Tokamak Plasmas with Density up to 10 Times the Greenwald Limit.

Current-carrying, toroidal laboratory plasmas typically cannot be sustained with an electron density above the empirical Greenwald limit. Presented here are tokamak experiments in the Madison Symmetric Torus with a density up to an unprecedented level about 10 times this limit. This is thought to be made possible in part by a thick, stabilizing, conductive wall, and a high-voltage, feedback-controlled power supply driving the plasma current. The radial profile of the toroidal current flattens around twice the limit, without the edge collapse routinely observed in other experiments.

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.

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.

All-in-one probe for exploring self-organized two-fluid equilibria in toroidal plasmas.

This paper presents the development of an all-in-one probe to simultaneously measure all components of the generalized Ohm's law in reversed-field pinch plasmas and tokamaks. The polyhedral configuration of the Mach probe is achieved through the specific arrangement, angle, and depth of the collimator channel apertures drilled into the surface of a hollow boron nitride cylinder encasing it. This probe includes a central Mach probe to assess the ion velocity field in three dimensions. Initial tests at the RELAX and Madison Symmetric Torus machines have confirmed the probe's effectiveness, revealing an octahedron form similar to a tetrahedron. The probe seems to function correctly and is expected to facilitate the empirical validation of two-fluid equilibria at the periphery of toroidal plasmas.

An octahedral Mach B-dot probe for 3D flows and magnetic fields in the edge of reversed field pinches.

Measurements and simulations show that plasma relaxation processes in the reversed field pinch drive and redistribute both magnetic flux and momentum. To examine this relaxation process, a new 3D Mach B-dot probe has been constructed. This probe collects ion saturation currents through six molybdenum electrodes arranged on the flattened vertices of an octahedron made of boron nitride (BN). The ion saturation current flows through configurable voltage dividers for measurement and returns through one of six selectable return electrodes equally spaced along the 12 cm BN probe arm. In addition, the probe arm houses three B-dot magnetic pickup coils in the BN stalk immediately below to the octahedron, to measure the local magnetic field. Inserted in the Madison Symmetric Torus (MST) during deuterium discharges with 220 kA plasma current, density of 0.8 × 1013 cm-3, the probe collects ion saturation currents with sawtooth-like peaks correlated with relaxation events. This compact octahedral design fitting six Mach electrode surfaces within a 1 cm3 cube will enable future multi-point, multi-field probes compatible with the 1.5 in. ports of MST. Such probes will allow for flow circulation, current, and canonical vorticity to be calculated in the center of the finite difference stencil formed by the measurement locations.

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.

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.

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.

Anisotropic ion heating and tail generation during tearing mode magnetic reconnection in a high-temperature plasma.

Complementary measurements of ion energy distributions in a magnetically confined high-temperature plasma show that magnetic reconnection results in both anisotropic ion heating and the generation of suprathermal ions. The anisotropy, observed in the C(+6) impurity ions, is such that the temperature perpendicular to the magnetic field is larger than the temperature parallel to the magnetic field. The suprathermal tail appears in the majority ion distribution and is well described by a power law to energies 10 times the thermal energy. These observations may offer insight into the energization process.

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.

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.

Development towards a fast ion loss detector for the reversed field pinch.

A fast ion loss detector has been constructed and implemented on the Madison Symmetric Torus (MST) to investigate energetic ion losses and transport due to energetic particle and MHD instabilities. The detector discriminates particle orbits solely on pitch and consists of two thin-foil, particle collecting plates that are symmetric with respect to the device aperture. One plate collects fast ion signal, while the second aids in the minimization of background and noise effects. Initial measurements are reported along with suggestions for the next design phase of the detector.

An upgraded x-ray spectroscopy diagnostic on MST.

An upgraded x-ray spectroscopy diagnostic is used to measure the distribution of fast electrons in MST and to determine Z(eff) and the particle diffusion coefficient D(r). A radial array of 12 CdZnTe hard-x-ray detectors measures 10-150 keV Bremsstrahlung from fast electrons, a signature of reduced stochasticity and improved confinement in the plasma. A new Si soft-x-ray detector measures 2-10 keV Bremsstrahlung from thermal and fast electrons. The shaped output pulses from both detector types are digitized and the resulting waveforms are fit with Gaussians to resolve pileup and provide good time and energy resolution. Lead apertures prevent detector saturation and provide a well-known etendue, while lead shielding prevents pickup from stray x-rays. New Be vacuum windows transmit >2 keV x-rays, and additional Al and Be filters are sometimes used to reduce low energy flux for better resolution at higher energies. Measured spectra are compared to those predicted by the Fokker-Planck code CQL3D to deduce Z(eff) and D(r).

Energetic-electron-driven instability in the helically symmetric experiment.

Energetic electrons generated by electron cyclotron resonance heating are observed to drive instabilities in the quasihelically symmetric stellarator device. The coherent, global fluctuations peak in the plasma core and are measured in the frequency range of 20-120 kHz. Mode propagation is in the diamagnetic drift direction of the driving species. When quasihelical symmetry is broken, the mode is no longer observed. Experimental observations indicate that the unstable mode is acoustic rather than Alfvénic.

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.