurity ion dynamics provide first-time evidence of classical ion confinement in a toroidal, magnetically confined plasma. The density profile evolution of fully stripped carbon is measured in MST reversed-field pinch plasmas with reduced magnetic turbulence to assess Coulomb-collisional transport without the neoclassical enhancement from particle drift effects. The impurity density profile evolves to a hollow shape, consistent with the temperature screening mechanism of classical transport. Corroborating methane pellet injection experiments expose the sensitivity of the impurity particle confinement time to the residual magnetic fluctuation amplitude.

Experimental observation of anisotropic magnetic turbulence in a reversed field pinch plasma.

In this Letter we report an experimental study of fully developed anisotropic magnetic turbulence in a laboratory plasma. The turbulence has broad (narrow) spectral power in the perpendicular (parallel) direction to the local mean magnetic field extending beyond the ion cyclotron frequency. Its k[see symbol] spectrum is asymmetric in the ion and electron diamagnetic directions. The wave number scaling for the short wavelength fluctuations shows exponential falloff indicative of dissipation. A standing wave structure is found for the turbulence in the minor radial direction of the toroidal plasma.

Powered oscillator using ignitron switches.

A 10-MVA-scale resonant oscillator, powered by a pulse-forming network and switched with a pair of commutating mercury ignitrons, was developed for the MST reversed-field pinch plasma-confinement experiment. A novel feature of this circuit is its commutation mechanism, wherein each turning on of one ignitron causes a reverse voltage transient that turns off the other. Two of these oscillators are used in oscillating-field current-drive tests, in which they are capable of nearly 1MW net input power to the plasma, with resonant frequencies of a few 100 Hz for pulse durations of a few tens of ms, being precharged for immediate full amplitude. We describe the circuit and its operation, and discuss features that allow reliable, high-current commutation of the ignitrons and exploit their low switching impedance.

Stabilization of the resistive wall mode by a rotating solid conductor.

Stabilization of the resistive wall mode (RWM) by high-speed differentially rotating conducting walls is demonstrated in the laboratory. To observe stabilization intrinsic azimuthal plasma rotation must be braked with error fields. Above a critical error field the RWM frequency discontinuously slows (locks) and fast growth subsequently occurs. Wall rotation is found to reduce the locked RWM saturated amplitude and growth rate, with both static (vacuum vessel) wall locked and slowly rotating RWMs observed depending on the alignment of wall to plasma rotation. At high wall rotation RWM onset is found to occur at larger plasma currents, thus increasing the RWM-stable operation window.

Bifurcation to 3D helical magnetic equilibrium in an axisymmetric toroidal device.

We report the first direct measurement of the internal magnetic field structure associated with a 3D helical equilibrium generated spontaneously in the core of an axisymmetric toroidal plasma containment device. Magnetohydrodynamic equilibrium bifurcation occurs in a reversed-field pinch when the innermost resonant magnetic perturbation grows to a large amplitude, reaching up to 8% of the mean field strength. Magnetic topology evolution is determined by measuring the Faraday effect, revealing that, as the perturbation grows, toroidal symmetry is broken and a helical equilibrium is established.

Mass-dependent ion heating during magnetic reconnection in a laboratory plasma.

Noncollisional ion heating in laboratory and astrophysical plasmas and the mechanism of conversion of magnetic energy to ion thermal energy are not well understood. In the Madison Symmetric Torus reversed-field pinch experiment, ions are heated rapidly during impulsive reconnection, attaining temperatures exceeding hundreds of eV, often well in excess of the electron temperature. The energy budget of the ion heating and its mass scaling in hydrogen, deuterium, and helium plasmas were determined by measuring the fraction of the released magnetic energy converted to ion thermal energy. The fraction ranges from about 10%-30% and increases approximately as the square root of the ion mass. A simple model based on stochastic ion heating is proposed that is consistent with the experimental data.

Magnetic-fluctuation-induced particle transport and density relaxation in a high-temperature plasma.

The first direct measurement of magnetic-fluctuation-induced particle flux in the core of a high-temperature plasma is reported. Transport occurs due to magnetic field fluctuations associated with global tearing instabilities. The electron particle flux, resulting from the correlated product of electron density and radial magnetic fluctuations, accounts for density profile relaxation during a magnetic reconnection event. The measured particle transport is much larger than that expected for ambipolar particle diffusion in a stochastic magnetic field.

Probes for measuring fluctuation-induced Maxwell and Reynolds stresses in the edge of the Madison Symmetric Torus reversed field pinch.

Several probes have been constructed to measure fluctuation-induced Maxwell and Reynolds stresses in the edge of the Madison Symmetric Torus reversed field pinch (RFP). The magnetic probe is composed of six magnetic pickup coil triplets. The triplets are separated spatially, which allows for local measurements of the Maxwell stress. To measure the plasma flow components for evaluation of the Reynolds stress, we employ a combination of an optical probe [Kuritsyn et al., Rev. Sci. Indrum. 77, 10F112 (2006)] and a Mach probe. The optical probe measures the radial ion flow locally using Doppler spectroscopy. The Mach probe consists of four current collectors biased negatively with respect to a reference tip and allows for measurements of the poloidal and toroidal components of the bulk plasma flow. The stresses are observed to play an important role in the momentum balance in the RFP edge during internal reconnection events.