We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented

Edge localized mode (ELM) characteristics in a large spherical tokamak (ST) with significant auxiliary heating are explored. High confinement is achieved in mega ampere spherical tokamak (MAST) at low ELM frequencies even though the ELMs exhibit many type III characteristics. These ELMs are associated with a reduction in the pedestal density but no significant change in the pedestal temperature or temperature profile, indicating that energy is convected from the pedestal region into the scrape-off layer. Power to the targets during an ELM arrives predominantly at the low field outboard side. ELM effluxes are observed up to 20 cm from the plasma edge at the outboard mid-plane and are associated with the radial motion of a feature at an average velocity of 0.75 km s −1. The target balance observed in MAST is potentially rather favourable for the ST since H-mode access is facilitated in a regime where ELM losses flow mostly to the large wetted area, outboard targets and, in addition, the target heat loads are reduced by an even distribution of power between the upper and lower targets.

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.

Magnetic fluctuations at frequencies ω < ∼ ω ci driven by Neutral Beam Injection heating and identified as Compressional Alfvén Eigenmodes (CAEs) have been observed on MAST. The measured toroidal mode numbers are in the range 4 < |n| < 10 and waves rotate in both co-and counter-current directions. The frequency variation is consistent with an Alfvénic scaling, and modes are elliptically polarised with a significant magnetic field component aligned parallel to the equilibrium field. Frequency clustering of modes occurs on three frequency scales. At the finest scale there are multiple modes each separated by a constant frequency ∼10-20kHz; this is shown to be a result of modulation by low frequency tearing modes. A larger scale frequency splitting exists in the range 100-150kHz; these have consecutive toroidal mode numbers and are in agreement with numerical modelling. Finally, modes exist at frequencies close to ω = ω ci and ω ci /2 consistent with previous observations on START and DIII-D suggesting that the CAEs exist in two distinct ranges of k . Calculations of CAEs suggest that the modes are localised at r/a ∼ 0.5. The modes form within a potential well due to the variation of (nq/κρ) 2 , and are not directly influenced by variations in v A . This is distinct from observations based on ion cyclotron emission in conventional aspect ratio tokamaks which indicate that CAE modes occur closer to the plasma edge and that their existence relies on a competition between k ⊥ and 1/v A .

We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions, each of which are separated by an ideal MHD barrier. A principle motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically 3D equilibria, with nonzero internal pressure. A second application is the description of transport barriers as constrained minimum energy states. As a first example, we calculate the plasma solution in a periodic cylinder, generalizing the analysis of the treatment of Kaiser and Uecker, Q. Jl. Mech. Appl. Math.,57(1), 2004, who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak like equilibria, with increasing safety factor and stepped-pressure profiles. A stability treatment of the multiple barrier configuration reduces to an eigenvalue problem, where the eigenvectors are the normal displacements of the ideal barriers, and the eigen-matrix has tridiagonal structure. Next, marginal stability thresholds are explored in parameter space. For a single interface, results are benchmarked to Kaiser and Uecker. For multiple interfaces, we check our working via convergence tests, which reveal that the system approaches the single barrier case in the limit of vanishing interface width. The analysis provides a foundation upon which to study the stability of systems with a single internal barrier, placed at the reverse shear point.