Madison Symmetric Torus Reversed-field Pinch Research Articles

Global linear and nonlinear gyrokinetic simulations of tearing modes

To better understand multi-scale interactions between global tearing modes and microturbulence in the Madison Symmetric Torus (MST) reversed-field pinch (RFP), the global gyrokinetic code Gene is modified to describe global tearing mode instability via a shifted Maxwellian (SM) distribution consistent with experimental equilibria. The implementation of the SM is tested and benchmarked by comparisons with different codes and models. Good agreement is obtained in code-code and code-theory comparisons. Linear stability of tearing modes of a non-reversed MST discharge is studied. A collisionality scan is performed to the lowest order unstable modes (n = 5, n = 6) and shown to behave consistently with theoretical scaling. The nonlinear evolution is simulated, and saturation is found to arise from mode coupling and transfer of energy from the most unstable tearing mode to small-scale stable modes mediated by the m = 2 tearing mode. The work described herein lays the foundation for nonlinear simulation and analysis of the interaction of tearing modes and gyroradius-scale instabilities in RFP plasmas.

Robust analysis of space-, time-, and energy-resolved soft x-ray measurements of magnetically confined fusion plasmas (invited).

A novel compact multi-energy soft x-ray (ME-SXR) diagnostic based on the PILATUS3 100K x-ray detector has been developed in collaboration between the Princeton Plasma Physics Laboratory and the University of Wisconsin-Madison and tested on the Madison Symmetric Torus (MST) reversed-field pinch. This solid-state photon-counting detector consists of a two-dimensional array of ∼100 000 pixels for which the lower photon absorption cutoff energy can be independently set, allowing it to be configured for a unique combination of simultaneous spatial, spectral, and temporal resolution of ∼1cm, 100eV, and 500Hz, respectively. The diagnostic is highly versatile and can be readily adapted to diverse plasma operating conditions and scientific needs without any required downtime. New results from improved-confinement and quasi-single helicity plasmas in the MST demonstrate how the detector can be applied to study multiple aspects of the evolution of magnetically confined fusion-grade plasmas. These include observing the evolution of thermal emissivity, characterizing the energy of mid-Z excitation lines, extracting the Te profile, and observing the evolution of non-thermal populations. A technique for integrating the ME-SXR diagnostic into an integrated data analysis framework based on Bayesian inference is also presented. This allows ME-SXR measurements to be combined with data for complementary diagnostics in order to simultaneously infer Te and nZ from all available information.

A versatile multi-energy soft x-ray diagnostic for Te measurements in the Madison Symmetric Torus

A multi-energy soft x-ray (ME-SXR) diagnostic based on the PILATUS3 100K x-ray camera, produced commercially by DECTRIS Ltd., has been installed on the Madison Symmetric Torus (MST) reversed-field pinch. This photon-counting camera consists of a two-dimensional array of ∼100,000 pixels for which the lower photon absorption cutoff energy can be independently set. This allows it to be configured for a unique combination of simultaneous spatial and spectral resolution. First plasma data has now been collected, and challenges with detector saturation have been sucessfully resolved. Analysis is complicated by the presence of bright Al+11 and Al+12 emission lines at ∼ 2 keV. In order to properly interpret this data a full forward model has been developed which produces realistic chord-integrated ME-SXR synthetic measurement given the underlying Te, ne, neutral density, and impurity density profiles. A method for using this model in a Bayesian framework to extract equilibrium Te measurements from MST high-temperature plasma data is presented. Resulting profiles show good agreement with Thomson scattering measurements in the core.

Effects of oscillating poloidal current drive on magnetic relaxation in the Madison Symmetric Torus reversed-field pinch

Magnetic relaxation behavior in reversed-field pinch (RFP) experiments on the Madison Symmetric Torus device is modified by oscillating poloidal current drive (OPCD). We observe that OPCD modulates the nonlinear magnetic fluctuation dynamics of the RFP as it modulates the equilibrium and its linear stability properties. In particular, OPCD can entrain the RFP’s nonlinear magnetic relaxation cycle and can therefore modify the frequency of the discrete relaxation events called sawtooth crashes. These crashes, which are intermittent or quasiperiodic in standard RFP plasmas without oscillating voltages, can be entrained by OPCD to become nearly periodic. The entrainment of the RFP sawtooth cycle is investigated by varying OPCD amplitude and frequency, as well as plasma equilibrium magnetic field reversal. Impurity ion (C+4) heating induced and modulated by OPCD is measured by ion Doppler spectrometry and is ascribed to the modulation of magnetic reconnection activity.

Construction of an EBW Heating System for the MST RFP

The first observation of rf heating in a reversed field pinch (RFP) using the electron Bernstein wave (EBW) has been demonstrated on Madison Symmetric Torus (MST). The design of the RF heating system used in this experiment is described. Klystron and antenna limitations are examined during launch into the plasma.

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.

Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

A multi-channel capacitive probe for electrostatic fluctuation measurement in the Madison Symmetric Torus reversed field pinch.

A 40-channel capacitive probe has been developed to measure the electrostatic fluctuations associated with the tearing modes deep into Madison Symmetric Torus (MST) reversed field pinch plasma. The capacitive probe measures the ac component of the plasma potential via the voltage induced on stainless steel electrodes capacitively coupled with the plasma through a thin annular layer of boron nitride (BN) dielectric (also serves as the particle shield). When bombarded by the plasma electrons, BN provides a sufficiently large secondary electron emission for the induced voltage to be very close to the plasma potential. The probe consists of four stalks each with ten cylindrical capacitors that are radially separated by 1.5 cm. The four stalks are arranged on a 1.3 cm square grid so that at each radial position, there are four electrodes forming a square grid. Every two adjacent radial sets of four electrodes form a cube. The fluctuating electric field can be calculated by the gradient of the plasma potential fluctuations at the eight corners of the cube. The probe can be inserted up to 15 cm (r/a = 0.7) into the plasma. The capacitive probe has a frequency bandwidth from 13 Hz to 100 kHz, amplifier-circuit limit, sufficient for studying the tearing modes (5-30 kHz) in the MST reversed-field pinch.

Multifield measurement of magnetic fluctuation-induced particle flux in a high-temperature toroidal plasma

Magnetic fluctuation-induced particle transport is explored in the high-temperature, high-beta interior of the Madison symmetric torus (MST) reversed-field pinch by performing a multifield measurement of the correlated product of magnetic and density fluctuations associated with global resistive tearing modes. Local density fluctuations are obtained by inverting the line-integrated interferometry data after resolving the mode helicity through correlation techniques. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of Faraday-effect polarimetry measurements. Reconstructed 2D images of density and current density perturbations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved. The convective magnetic fluctuation-induced particle flux profile is measured for both standard and high-performance plasmas in MST with tokamak-like confinement, showing large reduction in the flux during improved confinement.

Identification of island-induced Alfvén eigenmodes in a reversed field pinch

The modification of the shear Alfvén spectrum due to a core resonant magnetic island is used to explain the Alfvénic activity observed on the Madison symmetric torus (MST) reversed-field pinch during neutral beam injection. Theoretical studies show that the Alfvén continua in the core of the island provide a gap in which the observed Alfvénic bursts reside. Numerical simulations using a new code called SIESTAlfvén have identified the bursts as the first observation of an island-induced Alfvén eigenmode (IAE) in an RFP. The IAE arises from a helical coupling of harmonics due to the magnetic island.

Effect of resonant magnetic perturbations on three dimensional equilibria in the Madison Symmetric Torus reversed-field pinch

The orientation of 3D equilibria in the Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch can now be controlled with a resonant magnetic perturbation (RMP). Absent the RMP, the orientation of the stationary 3D equilibrium varies from shot to shot in a semi-random manner, making its diagnosis difficult. Produced with a poloidal array of saddle coils at the vertical insulated cut in MST's thick conducting shell, an m = 1 RMP with an amplitude br/B ∼ 10% forces the 3D structure into any desired orientation relative to MST's diagnostics. This control has led to improved diagnosis, revealing enhancements in both the central electron temperature and density. With sufficient amplitude, the RMP also inhibits the generation of high-energy (>20 keV) electrons, which otherwise emerge due to a reduction in magnetic stochasticity in the core. Field line tracing reveals that the RMP reintroduces stochasticity to the core. A m = 3 RMP of similar amplitude has little effect on the magnetic topology or the high-energy electrons.

Three dimensional equilibrium solutions for a current-carrying reversed-field pinch plasma with a close-fitting conducting shell

In order to characterize the Madison Symmetric Torus (MST) reversed-field pinch (RFP) plasmas that bifurcate to a helical equilibrium, the V3FIT equilibrium reconstruction code was modified to include a conducting boundary. RFP plasmas become helical at a high plasma current, which induces large eddy currents in MST's thick aluminum shell. The V3FIT conducting boundary accounts for the contribution from these eddy currents to external magnetic diagnostic coil signals. This implementation of V3FIT was benchmarked against MSTFit, a 2D Grad-Shafranov solver, for axisymmetric plasmas. The two codes both fit Bθ measurement loops around the plasma minor diameter with qualitative agreement between each other and the measured field. Fits in the 3D case converge well, with q-profile and plasma shape agreement between two distinct toroidal locking phases. Greater than 60% of the measured n = 5 component of Bθ at r = a is due to eddy currents in the shell, as calculated by the conducting boundary model.

Runaway of energetic test ions in a toroidal plasma

Ion runaway in the presence of a large-scale, reconnection-driven electric field has been conclusively measured in the Madison Symmetric Torus reversed-field pinch (RFP). Measurements of the acceleration of a beam of fast ions agree well with test particle and Fokker-Planck modeling of the runaway process. However, the runaway mechanism does not explain all measured ion heating in the RFP, particularly previous measurements of strong perpendicular heating. It is likely that multiple energization mechanisms occur simultaneously and with differing significance for magnetically coupled thermal ions and magnetically decoupled tail and beam ions.

Full particle orbit tracing with the RIO code in the presence of broad-spectrum MHD activity in a reversed-field pinch

In order to better understand the behaviour of both neutral beam injected and spontaneously generated fast ions in the Madison Symmetric Torus reversed-field pinch, we have developed the full orbit-following code random ion orbits (RIO). The low magnetic field and relatively large level of MHD activity present in MST require a full orbit code as the guiding centre assumptions are violated even for ions with modest energy. Furthermore, quasi-periodic bursts of MHD activity (sawteeth) generate large transient electric fields and significant modifications to the equilibrium magnetic fields. Understanding the full effect of these sawteeth on the spatial and velocity distribution of the fast ions is of great interest. To this end, RIO now has the ability to take the full 3D, time evolving, magnetic and electric fields produced by the visco-resistive MHD code DEBS as input. In static cases, where broad-spectrum magnetic perturbations from DEBS are input, but fixed in time, beam injected ions are found to be generally well confined with the core fast ion density profile largely unaffected by the magnetic modes while the fast ion density in the mid-radius is substantially reduced. In the dynamic case, the large amplitude magnetic fluctuations that occur at the sawtooth crash produce substantial fast ion loss. Those fast ions that are not lost are accelerated by a large, transient, parallel electric field in the co-current direction. This causes the average energy of the beam ions to increase by ∼20%, consistent with recent experimental measurements.

Impurity transport studies in the Madison Symmetric Torus reversed-field pinch during standard and pulsed poloidal current drive regimes

The transport of intrinsic impurities is investigated during standard and improved confinement regimes of the Madison Symmetric Torus (MST) reversed-field pinch. The impurity diffusion coefficient (D) and pinch velocity (v) are obtained through comparing the time evolution of experimental impurity density profiles with the results of a one-dimensional impurity transport code. Experimental hollow fully stripped (C, O, B) ion populations in improved confinement discharges are reproduced with the transport code indicating outward convection of impurity ions. Estimated D and v are low and close to classical values. Standard MST discharges are characterized by a high level of stochasticity and nearly flat radial profiles of the fully stripped carbon. To reproduce this flat impurity profile a high outward convective velocity and high central D are assumed in the simulation.

Calibration of an advanced neutral particle analyzer for the Madison Symmetric Torus reversed-field pinch

A new E∥B neutral particle analyzer, which has recently been installed on Madison Symmetric Torus (MST) reversed-field pinch (RFP), has now been calibrated, allowing the measurement of the fast ion density and energy distribution. This diagnostic, dubbed the advanced neutral particle analyzer (ANPA), can simultaneously produce time resolved measurements of the efflux of both hydrogen and deuterium ions from the plasma over a 35 keV energy range with an energy resolution of 2-4 keV and a time resolution of 10 μs. These capabilities are needed to measure both majority ion heating that occurs during magnetic reconnection events in MST and the behavior of the fast ions from the 1 MW hydrogen neutral beam injector on MST. Calibration of the ANPA was performed using a custom ion source that resides in the flight tube between the MST and the ANPA. In this work, the ANPA will be described, the calibration procedure and results will be discussed, and initial measurements of the time evolution of 25 keV neutral beam injection-born fast ions will be presented.

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch

Drift and Hall effects on magnetic tearing, island evolution, and relaxation in pinch configurations are investigated using a non-reduced first-order finite-Larmor-radius (FLR) fluid model with the nonideal magnetohydrodynamics (MHD) with rotation, open discussion (NIMROD) code [C.R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)]. An unexpected result with a uniform pressure profile is a drift effect that reduces the growth rate when the ion sound gyroradius (ρs) is smaller than the tearing-layer width. This drift is present only with warm-ion FLR modeling, and analytics show that it arises from ∇B and poloidal curvature represented in the Braginskii gyroviscous stress. Nonlinear single-helicity computations with experimentally relevant ρs values show that the warm-ion gyroviscous effects reduce saturated-island widths. Computations with multiple nonlinearly interacting tearing fluctuations find that m = 1 core-resonant-fluctuation amplitudes are reduced by a factor of two relative to single-fluid modeling by the warm-ion effects. These reduced core-resonant-fluctuation amplitudes compare favorably to edge coil measurements in the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. The computations demonstrate that fluctuations induce both MHD- and Hall-dynamo emfs during relaxation events. The presence of a Hall-dynamo emf implies a fluctuation-induced Maxwell stress, and the simulation results show net transport of parallel momentum. The computed magnitude of force densities from the Maxwell and competing Reynolds stresses, and changes in the parallel flow profile, are qualitatively and semi-quantitatively similar to measurements during relaxation in MST.

Electron temperature fluctuations during sawtooth events in a reversed-field pinch

Electron temperature fluctuations are correlated with the dominant (m, n) = (0, 1) edge-resonant magnetic tearing mode during sawtooth events in the Madison Symmetric Torus reversed-field pinch. Electron temperature fluctuations in phase with the (0, 1) tearing mode are measured using high-repetition-rate Thomson scattering. Immediately prior to the sawtooth the (0, 1) island structure appears to be heat-confining, while during the sawtooth it assumes an isothermal character. Core electron temperature variation is also phase correlated with the (0, 1) mode, suggesting that the edge-resonant tearing mode has an effect on core electron thermal confinement during sawtooth events.

Experimental Evidence for a Reduction in Electron Thermal Diffusion due to Trapped Particles

New high time resolution measurements of the electron thermal diffusion χ(e) throughout the sawtooth cycle of the Madison Symmetric Torus reversed-field pinch have been made by utilizing the enhanced capabilities of the upgraded multipoint, multipulse Thomson scattering system. These measurements are compared to the χ(e) due to magnetic diffusion predicted by using information from a new high spectral resolution zero-β nonlinear resistive magnetohydrodynamic simulation performed, for the first time, at the Lundquist number of high current Madison Symmetric Torus plasmas (S≈4×10(6)). Agreement between the measured and predicted values is found only if the reduction in thermal diffusion due to trapped particles is taken into account.

Advances in Time-Resolved Measurement of Magnetic Field and Electron Temperature in Low-Magnetic-Field Plasmas

Internal time-resolved measurement of magnetic field and electron temperature in low-field (≤ 1 T) plasmas is a difficult diagnostic challenge. To meet this diagnostic challenge in the Madison Symmetric Torus reversed-field pinch, two techniques are being developed: 1) spectral motional Stark effect (MSE) and 2) Fast Thomson scattering. For spectral MSE, the entire Stark-split Hα spectrum emitted by hydrogen neutral beam atoms is recorded and analyzed using a newly refined atomic emission model. A new analysis scheme has been developed to infer both the polarization direction and the magnitude of Stark splitting, from which both the direction and magnitude of the local magnetic field can be derived. For Fast Thomson scattering, two standard commercial flashlamp-pumped Nd:YAG lasers have been upgraded to “pulse-burst” capability. Each laser produces a burst of up to fifteen pulses at repetition rates 1–12.5 kHz, thus enabling recording of the dynamic evolution of the electron temperature profile and electron temperature fluctuations. To further these capabilities, a custom pulse-burst laser system is now being commissioned. This new laser is designed to produce a burst of laser pulses at repetition frequencies 5–250 kHz.