Colin Malcolm Roach

This paper presents gradient-driven global electromagnetic gyrokinetic simulations for a conceptual burning flat-top operating point of STEP (Tholerus et al 2024 Nucl. Fusion 64 106030), STEP-EC-HD, and investigates how non-local effects influence the nonlinear saturation and transport of the electromagnetic turbulence at finite β . Local gyrokinetic simulations have shown that including δ B ∥ is essential for the dominant hybrid kinetic ballooning modes, or hKBMs, to be unstable in STEP (Kennedy et al 2024 Nucl. Fusion 64 086049). Using the long-wavelength δ B ∥ solver (Sheffield et al 2024 Plasma Phys. Control. Fusion 67 015028) implemented in GENE (Jenko et al 2000 Phys. Plasmas 7 1904–10), this work demonstrates that the linear mode spectrum can be accurately captured in global geometry, which results in good agreement with an ensemble of local flux-tube simulations. The global framework reproduces the hKBMs identified in Kennedy et al (2023 Nucl. Fusion 63 126061), while microtearing modes remain challenging to resolve due to their shorter radial scales. Nonlinear simulations reveal clear evidence of an electromagnetic transition to states with extremely large heat fluxes, consistent with local simulations and with the predicted loss of zonal-flow regulation for this proposed operating point (Kennedy et al 2026 Nucl. Fusion ). These findings establish the capability of global gyrokinetics to capture finite- β dynamics in STEP-like plasmas and motivate future work to identify the conditions governing this transition.

This work investigates the nonlinear transition to large heat fluxes observed in local gyrokinetic (GK) simulations of electromagnetic (EM) turbulence in STEP (Meyer 2024 Phil. Trans. R. Soc. 382 20230406). Using the stress-balance framework of (Zhang et al 2026 J. Plasma Phys. ) we confirm that the onset of extreme transport correlates with a critical value of q 2 β e , where q is the safety factor and β e is the ratio of electron thermal pressure to magnetic pressure, and relate this to a limit on the poloidal beta β pol . Crucially, this critical value lies below any relevant linear stability limit in the ( q , β e ) space (e.g. the onset of ideal or kinetic ballooning modes). Using an extensive set of nonlinear GK simulations, we demonstrate that the transition to large fluxes in STEP is governed by a balance between the electrostatic and magnetic-flutter stresses. We argue, and also show numerically, that larger-major-radius tokamaks reach the EM non-zonal regime at lower β e , making this MHD-controlled saturation limit more accessible in reactor-scale devices than in small spherical tokamaks. We also demonstrate that access to a second-stable regime enables re-saturation at larger values of β ′ . We further show that the ideal ballooning mode (IBM) threshold serves as a useful proxy for delineating this second-stable region and also tracks the onset of large fluxes. These results provide a predictive framework for identifying no-go zone predictions from local GKs and offer new insight into the EM saturation physics relevant to STEP and other high- β e devices.

The ability to capture the isotope mass scaling of core confinement seen in experiment is validated with JETTO-TGLF for low power JET-ILW discharges across H, D and T. The cases analysed include Ohmic discharges spanning the linear and saturated Ohmic confinement regimes as well as a trio of L-modes. The TGLF saturation rules SAT1-SAT3 are seen to predict a similar isotope scaling across both the ITG- and TEM-dominated discharges simulated, despite for the latter case the inclusion of the TEM branch of SAT3. The models demonstrate good agreement with experiment for the scaling between D and T plasmas, however a discrepancy is observed for H in the ITG-dominated discharges of higher density, as well as a systematic overprediction of the confinement time on the order of 20% in most cases. A retuned version of the SAT3 model, which was fit to better recreate fluxes close to the transport threshold, is seen to improve the magnitude of confinement predictions across all shots owing to an increased transport stiffness. This retuning was not seen to influence the confinement isotope scaling however, and possible transport mechanisms responsible for the continued discrepancy of higher density Ohmic and L-mode discharges in H are discussed.

The toroidal Alfvén eigenmode (TAE) is an Alfvénic gap mode, which when driven unstable, can lead to anomalous energetic particle (EP) transport or even direct expulsion of EPs to the first wall. Whether TAEs become unstable depends on the combined effects of various drive and damping channels, which have strong and distinct dependence on system parameters. To enable predictive modelling of current and future devices, the global gyrokinetic code ORB5 has been used to study linear TAE phenomena with a focus on investigating individual damping and drive channels. This is enabled by code diagnostics that measure the energy transfer per-species and in terms of specific (e.g. parallel and perpendicular) components of particle motion. These diagnostics allow a straightforward study of the damping and driving mechanisms of modes that would otherwise be stable, and difficult to isolate in initial value simulations. This new method was benchmarked against other codes by calculating the energy transfer between EPs and the TAE mode with good agreement found. ORB5 has also been used to study the physics of Alfvén eigenmodes in specific MAST-U shots, with the aim of developing a predictive capability for the excitation of these modes in regimes where high beta and inverse aspect ratio mean the drive and damping of TAEs differ significantly to those applicable to conventional tokamaks and theory-based estimates. Additionally, typical kinetic- magnetohydrodynamic approaches to modelling might be inappropriate as they do not capture bulk plasma kinetic effects, which can affect TAE damping. We find that an experimentally observed n = 3 TAE is marginally unstable in the MAST-U shot examined, and that radiative, ion Landau and a small degree of electron Landau damping are all present at the experimental values. We also find that an increase in beta leads to ion Landau damping beginning to dominate, confirming its expected strong dependence on β , which will be even more important in burning reactor plasmas.

Strong E × B plasma flow shear is beneficial for reducing turbulent transport. However, traditional methods of driving flow shear do not scale well to large devices such as future fusion power plants. In this paper, we use a large number of nonlinear gyrokinetic simulations to study a novel approach to increase flow shear: decreasing the momentum diffusivity to make the plasma ‘easier to push’. We first use an idealized circular geometry and find that one can obtain low momentum diffusivity (LMD) at tight aspect ratio, low safety factor, high magnetic shear and low temperature gradient. This is the so-called LMD regime. To drive intrinsic momentum flux, we then tilt the flux surface, making it up–down asymmetric. In the LMD regime, this intrinsic momentum flux drives strong flow shear that can significantly reduce the heat flux and increase the critical temperature gradient. We also consider the actual experimental geometry of the Mega Ampere Spherical Tokamak (MAST) to illustrate that this strategy can be practical and create experimentally significant flow shear. Lastly, a preliminary prediction for the SMall Aspect Ratio Tokamak (SMART) is made.

The plasma pressure achievable in a tokamak fusion reactor may be limited by instabilities like the ideal ballooning mode, a pressure-driven instability that acts to degrade plasma confinement. Here we investigate the sensitivity of the shape of the magnetic flux surface to the ideal ballooning mode; in particular, we modify the parameters describing the shape of magnetic flux surfaces of the equilibrium and perform infinite-n ideal ballooning scans to assess how shaping affects proximity to marginal instability. We find that for the parameter space considered, increasing squareness and elongation could help stabilise the plasma against the ideal ballooning mode instability.

Based on the analysis of a large number of high-fidelity nonlinear gyrokinetic simulations, we propose a novel strategy to improve confinement in spherical tokamak plasmas by combining up-down asymmetric flux surface shaping with the Low Momentum Diffusivity (LMD) regime. We show that the intrinsic momentum flux driven by up-down asymmetry creates strong flow shear in the LMD regime that can significantly reduce energy transport, increasing the critical gradient by up to 25%. In contrast to traditional methods for generating flow shear, such as neutral beam injection, this approach requires no external momentum source and is expected to scale well to large fusion devices. The experimental applicability of this strategy in spherical tokamaks is addressed via simulations by considering actual equilibria from Mega Ampere Spherical Tokamak and a preliminary equilibrium from SMART.

Magnetic stochastic perturbations can strongly influence cross-field transport in high β tokamak plasmas. The impact of stochastic magnetic fields on electron heat transport in MAST/MAST-U is studied over a range in collisionality. The physics guided semi-empirical Rechester-Rosenbluth and Rebut-Lallia-Walkins models are separately used to describe the stochastic field contribution to electron heat transport, and to supplement TGLF reduced model predictions of the transport from electrostatic turbulence. These combined models of anomalous transport are implemented in the JINTRAC code, and applied to transport simulations of the flat-top phase in MAST/MAST-U. The different ranges of validity of the stochastic transport models are briefly reviewed, focusing on the length-scales involved in the transport process. The principal relevant length-scales have been calculated using the plasma equilibrium characteristics, and used to determine the most appropriate stochastic transport model that is then applied in each shot. This analysis strongly suggests that stochasticity is an important transport mechanism in spherical tokamaks that should be included in ST plasma scenarios where strong electron heat transport is not described by other instabilities.

Electromagnetic geodesic acoustic modes are analytically investigated in tokamak plasmas with anisotropy, utilizing gyro-kinetic equations and a rigorously self-consistent anisotropic distribution. When including first-order finite-orbit-width effects and first-order finite-Larmor-radius effects, it is proven that the anisotropy with an arbitrary strength does not induce the m = ± 1 harmonics of A ‖ , where m and A ‖ denote the poloidal wavenumber and the parallel component of the perturbed magnetic vector potential, respectively. The rigorously self-consistent anisotropy introduces an equilibrium electrostatic field with poloidally asymmetric structure, and consequently induces an additional E → × B → drift term within the gyro-kinetic equation. This equilibrium electrostatic field inhibits the anisotropy from generating non-zero m = ± 1 harmonics of A ‖ . Indeed we demonstrate that introducing anisotropy self-consistently into the equilibrium quantitatively influences m = ± 1 , ± 2 harmonics of the perturbed electrostatic potential, but only the m = ± 2 harmonics of A ‖ .