Theoretical and experimental research in the reversed-field pinch (RFP) is reviewed. In this system, Bθ ∼ Bϕ, q < 1 and Bϕ reverses in the outer regions of the plasma; stability at relatively high values of β is possible because there is high shear and, experimentally, confinement with β > 10% has been observed. Following a historical review of pinch research, the basic theoretical properties of the RFP are established including the equilibrium, toroidal displacement, diffusion and confinement; studies of ideal and dissipative MHD stability theory are then described. Experimental and theoretical work on relaxation and self-reversal, the process whereby an RFP distribution can be set up spontaneously and subsequently sustained, is presented and discussed. There follows a general account of RFP experiments. These are divided into ‘fast experiments’, which utilize small-bore insulating tori in which the distribution is usually set up by fast programming on microsecond timescales, and ‘slow experiments’, carried out in large metal-walled tori in which the field configuration is set up slowly by self-reversal on millisecond timescales. A brief account of RFP reactor studies and of new and future experiments is then given, followed finally by a general discussion in which the main conclusions are presented.

The paper summarizes the theoretical basis for the RFP and reviews the status of research in this field. The RFP is a relaxed state system well described by Taylor's theory which explains many observations. The RFP is of interest because its study will increase the understanding of toroidal confinement in general, which might lead to better reactor designs, and the RFP itself has potential as a reactor, for example the improved, high energy density, compact RFP reactor. In the last five or ten years, RFP research has expanded, with some 15-20 machines operating or under construction, and the plasma parameters have improved substantially, with a confinement time of 0.5-1 ms and temperatures approaching 1 keV; values of (3 e -5-15% are reached routinely. Following an overview of recent results, three key problems are discussed in more detail: (1) resistivity, edge physics and ion heating (the ions are heated by fluctuations which drive the RFP dynamo); (2) operation of the RFP with an (electrically) thin shell which permits the growth of new unstable modes which degrade the confinement; and (3) scaling. Over the current range of 0.5 MA, favourable scaling trends of temperature and confinement with current are identified, but experiments at much higher currents on the two mega-ampere machines -RFX at Padua and CPRF at Los Alamosdue to operate in the early 1990s, are needed. A brief account of the compact RFP reactor is given, followed by a summary with an indication of future trends.

Results are presented from thin (resistive) shell experiments on HBTX and compared with theoretical (linear and non-linear) studies of the plasma stability. Current pulses of 3--5 ms are obtained, compared with the shell time constant for vertical field penetration of 0.5 ms. Theoretically predicted thin shell modes, phase locked to the wall, are prominent experimentally.

An experimental study of the rotation and associated instability was made in a theta pinch with a peak field of 85 kG reached in 2.3 μsec. The starting deuterium gas pressure was in the range 50–150 μ Hg, and for operation on the second half-cycle of the sinusoidal driving field the magnetic flux trapped within the plasma varied between ±100 kMx. In most conditions the circular cross section of the plasma became perturbed along its length by the growth of two flutes which rotated at an angular velocity of up to 6 × 107 rad/sec. It is deduced from measurements on the rotation that the plasma acquires its angular momentum at the start of the half-cycle, and the results are interpreted on the basis that the angular momentum is initially in a diamagnetic (azimuthal) ion current. A model is described for establishing this current as a consequence of contact between the plasma and the walls. Results on the time of onset of the instability, and on the growth rate of the flutes, point to the existence of some damping or stabilizing process; it is found that field diffusion, or a rapid axial contraction of the plasma (due to closed reversed field loops), can lead to instability, and when these are reduced the stable time is increased. The possible influence of finite Larmor radius stabilization is discussed. The stability condition, originally derived for low β but recently shown to have more general validity, is in qualitative agreement with the results.

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A direct measurement is described of the perpendicular diffusion coefficient in a theta pinch operating in the low-pressure regime with zero bias field. The diffusion was studied by comparing the measured time variation of the radial electron density distribution with computations assuming classical and other resistivities. A coil 8 m long is used in order to delay end effects and measurements confirm theoretical predictions that the plasma in the midplane is uninfluenced by the ends and free of energy losses for about 25 μsec. The plasma temperature was varied from 90 to 160 eV and the values of density and beta on the axis are 3−4 × 1016/cm3 and 0.7, respectively. In the early stages (before 2 μsec) diffusion at approximately the Bohm rate is found, and this is believed to be due to a streaming mechanism. At later times the measured diffusion coefficient is in good agreement with the classical value in all conditions studied, and the experimental error is such that diffusion is unlikely to exceed 110 of the Bohm rate.

A high-speed framing camera has been used to photograph deuterium and helium discharges in which flute instabilities are driven by the inertial force of a radial acceleration. The wavelength of the instability increases with decreasing initial pressure, suggesting the damping effect of viscosity; in some cases this damping apparently prevents the growth of flutes entirely. A simple theory of viscous damping is in qualitative agreement with the observations. An instability due to the radial acceleration accompanying a rotation of the plasma appears at about peak field.

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