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Martin David Kruskal was one of the most versatile theoretical physicists of his generation and is distinguished for his enduring work in several different areas, most notably plasma physics, a memorable detour into relativity and his pioneering work in nonlinear waves. In the latter, together with Norman Zabusky, he invented the concept of the soliton and, with others, developed its application to classes of partial differential equations of physical significance.

Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a meanfield dynamo. Exponential growth of magnetic field at scales larger than the outer forcing scale of the turbulence is found. Over a range of values of the shearing rate Sspanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, γ ∝ S, while the characteristic spatial scale of the field is lB∝ S–12. The effect is quite general: earlier results for the nonrotating case by Yousef et al. 2008 are extended to shearing boxes with Keplerian rotation; it is also shown that the shear dynamo mechanism operates both below and above the threshold for the fluctuation dynamo. The apparently generic nature of the shear dynamo effect makes it an attractive object of study for the purpose of understanding the generation of magnetic fields in astrophysical systems. © 2008 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim

We propose a model of magnetic-field growth in galaxy clusters whereby the field is ampli.fied by a factor of about 108 over a cosmologically short time of ∼ 108 yr. Our model is based on the idea that the viscosity of the intracluster medium during the field-amplification epoch is determined not by particle collisions but by plasma microinstabilities: these give rise to small-scale .uctuations, which scatter particles, increasing their effective collision rate and, therefore, the effective Reynolds number. This gives rise to a bootstrap effect as the growth of the field triggers the instabilities which increase the Reynolds number which, in turn, accelerates the growth of the field. The growth is explosive and the result is that the observed field strength is reached over a fraction of the cluster lifetime independent of the exact strength of the seed field (which only needs to be above ∼ 10–15 G to trigger the explosive growth). (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Gyrokinetic simulation of a MAST-like equilibrium is used to establish the turbulent transport resulting from the electron temperature gradient driven mode for core and edge parameters. The thermal diffusion coefficients calculated in these simulations are found to be experimentally significant for core parameters but underestimate the observed transport on outer flux-surfaces.

The progress that has been made in understanding the processes responsible for edge localized modes is reviewed. Attention is restricted to the role of ideal magneto-hydrodynamics and extensions of this model. As well as reviewing the current understanding, future research needs are discussed and speculative ideas for further development are proposed.

Spherical tokamaks (STs) have attractive features for fusion, and there is considerable interest in understanding their transport properties which depend on the underlying microinstabilities. STs are capable of operation with low magnetic fields and exhibit large inhomogeneity in the toroidal magnetic field. These factors strongly affect particle dynamics and the potency of magnetic perturbations, which correspondingly impact on the microstability properties of STs. This paper reviews previous microstability studies in ST plasma configurations and presents gyrokinetic microstability calculations for a range of ST equilibria, using the gyrokinetic code GS2. Microstability properties of L-mode and H-mode equilibria, from the MAST experiment at Culham, are compared. In MAST the shearing rates of equilibrium E× Bflows usually exceed the growth rates of microinstabilities with k??i< 1 (including ion temperature gradient, ITG, driven drift waves) and are generally smaller than the growth rates of shorter wavelength modes with k??i> 1 (electron temperature gradient, ETG, driven drift waves). Electromagnetic effects are significant at mid-radius in these MAST equilibria, where the local ? ? 0.1. At k??i< 1, strongly electromagnetic modes dominate over ITG instabilities, and these modes are found to have tearing parity in the H-mode plasma and twisting parity in the L-mode plasma. Numerical experiments have been carried out to assess the properties of the tearing parity modes and to probe the underlying physical drive mechanism. At shorter wavelengths the electromagnetic effects can significantly stabilize the ETG instabilities. Nonlinear electron scale microturbulence calculations for two surfaces of a MAST H-mode plasma suggest that significant electron heat transport can be carried via this mechanism. In an extremely high ? ST equilibrium, which has been proposed as the basis of a conceptual ST power plant, electrostatic instabilities are fully stabilized, but tearing parity modes are predicted to be unstable over-wide range of length scales.

This paper presents a description of the spatial and temporal structure of edge-localized modes (ELMs) observed in the MAST tokamak. Filamentary enhancements of visible light are observed on photographic images of the plasma obtained during ELMs. Comparisons with simulations show that these filaments are consistent with following field lines at the outboard edge of the plasma. The toroidal mode number of these filaments has been extracted from a study of the discrete peaks observed in the ion saturation current recorded by a mid-plane reciprocating probe. A study of the time delay of these peaks with respect to the onset of the ELM has been used to calculate an effective radial velocity for the expansion of the filaments. A comparison of this derived radial velocity as a function of distance from the last closed flux surface with simulations indicates that the filament is accelerating away from the plasma. Evidence for the temporal evolution of the ELM comes from studies of outboard mid-plane Thomson scattering density profiles. In addition, a study of the toroidal velocity as a function of radius shows that during an ELM the strong velocity shear near the edge of the plasma, normally present in H-modes, is strongly reduced. The picture that emerges is that the ELM can be viewed as being composed of filamentary structures that are generated on a 100?µs timescale, accelerate away from the plasma edge, are extended along a field line and have a typical toroidal mode number ~10. The implications of these filaments for the energy deposition on plasma facing components are discussed.