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The Mega Ampere Spherical Tokamak (MAST) programme is strongly focused on addressing key physics issues in preparation for operation of ITER as well as providing solutions for DEMO design choices. In this regard, MAST has provided key results in understanding and optimizing H-mode confinement, operating with smaller edge localized modes (ELMs), predicting and handling plasma exhaust and tailoring auxiliary current drive. In all cases, the high-resolution diagnostic capability on MAST is complemented by sophisticated numerical modelling to facilitate a deeper understanding. Mitigation of ELMs with resonant magnetic perturbations (RMPs) with toroidal mode number n(RMP) = 2, 3, 4, 6 has been demonstrated: at high and low collisionality; for the first ELM following the transition to high confinement operation; during the current ramp-up; and with rotating n(RMP) = 3 RMPs. n(RMP) = 4, 6 fields cause less rotation braking whilst the power to access H-mode is less with n(RMP) = 4 than n(RMP) = 3, 6. Refuelling with gas or pellets gives plasmas with mitigated ELMs and reduced peak heat flux at the same time as achieving good confinement. A synergy exists between pellet fuelling and RMPs, since mitigated ELMs remove fewer particles. Inter-ELM instabilities observed with Doppler backscattering are consistent with gyrokinetic simulations of micro-tearing modes in the pedestal. Meanwhile, ELM precursors have been strikingly observed with beam emission spectroscopy (BES) measurements. A scan in beta at the L-H transition shows that pedestal height scales strongly with core pressure. Gyro-Bohm normalized turbulent ion heat flux (as estimated from the BES data) is observed to decrease with increasing tilt of the turbulent eddies. Fast ion redistribution by energetic particle modes depends on density, and access to a quiescent domain with 'classical' fast ion transport is found above a critical density. Highly efficient electron Bernstein wave current drive (1 A W-1) has been achie

New diagnostic, modelling and plant capability on the Mega Ampere Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved T-i measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L-H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. T-e inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfven eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows.

The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics (MHD), is not fully understood. This is especially true in configurations with no continuous geometric symmetry, such as in a real tokamak when the discrete nature of the external magnetic field coils is taken into account, or the alternative fusion concept, the stellarator, where axisymmetry is deliberately broken to provide a nonzero winding number (rotational transform) on each invariant torus of the magnetic field line dynamics (assumed for present purposes to be an integrable Hamiltonian system). Quantum (wave) chaos theory provides tools for characterizing the spectrum statistically, from the regular spectrum of the separable case (integrable semiclassical dynamics) to that where the semiclassical ray dynamics is so chaotic that no simple classification of the individual eigenvalues is possible (quantum chaos). The MHD spectrum exhibits certain nongeneric properties, which we show, using a toy model, to be understable from the number-theoretic properties of the asymptotic spectrum in the limit of large toroidal and poloidal mode (quantum) numbers when only a single radial mode number is retained. Much more realistically, using the ideal MHD code CAS3D, we have constructed a data set of several hundred growth-rate eigenvalues for an interchange-unstable three-dimensional stellarator equilibrium with a rather flat, nonmonotonic rotational transform profile. A statistical analysis of eigenvalue spacings shows evidence of generic quantum chaos, which we attribute to the mixing effect of having a large number of radial mode numbers.

SPECTOE3D is a magnetohydrodynamic (MHD) code designed to study the resistive stability and mode spectrum of stellar ators. It finds the spectrum of the linearized, compressible, resistive MHD equations. Some typical results are given for a tokamak model

Ballooning modes are usually the most dangerous ideal MHD instabilities in stellarators, but the unstable ballooning modes often have such short perpendicular wavelengths that finite Larmor radius effects are sufficient to stabilize the plasma. We use semiclassical techniques to analyse this effect. In tokamaks the ignorable toroidal coordinate leads to a simple quantization of the ballooning mode, but this is not the case for stellarators. The ballooning mode dynamics in a stellarator model may possess a separation of timescales, in which case the system is integrable and quantization is straightforward, but we also present a method for determining marginal stability which is applicable to the non-integrable case.

A significant deviation of the statistical nature of the ideal-magnetohydrodynamics (MHD) interchange spectrum from the random Poisson process of generic separable systems was analyzed. It was shown that the normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The statistics of the ideal-MHD spectrum departed somewhat from the Poisson distribution, even for arbitrarily large mmax, unlike the generic separable two-dimensional system. It was found that this departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.

A direct method is described for finding optimal coils, and 'flexibility' coils are presented which have been determined by this method. The method proceeds straight to a coil design from the required vacuum magnetic configuration parameters for the desired plasma, rather than producing an intermediate 'surface current' description. This allows engineering requirements to be faithfully reproduced. The method has been applied by implementing a perturbative vacuum rotational transform evaluator as an optimality criterion. The speed of this evaluation step allows a thorough exploration of the set of possible coil trajectories and permits a high degree of confidence in the optimality of the best candidate. It is shown that the flexible heliac winding is very near optimal for rotational transform generation.

We describe algorithms for tracing vacuum magnetic field lines in complex geometries at interactive speeds (∼50,000 steps/s on a personal computer), and a post-processing perturbation method for optimization of magnetic surface properties. Algorithms in