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Electromagnetic microtearing modes (MTMs) have been observed in many different spherical tokamak regimes. Understanding how these and other electromagnetic modes nonlinearly saturate is likely critical in understanding the confinement of a high $\beta$ spherical tokamak (ST). Equilibrium $E\times B$ sheared flows have sometimes been found to significantly suppress low $\beta$ ion scale transport in both gyrokinetic simulations and in experiment. This work aims to understand the conditions under which $E\times B$ sheared flow impacts on the saturation of MTM simulations. Two experimental regimes are examined from MAST and NSTX, on surfaces that have unstable MTMs. The MTM driven transport on a local flux surface in MAST is shown to be more resilient to suppression via $E\times B$ shear, compared to the case from NSTX where the MTM transport is found to be significantly suppressed. This difference in the response to flow shear is explained through the impact of magnetic shear, $\hat{s}$ on the MTM linear growth rate dependence on ballooning angle, $\theta_0$. At low $\hat{s}$, the growth rate depends weakly on $\theta_0$, but at higher $\hat{s}$, the MTM growth rate peaks at $\theta_0 = 0$, with regions of stability at higher $\theta_0$. Equilibrium $E\times B$ sheared flows act to advect the $\theta_0$ of a mode in time, providing a mechanism which suppresses the transport from these modes when they become stable. The dependence of $\gamma^{MTM}$ on $\theta_0$ is in qualitative agreement with a recent theory [M.R. Hardman et al (2023)] at low $\beta$ when $q\sim1$, but the agreement worsens at higher $q$ where the theory breaks down. This work highlights the important role of the safety factor profile in determining the impact of equilibrium $E\times B$ shear on the saturation level of MTM turbulence., Comment: 20 pages, 16 figures

A quasi-linear reduced transport model is developed from a database of high-$\beta$ electromagnetic nonlinear gyrokinetic simulations performed with Spherical Tokamak for Energy Production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid-KBM turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat-top of the conceptual design, but do not demonstrate how this state can be accessed.

STEP is a spherical tokamak prototype power plant that is being designed to demonstrate net electric power. The design phase involves the exploitation of plasma models to optimise fusion performance subject to satisfying various physics and engineering constraints. A modelling workflow, including integrated core plasma modelling, MHD stability analysis, SOL and pedestal modelling, coil set and free boundary equilibrium solvers, and whole plant design, has been developed to specify the design parameters and to develop viable scenarios. The integrated core plasma model JETTO is used to develop individual flat-top operating points that satisfy imposed criteria for fusion power performance within operational constraints. Key plasma parameters such as normalised beta, Greenwald density fraction, auxiliary power and radiated power have been scanned to scope the operational space and to derive a collection of candidate non-inductive flat-top points. The assumed auxiliary heating and current drive is either from electron cyclotron systems only or a combination of electron cyclotron and electron Bernstein waves. At present stages of transport modelling, there is a large uncertainty in overall confinement for relevant parameter regimes. For each of the two auxiliary heating and current drive systems scenarios, two candidate flat-top points have been developed based on different confinement assumptions, totalling to four operating points. A lower confinement assumption generally suggests operating points in high-density, high auxiliary power regimes, whereas higher confinement would allow access to a broader parameter regime in density and power while maintaining target fusion power performance., Comment: 44 pages, 15 figures. Submitted to Nucl. Fusion (IOP)

[ABRIDGED] This paper discusses the importance of parallel perturbations of the magnetic-field in gyrokinetic simulations of electromagnetic instabilities and turbulence at mid-radius in the burning plasma phase of the conceptual high-$\beta$, reactor-scale, tight-aspect-ratio tokamak STEP. Previous studies have revealed the presence of unstable hybrid kinetic ballooning modes (hKBMs) at binormal scales approaching the ion Larmor radius. In this STEP plasma it was found that the hKBM requires the inclusion of parallel magnetic-field perturbations to be linearly unstable. Here, the extent to which the inclusion of fluctuations in the parallel magnetic-field can be relaxed is explored through gyrokinetic simulations. In particular, the frequently used MHD approximation (dropping $\delta \! B_{\parallel}$ and setting the $\nabla B$ drift frequency equal to the curvature drift frequency) is discussed and simulations explore whether this approximation is useful for modelling STEP plasmas. It is shown that the MHD approximation can reproduce some of the linear properties of the full STEP gyrokinetic system, but is too stable at low $k_y$ and nonlinear simulations using the MHD approximation result in very different transport states. It is demonstrated that the MHD approximation is challenged by the high $\beta^{\prime}$ values in STEP, and that the approximation improves considerably at lower $\beta^{\prime}$. Furthermore, it is shown that the sensitivity of STEP to $\delta \! B_{\parallel}$ fluctuations is primarily because the plasma sits close to marginality and it is shown that in slightly more strongly driven conditions the hKBM is unstable without $\delta \! B_{\parallel}.$ Crucially, it is demonstrated that the state of large transport typically predicted by local electromagnetic gyrokinetic simulations of STEP plasmas is not solely due to $\delta \! B_{\parallel}$ physics., Comment: 29th IAEA FEC conference

First nonlinear gyrokinetic simulations of microtearing modes in the core of a MAST case are performed on two surfaces of the high-collisionality discharge used in Valovi\v{c} et al. Nucl. Fusion 51.7 (2011) to obtain the favorable energy confinement scaling with collisionality, $\tau_E\propto\,\nu_*^{-1}$. On the considered surfaces microtearing modes dominate linearly at binormal length scales of the order of the ion Larmor radius. While the effect of electron collision frequency is moderate in linear simulations, a strong dependence on this parameter is found in nonlinear simulations at $r/a=0.5$, where $r$ and $a$ are the surface and tokamak minor radius, respectively. The dynamics of magnetic islands generated by microtearing modes is analysed, showing that the radial extent of the stochastic region caused by islands overlapping plays an important role in determining the saturation level of the microtearing mode driven heat flux. Local nonlinear gyrokinetic simulations show that the microtearing mode driven heat flux, $Q_e^\mathrm{MTM}$, is largely dominated by magnetic flutter and depends strongly on the magnetic shear, $\hat{s}$. Comparing two surfaces, $r/a=0.5$ and $r/a=0.6$, reveals that $Q_e^\mathrm{MTM}$ is negligible at $r/a=0.5$ ($\hat{s}=0.34$), with the electron temperature gradient driven heat flux, $Q_e^\mathrm{ETG}$, comparable to the experimental electron heat flux, $Q_e^\mathrm{exp}$, while $Q_e^\mathrm{MTM}$ is significantly larger and comparable to $Q_e^\mathrm{ETG}$ and $Q_e^\mathrm{exp}$ at $r/a=0.6$ ($\hat{s}=1.1$). Microtearing modes cause more experimentally significant transport in higher $\hat{s}$ regions and may influence (together with electron temperature gradient modes) the observed scaling of energy confinement time with collisionality (Valovi\v{c} et al. Nucl. Fusion 51.7 (2011)).

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, $\beta$, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that $\beta$ is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective $\beta$ that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective $\beta$ can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter $\theta_0$ -- possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport., Comment: 29 pages, 14 figures

Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma ? and having increased vertical stability. To understand the confinement properties that might be expected in the conceptual design for a high $\beta$ ST fusion reactor, a 1GW ST plasma equilibrium was analysed using local linear gyrokinetics to determine the type of micro-instabilities that arise. Kinetic ballooning modes (KBMs) and micro-tearing modes (MTMs) are found to be the dominant instabilities. The parametric dependence of these linear modes was determined and from the insights gained, the equilibrium was tuned to find a regime marginally stable to all micro-instabilities at $\theta_0$ = 0:0. This work identifies the most important micro-instabilities expected to generate turbulent transport in high $\beta$ STs. The impact of such modes must be faithfully captured in first principles based reduced models of anomalous transport that are needed for predictive simulations., Comment: 43 pages, 67 figures, 4 tables

Fusion energy is often regarded as a long-term solution to the world's energy needs. However, even after solving the critical research challenges, engineering and materials science will still impose significant constraints on the characteristics of a fusion power plant. Meanwhile, the global energy grid must transition to low-carbon sources by 2050 to prevent the worst effects of climate change. We review three factors affecting fusion's future trajectory: (1) the significant drop in the price of renewable energy, (2) the intermittency of renewable sources and implications for future energy grids, and (3) the recent proposition of intermediate-level nuclear waste as a product of fusion. Within the scenario assumed by our premises, we find that while there remains a clear motivation to develop fusion power plants, this motivation is likely weakened by the time they become available. We also conclude that most current fusion reactor designs do not take these factors into account and, to increase market penetration, fusion research should consider relaxed nuclear waste design criteria, raw material availability constraints and load-following designs with pulsed operation., Comment: 31 pages, 3 figures, submitted to Energy Policy