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.

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 improvedconfinement 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 × 10 20 m 3 (n/n G = 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.

Oscillating-field current drive ͑OFCD͒ is a proposed method of steady-state toroidal plasma sustainment in which ac poloidal and toroidal loop voltages are applied to produce a dc plasma current. OFCD is added to standard, inductively sustained reversed-field pinch plasmas in the Madison Symmetric Torus ͓R. N. Dexter et al., Fusion Technol. 19, 131 ͑1991͔͒. Equilibrium profiles and fluctuations during a single cycle are measured and analyzed for different relative phases between the two OFCD voltages and for OFCD off. For OFCD phases leading to the most added plasma current, the measured energy confinement is slightly better than that for OFCD off. By contrast, the phase of the maximum OFCD helicity-injection rate also has the maximum decay rate, which is ascribed to transport losses during discrete magnetic-fluctuation events induced by OFCD. Resistive-magnetohydrodynamic simulations of the experiments reproduce the observed phase dependence of the added current.

Our understanding of the dynamics of the Earth's core can be advanced by a combination of observation, experiments, and simulations. A crucial aspect of the core is the interplay between the flow of the conducting liquid and the magnetic field this flow sustains via dynamo action. This non-linear interaction, and the presence of turbulence in the flow, precludes direct numerical simulation of the system with realistic turbulence. Thus, in addition to simulations and observations (both seismological and geomagnetic), experiments can contribute insight into the core dynamics. Liquid sodium laboratory experiments can serve as models of the Earth's core with the key ingredients of conducting fluid, turbulent flow, and overall rotation, and can also approximate the geometry of the core. By accessing regions of parameter space inaccessible to numerical studies, experiments can benchmark simulations and reveal phenomena relevant to the Earth's core and other planetary cores. This review focuses on the particular contribution of liquid sodium spherical Couette devices to this subject matter.

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.