MST Reversed Field Pinch Research Articles

Overview of gyrokinetic studies of finite-β microturbulence

Recent results on electromagnetic turbulence from gyrokinetic studies in different magnetic configurations are overviewed, detailing the physics of electromagnetic turbulence and transport, and the effect of equilibrium magnetic field scale lengths. Ion temperature gradient (ITG) turbulence is shown to produce magnetic stochasticity through nonlinear excitation of linearly stable tearing-parity modes. The excitation, which is catalyzed by the zonal flow, produces an electron heat flux proportional to β2 that deviates markedly from quasilinear theory. Above a critical beta known as the non-zonal transition (NZT), the magnetic fluctuations disable zonal flows by allowing electron streaming that shorts zonal potential between flux surfaces. This leads to a regime of very high transport levels. Kinetic ballooning mode (KBM) saturation is described. For tokamaks saturation involves twisted structures arising from magnetic shear; for helical plasmas oppositely inclined convection cells interact by mutual shearing. Microtearing modes are unstable in the magnetic geometry of tokamaks and the reversed field pinch (RFP). In NSTX instability requires finite collisionality, large beta, and is favored by increasing magnetic shear and decreasing safety factor. In the RFP, a new branch of microtearing with finite growth rate at vanishing collisionality is shown from analytic theory to require the electron grad-B/curvature drift resonance. However, gyrokinetic modeling of experimental MST RFP discharges at finite beta reveals turbulence that is electrostatic, has large zonal flows, and a large Dimits shift. Analysis shows that the shorter equilibrium magnetic field scale lengths increase the critical gradients associated with the instability of trapped electron modes, ITG and microtearing, while increasing beta thresholds for KBM instability and the NZT.

Overview of results from the MST reversed field pinch experiment

An overview of recent results from the MST reversed field pinch programme is presented. With neutral beam injection, bursty energetic particle (EP) modes are observed. The profiles of the magnetic and density fluctuations associated with these EP modes are measured using a far infrared interferometer–polarimeter. Equilibrium reconstructions of the quasi-single-helicity 3D helical state are provided by the V3FIT code that now incorporates several of MST's advanced diagnostics. The orientation of the helical structure is controlled using a new resonant magnetic perturbation technique. Gyrokinetic simulations based on experimental equilibria predict unstable trapped-electron modes (TEMs), and small-scale density fluctuations are detected in improved-confinement plasmas with TEM-like features. Upgraded pellet injection permits study of density and beta limits over MST's full range of operation, and an MST-record line-average density of 0.9 × 1020 m3 (n/nG = 1.4) has been obtained. Impurity ion temperature measurements reveal a charge-to-mass-ratio dependence in the rapid heating that occurs during a sawtooth crash. Runaway of NBI-born fast ions during the impulsive sawtooth event agrees with test-particle theory. Magnetic self-organization studies include measurements of the dynamo emf with an applied ac inductive electric field using oscillating field current drive.

High-frequency fluctuation measurements by far-infrared laser Faraday-effect polarimetry-interferometry and forward scattering system on MST.

Magnetic fluctuation-induced transport driven by global tearing modes has been measured by Faraday-effect polarimetry and interferometry (phase measurements) in the MST reversed field pinch. However, the role of small-scale broadband magnetic and density turbulence in transport remains unknown. In order to investigate broadband magnetic turbulence, we plan to upgrade the existing detector system by using planar-diode fundamental waveguide mixers optimized for high sensitivity. Initial tests indicate these mixers have ×10 sensitivity improvement compared to currently employed corner-cube Schottky-diode mixers and ×5 lower noise. Compact mixer design will allow us to resolve the wavenumbers up to k ∼ 1-2 cm(-1) for beam width w = 1.5 cm and 15 cm(-1) for beam width w = 2 mm. The system can also be used to measure the scattered signal (amplitude measurement) induced by both plasma density and magnetic fluctuations.

High-repetition-rate pulse-burst laser for Thomson scattering on the MST reversed-field pinch

A new, high-repetition-rate pulse-burst laser system for the MST Thomson scattering diagnostic has operated with 2 J pulses at repetition rates up to 75 kHz within a burst. The 1064 nm laser currently employs a q-switched, diode pumped Nd:YVO4 master oscillator, four Nd:YAG amplifier stages, and a Nd:glass amplifier, with plans for an additional Nd:glass amplifier. The laser can maintain 1.5–2 J pulses in two operating modes: either at a uniform repetition rate of 5–10 kHz (sustained for 5–8 ms), or reach rates of up to 75 kHz in pulse-burst operation (for 10 bursts of 15 pulses each), limited by flashlamp explosion energy and wall loading. The full system, including an additional Nd:glass amplifier, is designed to produce bursts of 2 J pulses at a repetition rate of at least 250 kHz. Custom programmable square-pulse power supplies drive the amplifier flashlamps, providing fine control of pulse timing, duration, and repetition, and allow for pulse-burst operation. The new laser system integrates with the same collection optics and detectors as used by the previous MST Thomson laser: 21 spatial points across the MST minor radius, filter polychromators with 6 to 8 channels (10 eV–5 keV range), avalanche photodiode detectors, and 1 GSample/s/channel digitization. Use of the previous pulse-burst laser continues concurrently with new laser development. Additional notes on optimization of flashlamp simmering will also be covered, showing that an increase in simmer currents can improve pulse-to-pulse energy consistency on both the new and older lasers.

Overview of results from the MST reversed field pinch experiment

An overview of recent results from the MST programme on physics important for the advancement of the reversed field pinch (RFP) as well as for improved understanding of toroidal magnetic confinement more generally is reported. Evidence for the classical confinement of ions in the RFP is provided by analysis of impurity ions and energetic ions created by 1 MW neutral beam injection (NBI). The first appearance of energetic-particle-driven modes by NBI in a RFP plasma is described. MST plasmas robustly access the quasi-single-helicity state that has commonalities to the stellarator and ‘snake’ formation in tokamaks. In MST the dominant mode grows to 8% of the axisymmetric field strength, while the remaining modes are reduced. Predictive capability for tearing mode behaviour has been improved through nonlinear, 3D, resistive magnetohydrodynamic computation using the measured resistivity profile and Lundquist number, which reproduces the sawtooth cycle dynamics. Experimental evidence and computational analysis indicates two-fluid effects, e.g., Hall physics and gyro-viscosity, are needed to understand the coupling of parallel momentum transport and current profile relaxation. Large Reynolds and Maxwell stresses, plus separately measured kinetic stress, indicate an intricate momentum balance and a possible origin for MST's intrinsic plasma rotation. Gyrokinetic analysis indicates that micro-tearing modes can be unstable at high beta, with a critical gradient for the electron temperature that is larger than for tokamak plasmas by roughly the aspect ratio.

Neutral particle analyzer for studies of fast ion population in plasma

An advanced neutral particles analyzer for plasma diagnostic with possibility of simultaneous measurements of energy distributions of D and H ions has been developed in the Budker Institute of Nuclear Physics. The analyzer was used in two plasma facilities with injection of fast neutrals—on the MST reversed field pinch (University of Wisconsin) and the field reversed configuration C-2 (Tri Alpha Energy). In this paper, the design of the analyzer, calculation of efficiency of registration, results of analyzer calibration and experimental results from MST and C-2 experiments are presented.

Time-resolved ion energy distribution measurements using an advanced neutral particle analyzer on the MST reversed-field pinch

An advanced neutral particle analyzer (ANPA) capable of simultaneously measuring hydrogen and deuterium ions of energies up to 45 keV has recently been developed for use on the Madison Symmetric Torus. The charge-to-mass separation allows for separate analysis of bulk deuterium ions and hydrogen ions injected with a 1 MW, 25 keV neutral beam. Orientation of the ANPA allows sampling of different regions of ion velocity space; a radial viewport favors collection of ions with high v(perpendicular)∕|v| while a recently installed tangential viewport favors ions with high v(||)∕|v|, such as those from the core-localized fast ion population created by the neutral beam. Signals are observed in the ANPA's highest energy channels during periodic magnetic reconnection events, which are drivers of anisotropic, non-Maxwellian ion energization in the reversed-field pinch. ANPA signal strength is dependent on the background neutral density, which also increases during magnetic reconnection events, so careful analysis must be performed to identify the true change in the ion distribution. A Monte Carlo neutral particle tracing code (NENE) is used to reconstruct neutral density profiles based on D(α) line emission, which is measured using a 16-chord filtered photodiode array.

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.

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.

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.

A new double-foil soft x-ray array to measure Te on the MST reversed field pinch

A soft x-ray (SXR) diagnostic to measure electron temperature on the Madison Symmetric Torus using two complementary methods is presented. Both methods are based on the double-foil technique, which calculates electron temperature via the ratio of SXR bremsstrahlung emission from the plasma in two different energy ranges. The tomographic emissivity method applies the double-foil technique to a tomographic reconstruction of SXR emissivity, creating a two-dimensional map of temperature throughout the plasma. In contrast, the direct brightness method applies the double-foil technique directly to the measured brightness and generates vertical and horizontal radial profiles. Extensive modeling demonstrates advantages and limitations in both techniques. For example, although the emissivity technique provides a two-dimensional mapping of temperature, its reliance on multiple tomographic inversions introduces some artifacts into the results. On the other hand, the more direct brightness technique avoids these artifacts but is only able to provide a radial profile of electron temperature.

Pulse-burst laser systems for fast Thomson scattering (invited)

Two standard commercial flashlamp-pumped Nd:YAG (YAG denotes yttrium aluminum garnet) lasers have been upgraded to "pulse-burst" capability. Each laser produces a burst of up to 15 2 J Q-switched pulses (1064 nm) at repetition rates of 1-12.5 kHz. Variable pulse-width drive (0.15-0.39 ms) of the flashlamps is accomplished by insulated gate bipolar transistor (IGBT) switching of electrolytic capacitor banks. Direct control of the laser Pockels cell drive enables optimal pulse energy extraction, and up to four 2 J laser pulses during one flashlamp pulse. These lasers are used in the Thomson scattering plasma diagnostic system on the MST reversed-field pinch to record the dynamic evolution of the electron temperature profile and temperature fluctuations. To further these investigations, a custom pulse-burst laser system with a maximum pulse repetition rate of 250 kHz is now being commissioned.

Pulse-burst operation of standard Nd:YAG lasers

Two standard commercial flashlamp-pumped Nd:YAG lasers have been upgraded to "pulse-burst" capability. Each laser produces a burst of up to fifteen 2 J Q-switched pulses (1064 nm) at repetition rates 1–12.5 kHz. Variable pulse-width drive (0.15–0.39 ms) of the flashlamps is accomplished by IGBT (insulated gate bipolar transistor) switching of electrolytic capacitor banks. Direct control of the laser Pockels cell drive enables optimal pulse energy extraction, and up to four 2 J laser pulses during one flashlamp pulse. These lasers are used in the Thomson scattering plasma diagnostic system on the MST reversed-field pinch to study the dynamic evolution of the electron temperature.

Measurement of magnetic fluctuation-induced particle flux (invited)

Magnetic field fluctuation-induced particle transport has been directly measured in the high-temperature core of the MST reversed field pinch plasma. Measurement of radial particle transport is achieved by combining various interferometry techniques, including Faraday rotation, conventional interferometry, and differential interferometry. It is observed that electron convective particle flux and its divergence exhibit a significant increase during a sawtooth crash. In this paper, we describe the basic techniques employed to determine the particle flux.

Nonambipolar Magnetic-Fluctuation-Induced Particle Transport and Plasma Flow in the MST Reversed-Field Pinch

First direct measurements of nonambipolar magnetic fluctuation-induced charge transport in the interior of a high-temperature plasma are reported. Global resistive tearing modes drive the charge transport which is measured in the vicinity of the resonant surface for the dominant core resonant mode. Finite charge transport has two important consequences. First, it generates a potential well along with locally strong electric field and electric field shear at the resonant surface. Second, this electric field induces a spontaneous E x B driven zonal flow.

Flow Dynamics and Plasma Heating of Spheromaks in SSX

We report several new experimental results related to flow dynamics and heating from single dipole-trapped spheromaks and spheromak merging studies at SSX. Single spheromaks (stabilized with a pair of external coils, see Brown, Phys. Plasmas 13 102503 (2006)) and merged FRC-like configurations (see Brown, Phys. Plasmas 13, 056503 (2006)) are trapped in our prolate (R = 0.2 m, L = 0.6 m) copper flux conserver. Local spheromak flow is studied with two Mach probes (r 1 ≤ ρ i , r 2 ≥ ρ i ) calibrated by time-of-flight with a fast set of magnetic probes at the edge of the device. Both Mach probes feature six ion collectors housed in a boron nitride sheath. The larger Mach probe will ultimately be used in the MST reversed field pinch. Line averaged flow is measured by ion Doppler spectroscopy (IDS) at the midplane. The SSX IDS instrument measures with 1 μs or better time resolution the width and Doppler shift of the C III impurity (H plasma) 229.7 nm line to determine the temperature and line-averaged flow velocity (see Cothran, RSI 77, 063504 (2006)). We find axial flows up to 100 km/s during formation of the dipole trapped spheromak. Flow returns at the wall to form a large vortex. Recent high-resolution IDS velocity measurements during spheromak merging show bi-directional outflow jets at ±40 km/s (nearly the Alfven speed). We also measure T i ≥ 80 eV and T e ≥ 20 eV during spheromak merging events after all plasma facing surfaces are cleaned with helium glow discharge conditioning. Transient electron heating is inferred from bursts on a four-channel soft x-ray array. The spheromaks are also characterized by a suite of magnetic probe arrays for magnetic structure B(r,t), and interferometry for n e . Finally, we are designing a new oblate, trapezoidal flux conserver for FRC studies. Equilibrium and dynamical simulations suggest that a tilt-stable, oblate FRC can be formed by spheromak merging in the new flux conserver.

On the Physics of Improved Confinement During Pulsed Poloidal Current Drive in MST Reversed-Field Pinch

Reduction of core-resonant magnetic fluctuations and improved confinement in the Madison Symmetric Torus reversed-field pinch (MST RFP) have been routinely achieved by applying the surface poloidal electric field. The created inductive poloidal electric field drives current in plasma which leads to the improved confinement. To study the effect we developed a relatively simple 1-D model in cylindrical geometry which assumes poloidal and axial symmetry during the drive. We use resistive magnetohydrodynamics model with realistic plasma parameters and assume that there is a vacuum gap between plasma boundary and conducting wall of the vessel. Evolution of plasma density is taken into account and plasma boundary moves self-consistently with momentum equation. We start from an initial unstable equilibrium and examine stability of plasma configuration at intermediate moments of time during the drive. For this we calculate the growth rates of unstable eigenmodes in the plasma. Our results show that the modifications to the plasma current profile during the drive are stabilizing. The initial stabilization is due to the direct modification of the current profile near the edge. It enhances later in time due to the flattening of λ profile in the core region as plasma and magnetic field compress inward during the drive.

Two-dimensional time resolved measurements of the electron temperature in MST

Two-dimensional (2D) time resolved images of the electron temperature profile in the core of the MST reversed field pinch plasma are presented. The measurements have been obtained with a soft x-ray (SXR) tomographic diagnostic comprised of four cameras, each with a multichannel photodiode array, viewing the plasma at different poloidal angles, with a total of 74 channels. The 2D electron temperature profile is estimated by simultaneously measuring the SXR emissivity through different beryllium foils, using the standard double-filter technique. With these methods, fast temperature variation in the core of the plasma (up to 100kHz) can be analyzed.

Coupling to the electron Bernstein wave using a phased array of waveguides in MST reversed field pinch

Coupling to the electron Bernstein wave (EBW) via a phased array of waveguides is experimentally investigated in the Madison symmetric torus reversed field pinch (RFP). EBWs promise to provide localized heating and current drive in overdense plasmas such as those in the RFP, provided a technique can be developed to efficiently couple power from an externally launched electromagnetic wave to the electrostatic EBW. The choice of antenna structure and launched wave polarization are important factors in coupling waves with frequencies in the electron cyclotron range to EBW, especially on the RFP where the mode conversion to the EBW can take place in the near-field of the antenna. In this paper, a recently developed theory of coupling to EBW from a phased array of waveguides is tested against experiment. The theory predicts that coupling efficiency will vary with launch angle and that coupling depends sensitively upon the edge density profile. Amplitudes and phases of reflected power in each of the waveguides are measured experimentally and compared with predictions based upon density profiles measured by a Langmuir probe in the edge of the plasma. The parametric dependence of reflection has been studied for different polarizations, different launch angles, time varying density profiles and several frequencies of the launched wave. An asymmetry in reflection versus the launch angle predicted by theory was found experimentally for the X-mode, while the O-mode was symmetric. The dependence on density scale length predicted by theory was confirmed in the experiment. The phase of the reflected signal is shown to contain reflectometry-based information about the edge density profile. For appropriate phasing, measurements show that the total power reflection coefficient can be lower than 15%.

Overview of results in the MST reversed field pinch experiment

Confinement in the reversed field pinch (RFP) has been shown to increase strongly with current profile control. The MST RFP can operate in two regimes: the standard regime with a naturally occurring current density profile, robust reconnection and dynamo activity; and the improved confinement regime with strong reduction in reconnection, dynamo and transport. New results in standard plasmas include the observation of a strong two-fluid Hall effect in reconnection and dynamo, the determination that the m = 0 edge resonant mode is nonlinearly driven, and the determination that tearing modes can lock to the wall via eddy currents in the shell. New results in improved confinement plasmas include observations that such plasmas are essentially dynamo-free, contain several isolated magnetic islands (as opposed to a stochastic field) and contain reduced high frequency turbulence. Auxiliary current drive and heating is now critical to RFP research. In MST, a programme to apply auxiliary systems to the RFP is underway and progress has accrued in several techniques, including lower hybrid and electron Bernstein wave injection, ac helicity injection current drive, pellet injection and neutral beam injection.