### stella: An operator-split, implicit-explicit delta f-gyrokinetic code for general magnetic field configurations

*JOURNAL OF COMPUTATIONAL PHYSICS*

**391**(2019) 365-380

### Overview of new MAST physics in anticipation of first results from MAST Upgrade

*Nuclear Fusion*IOP Science

**59:11**(2019) 112011

#### Abstract:

The mega amp spherical tokamak (MAST) was a low aspect ratio device (R/a = 0.85/0.65 ~ 1.3) with similar poloidal cross-section to other medium-size tokamaks. The physics programme concentrates on addressing key physics issues for the operation of ITER, design of DEMO and future spherical tokamaks by utilising high resolution diagnostic measurements closely coupled with theory and modelling to significantly advance our understanding. An empirical scaling of the energy confinement time that favours higher power, lower collisionality devices is consistent with gyrokinetic modelling of electron scale turbulence. Measurements of ion scale turbulence with beam emission spectroscopy and gyrokinetic modelling in up-down symmetric plasmas find that the symmetry of the turbulence is broken by flow shear. Near the non-linear stability threshold, flow shear tilts the density fluctuation correlation function and skews the fluctuation amplitude distribution. Results from fast particle physics studies include the observation that sawteeth are found to redistribute passing and trapped fast particles injected from neutral beam injectors in equal measure, suggesting that resonances between the m = 1 perturbation and the fast ion orbits may be playing a dominant role in the fast ion transport. Measured D–D fusion products from a neutron camera and a charged fusion product detector are 40% lower than predictions from TRANSP/NUBEAM, highlighting possible deficiencies in the guiding centre approximation. Modelling of fast ion losses in the presence of resonant magnetic perturbations (RMPs) can reproduce trends observed in experiments when the plasma response and charge-exchange losses are accounted for. Measurements with a neutral particle analyser during merging-compression start-up indicate the acceleration of ions and electrons. Transport at the plasma edge has been improved through reciprocating probe measurements that have characterised a geodesic acoustic mode at the edge of an ohmic L-mode plasma and particle-in-cell modelling has improved the interpretation of plasma potential estimates from ball-pen probes. The application of RMPs leads to a reduction in particle confinement in L-mode and H-mode and an increase in the core ionization source. The ejection of secondary filaments following type-I ELMs correlates with interactions with surfaces near the X-point. Simulations of the interaction between pairs of filaments in the scrape-off layer suggest this results in modest changes to their velocity, and in most cases can be treated as moving independently. A stochastic model of scrape-off layer profile formation based on the superposition of non-interacting filaments is in good agreement with measured time-average profiles. Transport in the divertor has been improved through fast camera imaging, indicating the presence of a quiescent region devoid of filament near the X-point, extending from the separatrix to ψ n ~ 1.02. Simulations of turbulent transport in the divertor show that the angle between the divertor leg on the curvature vector strongly influences transport into the private flux region via the interchange mechanism. Coherence imaging measurements show counter-streaming flows of impurities due to gas puffing increasing the pressure on field lines where the gas is ionised. MAST Upgrade is based on the original MAST device, with substantially improved capabilities to operate with a Super-X divertor to test extended divertor leg concepts. SOLPS-ITER modelling predicts the detachment threshold will be reduced by more than a factor of 2, in terms of upstream density, in the Super-X compared with a conventional configuration and that the radiation front movement is passively stabilised before it reaches the X-point. 1D fluid modelling reveals the key role of momentum and power loss mechanisms in governing detachment onset and evolution. Analytic modelling indicates that long legs placed at large major radius, or equivalently low at the target compared with the X-point are more amenable to external control. With MAST Upgrade experiments expected in 2019, a thorough characterisation of the sources of the intrinsic error field has been carried out and a mitigation strategy developed.### A scale-separated approach for studying coupled ion and electron scale turbulence

*Plasma Physics and Controlled Fusion*IOP Science

**61**(2019) 065025

#### Abstract:

Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$ and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space–time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale-separation between ion scales (IS) and electron scales (ES), and expanding the gyrokinetic equations for the turbulence in ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$, we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The ES turbulence experiences a modified drive due to gradients in the IS distribution function, and is advected by the IS $E\times B$ drift, which varies in the direction parallel to the magnetic field line. The largest possible cross-scale term in the IS equations is sub-dominant in our ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$ expansion. Hence, in our model the IS turbulence evolves independently of the ES turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard 'twist-and-shift' boundary condition. This approach allows one to simulate multi-scale turbulence using ES flux tubes nested within an IS flux tube.### stella: an operator-split, implicit-explicit δf-gyrokinetic code for general magnetic field configurations

*Journal of Computational Physics*Elsevier

**391**(2019) 365-380

#### Abstract:

Here we present details of an operator-split, implicit-explicit numerical scheme for the solution of the gyrokinetic-Poisson system of equations in the local limit. This scheme has been implemented in a new code called stella, which is capable of evolving electrostatic fluctuations with full kinetic electron effects and an arbitrary number of ion species in general magnetic geometry. We demonstrate the advantages of this mixed approach over a fully explicit treatment and provide linear and nonlinear benchmark comparisons for both axisymmetric and non-axisymmetric magnetic equilibria.### Intrinsic rotation driven by turbulent acceleration

*Plasma Physics and Controlled Fusion*IOP Publishing (2019)