Recent gyrokinetic stability calculations have revealed that the spherical tokamak is susceptible to tearing parity instabilities with length scales of a few ion Larmor radii perpendicular to the magnetic field lines. Here we investigate this 'micro-tearing' mode in greater detail to uncover its key characteristics, and compare it with existing theoretical models of the phenomenon. This has been accomplished using a full numerical solution of the linear gyrokinetic-Maxwell equations. Importantly, the instability is found to be driven by the free energy in the electron temperature gradient as described in the literature. However, our calculations suggest it is not substantially affected by either of the destabilising mechanisms proposed in previous theoretical models. Instead the instability is destabilised by interactions with magnetic drifts, and the electrostatic potential. Further calculations reveal that the mode is not significantly destabilised by the flux surface shaping or the large trapped particle fraction present in the spherical tokamak. Its prevalence in spherical tokamak plasmas is primarily due to the higher value of plasma β, and the enhanced magnetic drifts due to the smaller radius of curvature.

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 × B flows usually exceed the growth rates of microinstabilities with k ⊥ ρ i < 1 (including ion temperature gradient, ITG, driven drift waves) and are generally smaller than the growth rates of shorter wavelength modes with k ⊥ ρ i > 1 (electron temperature gradient, ETG, driven drift waves). Electromagnetic effects are significant at mid-radius in these MAST equilibria, where the local β 0.1. At k ⊥ ρ 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 β ST equilibrium, which

Integrated modelling of important plasma physics issues related to the design of a steady-state spherical tokamak (ST) fusion power plant is described. The key is a steady-state current drive, and 92% of this is provided by a combination of bootstrap and diamagnetic currents, both of which have a substantial toroidal component in a ST. The remaining current is to be provided by either neutral beam injection or radio-frequency waves, and various schemes for providing this are discussed and quantified. The desire to achieve a high bootstrap current drives the design to high plasma pressure, β (normalized to the magnetic field pressure), and high elongation. Both these requirements have implications for ideal magneto-hydrodynamic instability which are discussed. Confinement is addressed both through comparison with the recent scaling laws developed from the conventional tokamak database and selfconsistent one-dimensional modelling of the transport processes. This modelling shows that the power required for the current drive (∼50 MW) is sufficient to heat the plasma to a regime where more than 3 GW of fusion power is produced, taking into account the dilution due to He ash and prompt α-particle losses, which are small. A preliminary study of the micro-instabilities, which may be responsible for the turbulent transport is provided. Given assumptions about the particle confinement, we make estimates of the fuelling requirements to maintain the steady state. Finally, the power loading due to the exhaust is derived using theory-based scalings for the scrape-off layer width.

Gyrokinetic microstability analyses, with and without electromagnetic effects, are presented for a spherical tokamak plasma equilibrium closely resembling that from a high confinement mode (H mode) discharge in the mega-ampere spherical tokamak (MAST) [A. Sykes et al., Nucl. Fusion 41, 1423 (2001)]. Electrostatic ion temperature gradient driven modes (ITG modes) were found to be unstable on all surfaces, though they are likely to be substantially stabilized by equilibrium E ϫ B flow shear. Electron temperature gradient driven modes (ETG modes) have stronger growth rates that substantially exceed the equilibrium flow shearing rates. Mixing length arguments suggest that ITG modes would give rise to significant transport if they are not stabilized by sheared flows, and predict weak transport from ETG turbulence. Significant plasma flows have been neglected in this first analysis, and are probably important in the delicate balance between ITG growth rates and flow shear, and in the formation of internal transport barriers on MAST. Electromagnetic effects are found to be important even in this low ␤ discharge, especially for longer length-scale modes with k Ќ i Ͻ O͑1͒ on the inner surfaces, where tearing parity modes are found to be the fastest growing modes, with growth rates that are sensitive to the electron collision frequency. These tearing parity microinstabilities are highly extended along the magnetic field, and have been reported in a number of spherical tokamak equilibria.

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.

At low ␤ it is common to neglect parallel magnetic field perturbations on the basis that they are of order ␤ 2 . This is only true if effects of order ␤ are canceled by a term in the ٌB drift also of order ␤ ͓H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 ͑1977͔͒. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2 ͓Kotschenreuther et al., Comput. Phys. Commun. 88, 128 ͑1995͔͒ to investigate whether the compressional magnetic field perturbation B ʈ is required for accurate gyrokinetic simulations at low ␤ for microinstabilities commonly found in tokamaks. The kinetic ballooning mode ͑KBM͒ demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient ͑ETG͒ driven modes do not typically exhibit this behavior; the effects of B ʈ are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with e . The effect of B ʈ on the ETG instability is shown to depend on the normalized pressure gradient ␤Ј at constant ␤.

Several improvements to the MAST plant and diagnostics have facilitated new studies advancing the physics basis for ITER and DEMO, as well as for future spherical tokamaks (STs). Using the increased heating capabilities P NBI ⩽ 3.8 MW H-mode at I p = 1.2 MA was accessed showing that the energy confinement on MAST scales more weakly with I p and more strongly with B t than in the ITER IPB98(y, 2) scaling. Measurements of the fuel retention of shallow pellets extrapolate to an ITER particle throughput of 70% of its original designed total throughput capacity. The anomalous momentum diffusion, χϕ, is linked to the ion diffusion, χi, with a Prandtl number close to P ϕ ≈ χϕ/χi ≈ 1, although χi approaches neoclassical values. New high spatial resolution measurements of the edge radial electric field, E r , show that the position of steepest gradients in electron pressure and E r (i.e. shearing rate) are coincident, but their magnitudes are not linked. The T e pedestal width on MAST scales with rather than ρpol. The edge localized mode (ELM) frequency for type-IV ELMs, new in MAST, was almost doubled using n = 2 resonant magnetic perturbations from a set of four external coils (n = 1, 2). A new internal 12 coil set (n ⩽ 3) has been commissioned. The filaments in the inter-ELM and L-mode phase are different from ELM filaments, and the characteristics in L-mode agree well with turbulence calculations. A variety of fast particle driven instabilities were studied from 10 kHz saturated fishbone like activity up to 3.8 MHz compressional Alfvén eigenmodes. Fast particle instabilities also affect the off-axis NBI current drive, leading to fast ion diffusion of the order of 0.5 m2 s−1 and a reduction in the driven current fraction from 40% to 30%. EBW current drive start-up is demonstrated for the first time in a ST generating plasma currents up to 55 kA. Many of these studies contributed to the physics basis of a planned upgrade to MAST.

Substantial advances have been made on the Mega Ampère Spherical Tokamak (MAST). The parameter range of the MAST confinement database has been extended and it now also includes pellet-fuelled discharges. Good pellet retention has been observed in H-mode discharges without triggering an ELM or an H/L transition during peripheral ablation of low speed pellets. Co-ordinated studies on MAST and DIII-D demonstrate a strong link between the aspect ratio and the beta scaling of H-mode energy confinement, consistent with that obtained when MAST data were merged with a subset of the ITPA database. Electron and ion ITBs are readily formed and their evolution has been investigated. Electron and ion thermal diffusivities have been reduced to values close to the ion neoclassical level. Error field correction coils have been used to determine the locked mode threshold scaling which is comparable to that in conventional aspect ratio tokamaks. The impact of plasma rotation on sawteeth has been investigated and the results have been well-modelled using the MISHKA-F code. Alfvén cascades have been observed in discharges with reversed magnetic shear. Measurements during off-axis NBCD and heating are consistent with classical fast ion modelling and indicate efficient heating and significant driven current. Central electron Bernstein wave heating has been observed via the O–X–B mode conversion process in special magnetically compressed plasmas. Plasmas with low pedestal collisionality have been established and further insight has been gained into the characteristics of filamentary structures at the plasma edge. Complex behaviour of the divertor power loading during plasma disruptions has been revealed by high resolution infra-red measurements.