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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.

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., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

We present the first observation of instability in weakly magnetized, pressure dominated plasma Couette flow firmly in the Hall regime. Strong Hall currents couple to a low frequency electromagnetic mode that is driven by high-β (>1) pressure profiles. Spectroscopic measurements show heating (factor of 3) of the cold, unmagnetized ions via a resonant Landau damping process. A linear theory of this instability is derived that predicts positive growth rates at finite β and shows the stabilizing effect of very large β, in line with observations.

Supermagnetosonic perpendicular flows are magnetically driven by a large radius theta-pinch experiment. Fine spatial resolution and macroscopic coverage allow the full structure of the plasma-piston coupling to be resolved in laboratory experiment for the first time. A moving ambipolar potential is observed to reflect unmagnetized ions to twice the piston speed. Magnetized electrons balance the radial potential via Hall currents and generate signature quadrupolar magnetic fields. Electron heating in the reflected ion foot is adiabatic.

A novel plasma equilibrium in the high-β, Hall regime that produces centrally peaked, high Mach number Couette flow is described. Flow is driven using a weak, uniform magnetic field and large, cross field currents. Large magnetic field amplification (factor 20) due to the Hall effect is observed when electrons are flowing radially inward, and near perfect field expulsion is observed when the flow is reversed. A dynamic equilibrium is reached between the amplified (removed) field and extended density gradients.

We have developed a low-cost spectrometer with simple optical design that achieves unprecedented precision measurements of ion temperature (±0.01 eV) and velocity (±20 m/s). A Fabry-Pérot étalon provides the simultaneous high resolving power and high throughput needed for the light levels available in singly ionized helium and argon plasmas. Reducing the systematic uncertainty in the absolute wavelength calibration needed for the specified velocity precision motivates a Bayesian analysis method called Nested Sampling to address the nontrivial uncertainty in the diffraction order. An initial emission measurement of a singly charged stationary argon plasma yields a temperature of 0.339 ± 0.007 eV and a velocity of -3 ± 4 m/s with a systematic uncertainty of 20 m/s.

Magnetic fields are ubiquitous in the Universe. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations. However, experimental demonstration of the turbulent dynamo mechanism has remained elusive, since it requires plasma conditions that are extremely hard to re-create in terrestrial laboratories. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization.

The first observation of rf heating in a reversed field pinch (RFP) using the electron Bernstein wave (EBW) is demonstrated on the Madison Symmetric Torus. Propagation across and heating in a stochastic magnetic field is observed. Novel techniques are required to measure the suprathermal electron tail generated by EBW heating in the presence of intense Ohmic heating. rf-heated electrons directly probe the edge transport properties in the RFP; measured loss rates imply a large noncollisional radial diffusivity.

A pulse height analyzing x-ray tomography system has been developed to detect x-rays from electron Bernstein wave heated electrons in the Madison symmetric torus reversed field pinch (RFP). Cadmium zinc telluride detectors are arranged in a parallel beam array with two orthogonal multi-chord detectors that may be used for tomography. In addition a repositionable 16 channel fan beam camera with a 55° field of view is used to augment data collected with the Hard X-ray array. The chord integrated signals identify target emission from RF heated electrons striking a limiter located 12° toroidally away from the RF injection port. This provides information on heated electron spectrum, transport, and diffusion. RF induced x-ray emission from absorption on harmonic electron cyclotron resonances in low current (<250 kA) RFP discharges has been observed.

The spontaneous formation of magnetic islands is observed in driven, antiparallel magnetic reconnection on the Terrestrial Reconnection Experiment. We here provide direct experimental evidence that the plasmoid instability is active at the electron scale inside the ion diffusion region in a low collisional regime. The experiments show the island formation occurs at a smaller system size than predicted by extended magnetohydrodynamics or fully collisionless simulations. This more effective seeding of magnetic islands emphasizes their importance to reconnection in naturally occurring 3D plasmas.

This Letter reports the first experimental investigation into a line-tied plasma with a reversed current profile. Discrete current sources create a cylindrical plasma equilibrium with an axial field and zero net current. Detailed magnetic measurements show that an internal m=1 mode with no external character grows exponentially. The nonlinear evolution of the mode drives 3D reconnection events that reorganize the plasma equilibrium. The plasma is turbulent and exhibits reconnection events on a range of scales. These data are consistent with recent simulations of coronal loops and the nanoflare coronal heating mechanism.

We numerically demonstrate the feasibility of kinematic fast dynamos for a class of time-periodic axisymmetric flows of conducting fluid confined inside a sphere. The novelty of our work is in considering the realistic flows, which are self-consistently determined from the Navier-Stokes equation with specified boundary driving. Such flows can be achieved in a new plasma experiment, whose spherical boundary is capable of differential driving of plasma flows in the azimuthal direction. We show that magnetic fields are self-excited over a range of flow parameters such as amplitude and frequency of flow oscillations, fluid Reynolds (Re) and magnetic Reynolds (Rm) numbers. In the limit of large Rm, the growth rates of the excited magnetic fields are of the order of the advective time scales and practically independent of Rm, which is an indication of the fast dynamo.

The magnetohydrodynamic dynamo effect is considered to be the major cause of magnetic field generation in geo- and astrophysical systems. Recent experimental and numerical results show that turbulence constitutes an obstacle to dynamos; yet its role in this context is not totally clear. Via numerical simulations, we identify large-scale turbulent vortices with a detrimental effect on the amplification of the magnetic field in a geometry of experimental interest and propose a strategy for facilitating the dynamo instability by manipulating these detrimental "hidden" dynamics.

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.

This paper presents an analysis of the Dudley-James two-vortex flow, which inspired several laboratory-scale liquid-metal experiments, in order to better demonstrate its relation to astrophysical dynamos. A coordinate transformation splits the flow into components that are axisymmetric and nonaxisymmetric relative to the induced magnetic dipole moment. The reformulation gives the flow the same dynamo ingredients as are present in more complicated convection-driven dynamo simulations. These ingredients are currents driven by the mean flow and currents driven by correlations between fluctuations in the flow and fluctuations in the magnetic field. The simple model allows us to isolate the dynamics of the growing eigenvector and trace them back to individual three-wave couplings between the magnetic field and the flow. This simple model demonstrates the necessity of poloidal advection in sustaining the dynamo and points to the effect of large-scale flow fluctuations in exciting a dynamo magnetic field.

A new concept for spinning unmagnetized plasma is demonstrated experimentally. Plasma is confined by an axisymmetric multicusp magnetic field and biased cathodes are used to drive currents and impart a torque in the magnetized edge. Measurements show that flow viscously couples momentum from the magnetized edge (where the plasma viscosity is small) into the unmagnetized core (where the viscosity is large) and that the core rotates as a solid body. To be effective, collisional viscosity must overcome the ion-neutral drag due to charge-exchange collisions.

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.

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.

Three-wave turbulent interactions and the role of eddy size on the turbulent electromotive force are studied in a spherical liquid-sodium dynamo experiment. A symmetric, equatorial baffle reduces the amplitude of the largest-scale turbulent eddies, which is inferred from the magnetic fluctuations spectrum (measured by a 2D array of surface probes). Differential rotation in the mean flow is >2 times more effective in generating mean toroidal magnetic fields from the applied poloidal field (via the Ω effect) when the largest-scale eddies are eliminated, thus demonstrating that the global turbulent resistivity (the β effect from the largest-scale eddies) is reduced by a similar amount.

The rotating wall machine, a basic plasma physics experimental facility, has been constructed to study the role of electromagnetic boundary conditions on current-driven ideal and resistive magnetohydrodynamic instabilities, including differentially rotating conducting walls. The device, a screw pinch magnetic geometry with line-tied ends, is described. The plasma is generated by an array of 19 plasma guns that not only produce high density plasmas but can also be independently biased to allow spatial and temporal control of the current profile. The design and mechanical performance of the rotating wall as well as diagnostic capabilities and internal probes are discussed. Measurements from typical quiescent discharges show the plasma to be high β (≤p>2μ(0)/B(z)(2)), flowing, and well collimated. Internal probe measurements show that the plasma current profile can be controlled by the plasma gun array.

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).

Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically forced two-vortex flow inside a sphere are reported. The simulations are performed in the intermediate regime between the laminar flow and developed turbulence, where a hydrodynamic instability is found to generate internal waves with a characteristic m=2 zonal wave number. It is shown that this time-periodic flow acts as a dynamo, although snapshots of the flow as well as the mean flow are not dynamos. The magnetic fields' growth rate exhibits resonance effects depending on the wave frequency. Furthermore, a cyclic self-killing and self-recovering dynamo based on the relative alignment of the velocity and magnetic fields is presented. The phenomena are explained in terms of a mixing of nonorthogonal eigenstates of the time-dependent linear operator of the magnetic induction equation. The potential relevance of this mechanism to dynamo experiments is discussed.

The resistive wall mode is experimentally identified and characterized in a line-tied, cylindrical screw pinch when the edge safety factor is less than a critical value. Different wall materials have been used to change the wall time and show that the growth rates for the RWM scale with wall time and safety factor as expected by theory. The addition of a ferritic wall material outside the conducting shell leads to growth rates larger than the observed RWM and larger than theoretical predictions for the ferritic wall mode.

The nature of Ohm's law is examined in a turbulent flow of liquid sodium. A magnetic field is applied to the flowing sodium, and the resulting magnetic field is measured. The mean velocity field of the sodium is also measured in an identical-scale water model of the experiment. These two fields are used to determine the terms in Ohm's law, indicating the presence of currents driven by a turbulent electromotive force. These currents result in a diamagnetic effect, generating magnetic field in opposition to the dominant fields of the experiment. The magnitude of the fluctuation-driven magnetic field is comparable to that of the field induced by the sodium's mean flow.

The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three-dimensional numerical computation. A simple impeller model drives a flow that can generate a growing magnetic field, depending on the magnetic Reynolds number Rm=micro0sigmaVa and the fluid Reynolds number Re=Vanu of the flow. For Re<420, the flow is laminar and the dynamo transition is governed by a threshold of Rmcrit=100, above which a growing magnetic eigenmode is observed that is primarily a dipole field transverse to the axis of symmetry of the flow. In saturation, the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For Re>420 and Rm approximately 100 the flow becomes turbulent and the dynamo eigenmode is suppressed. The mechanism of suppression is a combination of a time varying large-scale field and the presence of fluctuation driven currents (such as those predicted by the mean-field theory), which effectively enhance the magnetic diffusivity. For higher Rm, a dynamo reappears; however, the structure of the magnetic field is often different from the laminar dynamo. It is dominated by a dipolar magnetic field aligned with the axis of symmetry of the mean-flow, which is apparently generated by fluctuation-driven currents. The magnitude and structure of the fluctuation-driven currents have been studied by applying a weak, axisymmetric seed magnetic field to laminar and turbulent flows. An Ohm's law analysis of the axisymmetric currents allows the fluctuation-driven currents to be identified. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.

The magnetic field measured in the Madison dynamo experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest-growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.

An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the omega effect). Its potential role in the production of the induced dipole is discussed.

An internal kink instability is observed to grow and saturate in a line-tied screw pinch plasma. Detailed measurements show that an ideal, line-tied kink mode begins growing when the safety factor q = (4pi2r2B(z))/(mu0I(p)(r)L) drops below 1 inside the plasma; the saturated state corresponds to a rotating helical equilibrium. In addition to the ideal mode, reconnection events are observed to periodically flatten the current profile and change the magnetic topology.

New profile measurements have allowed the electron thermal diffusivity profile to be estimated from power balance in the Madison Symmetric Torus where magnetic islands overlap and field lines are stochastic. The measurements show that (1) the electron energy transport is conductive not convective, (2) the measured thermal diffusivities are in good agreement with numerical simulations of stochastic transport, and (3) transport is greatly reduced near the reversal surface where magnetic diffusion is small.

Confinement of runaway electrons has been observed for the first time in a reversed field pinch during improved-confinement plasmas in the Madison Symmetric Torus. Energy-resolved hard-x-ray flux measurements have been used to determine the velocity dependence of the electron diffusion coefficient, utilizing computational solutions of the Fokker-Planck transport equation. With improved-confinement, the fast electron diffusivity drops by 2 orders of magnitude and is independent of velocity. This suggests a change in the transport mechanism away from stochastic magnetic field diffusion.

First measurements of the current-density profile in the core of a high-temperature reversed-field pinch are presented. The current-density profile is observed to peak during the sawtooth cycle and broaden promptly at the crash. This change in profile can be linked to magnetic relaxation and the dynamo which is predicted to drive antiparallel current in the plasma core. For high-confinement discharges, the dynamo is suppressed and the current-density profile is observed to strongly peak.

Improved confinement has been achieved in the MST through control of the poloidal electric field, but it is now known that the improvement has been limited by bursts of an edge-resonant instability. Through refined poloidal electric field control, plus control of the toroidal electric field, we have suppressed these bursts. This has led to a total beta of 15% and a reversed-field-pinch-record estimated energy confinement time of 10 ms, a tenfold increase over the standard value which for the first time substantially exceeds the confinement scaling that has characterized most reversed-field-pinch plasmas.

A recent study conducted on the Madison Symmetric Torus reversed-field pinch has shown that control of density fluctuations can be achieved through modification of the current density profile. Most of the power in the density fluctuations is directly associated with core-resonant resistive tearing modes. We report that, during auxiliary current drive experiments, these density fluctuations are reduced about an order of magnitude over the entire plasma cross section and the resulting electron confinement is increased eightfold.