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.