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Turbulent transport in magnetically confined fusion plasma has conventionally been analyzed at the ion gyroradius scale based on the microturbulence theory. However, ion-scale turbulence analysis sometimes fails to predict the turbulent transport flux observed experimentally. Microturbulence at the electron gyroradius scale and cross-scale interactions between disparate-scale turbulences are possible mechanisms to resolve this issue. This overview discusses the recent progress in multiscale turbulence studies and presents future perspectives from recent experimental, theoretical, and numerical investigations. The following aspects are highlighted: (1) the importance of electron-scale effects in experiments, (2) the physical mechanisms of cross-scale interactions, (3) modeling electron-scale effects in quasilinear transport models, and (4) the impacts of cross-scale interactions on burning plasmas. Understanding multiscale turbulence is necessary to improve performance prediction and explore optimal operations for future burning plasmas. [ABSTRACT FROM AUTHOR]

We present the first nonlinear, gyrokinetic, surface-global simulations of a Wendelstein 7-X-like stellarator with kinetic electrons. As a first application, we investigate the interplay between Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) driven turbulence in a Full-Flux-Surface (FFS) approach, as well as the effect of a neoclassical radial electric field, something that escapes the capabilities of flux-tube simulations. We find that even in this more complex setup, ITG turbulence is stabilised through a finite density gradient while TEM turbulence remains relatively weak. Furthermore, we show that the effect of the radial electric field itself is small in comparison with the variation of the gradients. Nevertheless, we observe that for some of the cases shown here, there is not only quantitative but also qualitative disagreement between flux-tube and FFS simulations, in contrast to earlier studies with an adiabatic electron model. These results emphasise the potential importance of retaining geometrical variations on the flux-surface when describing stellarator turbulence under realistic conditions. [ABSTRACT FROM AUTHOR]

Plasmas with negative triangularity (NT) shape have been recently shown to be able to achieve H-mode levels of confinement in L-mode, avoiding detrimental edge localised modes. Therefore, this plasma geometry is now studied as a possible viable option for a future fusion reactor. Within this framework, an NT option is under investigation for the full power scenario of the Divertor Tokamak Test (DTT) facility, under construction in Italy, with $\delta_\mathrm{top} = -0.32/\delta_\mathrm{bottom}\simeq0.02$ top/bottom triangularity values at the separatrix. The transport properties of this scenario are studied in this work. Gyrokinetic GENE simulations and integrated modelling using ASTRA with the quasi-linear trapped gyro-Landau fluid (TGLF) model have been performed. The emerging picture from the ASTRA-TGLF runs with boundary conditions at $\rho_\mathrm{tor} = 0.94$ is that, in the L-mode NT option, the larger peaking of the kinetic profiles in the edge region is not sufficient to recover the loss of the PT H-mode pedestal, and reach similar central temperature values. Two additional shapes are also considered, obtained by flipping the triangularity of the scenarios, to single out the effect of the triangularity sign. A negligible ‘direct’ effect of the triangularity is found for the L-mode, while a small beneficial effect is observed for the H-mode. The ASTRA-TGLF results are validated by GENE and TGLF stand-alone at two selected radii. GENE shows ITG dominant micro-instability and explains the small beneficial effect of the NT for the H-mode as due to a strong reduction of the heat fluxes, when reversing the triangularity, with a relatively high $T_\mathrm{i}$ stiffness. An improvement of the predicted performances of the NT DTT scenario could come from $\rho_\mathrm{tor}\gtrsim0.9$ , as indicated by some recent experiments at the tokamak à configuration variable (TCV) and ASDEX Upgrade.

Turbulent transport in magnetically confined fusion plasma has conventionally been analyzed at the ion gyroradius scale based on the microturbulence theory. However, ion-scale turbulence analysis sometimes fails to predict the turbulent transport flux observed experimentally. Microturbulence at the electron gyroradius scale and cross-scale interactions between disparate-scale turbulences are possible mechanisms to resolve this issue. This overview discusses the recent progress in multiscale turbulence studies and presents future perspectives from recent experimental, theoretical, and numerical investigations. The following aspects are highlighted: (1) the importance of electron-scale effects in experiments, (2) the physical mechanisms of cross-scale interactions, (3) modeling electron-scale effects in quasilinear transport models, and (4) the impacts of cross-scale interactions on burning plasmas. Understanding multiscale turbulence is necessary to improve performance prediction and explore optimal operations for future burning plasmas.

The interaction between a plasma and a solid surface is studied in a (1D-1V) kinetic approach using immersed boundary conditions and penalization to model the wall. Two solutions for the penalized wall region are investigated that either allow currents to flow within the material boundary or not. Essential kinetic aspects of sheath physics are recovered in both cases and their parametric dependencies investigated. Importantly, we show how the two approaches can be reconciled when accounting for relevant kinetic effects. Non-Maxwellian features of the ion and electron distribution functions are essential to capture the value of the potential drop in the sheath. These features lead to a sheath heat transmission factor for ions 60% larger than usually predicted and 35% for electrons. The role of collisions is discussed and means of incorporating minimally-relevant kinetic sheath physics in the gyrokinetic framework are discussed.

This paper reports on the refinement (building on (Hatch D.R. et al 2022 Phys. Plasmas 29 062501)) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model’s applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: the model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature profile exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high $\eta_e = L_{ne}/L_{Te}$ scenarios but not for low η _e scenarios in which microtearing modes (MTMs) have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile.

A theoretical model is presented that for the first time matches experimental measurements of the pedestal width-height Diallo scaling in the low-aspect-ratio high- β tokamak NSTX. Combining linear gyrokinetics with self-consistent pedestal equilibrium variation, kinetic-ballooning, rather than ideal-ballooning plasma instability, is shown to limit achievable confinement in spherical tokamak pedestals. Simulations are used to find the novel Gyrokinetic Critical Pedestal constraint, which determines the steepest pressure profile a pedestal can sustain subject to gyrokinetic instability. Gyrokinetic width-height scaling expressions for NSTX pedestals with varying density and temperature profiles are obtained. These scalings for STs depart significantly from that of conventional aspect ratio tokamaks.

The effects of poloidally inhomogeneous heat sources are investigated through a gyrokinetic formula in collisionless toroidal plasmas. A gyrokinetic dispersion relation is newly derived under the assumption that equilibrium parallel heat flows are generated to remove the injected poloidally nonuniform heat source. The dispersion relation is numerically solved, considering both inboard and outboard heat source injections. In the case of the inboard source injection, both Stringer spin-up and geodesic acoustic mode (GAM) are excited. Conversely, outboard injection leads to the emergence of a heat source-driven GAM (referred to as Q-GAM), featuring a frequency around half that of the standard GAM. Various physical quantities of the Q-GAM, such as mode frequency and source threshold, are analyzed through parametric scans. The Q-GAM exhibits similarities with the energetic-particle-driven GAM (EGAM), particularly in its frequency range, and both belong to one of the strong Landau damped poles. Despite having distinct driving mechanisms and structural differences in parallel velocity and poloidal coordinates, the response function of the perturbed parallel pressure to the potential, mainly contributing to the destabilization of each mode around half of the GAM frequency, is derived to have a similar form for both the Q-GAM and EGAM cases.

This paper presents global gyrokinetic simulations on the transport time scale of an ASDEX Upgrade H-mode discharge showing a pronounced peaking of the on-axis ion temperature profiles. Leveraging the newly developed GENE-Tango tool, which combines the global gyrokinetic code GENE with the transport solver Tango, we investigate the impact of energetic particles and electromagnetic effects on the improved plasma performance observed in the experimental discharge. Our results reveal that a striking agreement between the GENE-Tango simulations and the experimental measurements can be achieved only when energetic particles and electromagnetic effects are simultaneously retained in the modeling. In contrast, when these are neglected we observed a significant underestimation of the on-axis ion temperature, aligning with profiles computed using TGLF-ASTRA. The peaking in the ion temperature profile observed in the simulations can be attributed to the effective suppression of turbulence by high-frequency electromagnetic modes, likely Kinetic Ballooning Modes/Alfvén eigenmodes. These modes play a critical role in enhancing zonal flow activity and shearing rate levels which thus lead to a localized increase in the temperature gradient. However, it is crucial to maintain these modes at a state of marginal stability or weak instability to prevent energetic particle turbulence destabilization. Otherwise, the result would be a flattening of all the thermal profiles. Interestingly, we found that global GENE-Tango simulations are required to model correctly the linear dynamics of these high-frequency modes. Additionally, global simulations demonstrate greater tolerance than flux-tube simulations for marginal instability of these high frequency modes while maintaining power balance agreement.

This work presents the PORTALS framework (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), which leverages surrogate modeling and optimization techniques to enable the prediction of core plasma profiles and performance with nonlinear gyrokinetic simulations at significantly reduced cost, with no loss of accuracy. The efficiency of PORTALS is benchmarked against standard methods, and its full potential is demonstrated on a unique, simultaneous 5-channel (electron temperature, ion temperature, electron density, impurity density and angular rotation) prediction of steady-state profiles in a DIII-D ITER Similar Shape plasma with GPU-accelerated, nonlinear CGYRO (Candy et al 2016 J. Comput. Phys. 324 73–93). This paper also provides general guidelines for accurate performance predictions in burning plasmas and the impact of transport modeling in fusion pilot plants studies.

A fundamental dynamical constraint—that fluctuation induced charge-weighted particle flux must vanish- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when large enough, lead to a violation of the constraint and hence preclude unstable modes and turbulent transport. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducive to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations.

A gyrokinetic threshold model for pedestal width–height scaling prediction is applied to multiple devices. A shaping and aspect ratio scan is performed on National Spherical Torus Experiment (NSTX) equilibria, finding $\Delta_{\mathrm{ped}} = 0.92 A^{1.04} \kappa^{-1.24} 0.38^{\delta} \beta_{\theta,\mathrm{ped}}^{1.05}$ for the wide-pedestal branch with pedestal width $\Delta_{\mathrm{ped}}$ , aspect ratio A , elongation κ , triangularity δ , and normalized pedestal height $\beta_{\theta,\mathrm{ped}}$ . The width–transport scaling is found to vary significantly if the pedestal height is varied either with a fixed density or fixed temperature, showing how fueling and heating sources affect the pedestal density and temperature profiles for the kinetic-ballooning-mode (KBM) limited profiles. For an NSTX equilibrium, at fixed density, the wide branch is $\Delta_{\mathrm{ped} } = 0.028 \left(q_\textrm e/\Gamma_\textrm e - 1.7 \right)^{1.5} \sim \eta_\textrm e ^{1.5}$ and at fixed temperature $\Delta_{\mathrm{ped} } = 0.31 \left(q_\textrm e/\Gamma_\textrm e - 4.7 \right)^{0.85}$ $ \sim \eta_\textrm e ^{0.85}$ , where $q_\textrm e$ and $\Gamma_\textrm e$ are turbulent electron heat and particle fluxes and $\eta_\textrm e = \nabla \ln T_\textrm e / \nabla \ln n_\textrm e$ for an electron temperature $T_\textrm e$ and density $n_\textrm e$ . Pedestals close to the KBM limit are shown to have modified turbulent transport coefficients compared to the strongly driven KBMs. The role of flow shear is studied as a width–height scaling constraint and pedestal saturation mechanism for a standard and lithiated wide pedestal discharge. Finally, the stability, transport, and flow shear constraints are combined and examined for an NSTX experiment.

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- β , reactor-scale, tight-aspect-ratio tokamak STEP. Previous studies have revealed the presence of unstable hybrid kinetic ballooning modes (hKBMs) and subdominant microtearing modes 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.

Strong poloidal refueling asymmetry in the DIII-D tokamak is inferred from line radiation measurements. Synthetic diagnostics in neutral transport modeling coupled to gyrokinetic simulations illuminate implications for the plasma flow profile in the scrape-off layer of single-null beam-driven discharges. Recycling occurs primarily either on the inner or outer divertor legs, depending on the toroidal magnetic field direction. By reversing the toroidal magnetic field, the observed line radiation asymmetry is nearly eliminated or reversed. It is determined that, while relatively simple physics can describe the observed ionization asymmetry, predicting the overall brightness of the hydrogenic Lyman- α signal requires detailed simulation of the plasma and resulting turbulence. To this end, kinetic plasma simulations fully coupled to comprehensive neutral transport calculations—a novel capability—provide first-principles reproduction of Lyman- α observations on DIII-D.

Experiments, gyrokinetic simulations and transport predictions were performed to investigate if a negative triangularity (NT) L-mode option for the Divertor Tokamak Test (DTT) full-power scenario would perform similarly to the positive triangularity (PT) H-mode reference scenario, avoiding the harmful edge localized modes (ELMs). The simulations show that a beneficial effect of NT coming from the edge/scrape-off layer (SOL) region $\rho_{\mathrm{tor}} \gt 0.9$ is needed to allow the actual NT L-mode option to perform like the PT H-mode. Dedicated experiments at TCV and AUG, with DTT-like shapes, show an optimistic picture. In TCV, experiments indicate that even with the relatively small triangularity of the DTT NT scenario, a large beneficial effect of NT comes from the plasma edge and SOL, allowing NT L-modes to outperform PT L-modes with the same power input, reaching the same central pressures as PT H-modes with twice as much applied heating power. For AUG, NT plasmas go into H-mode more easily than for TCV, but always present much smaller pedestals compared with PT plasmas with the same input power, showing a much weaker or absent ELM activity. However, NT has a smaller beneficial effect for AUG than for TCV, with NT pulses outperforming PT pulses with the same input power only for an ECRH-only case with relatively low input power. For the considered AUG cases, PT pulses perform better than NT ones at higher ECRH power or with mixed NBI and ECRH power. Based on this analysis, the NT option is a viable alternative for the DTT full power scenario, providing high performance plasmas with reduced or absent ELMs.

Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations. [ABSTRACT FROM AUTHOR]

In recent years tokamak experiments and modelling have increasingly indicated that the interaction between suprathermal (fast) ions and thermal plasma can lead to a reduction of turbulence and an improvement of confinement. The regimes in which this stabilization occurs are relevant to burning plasmas, and their understanding will inform reactor scenario optimization. This review summarizes observations, simulations, theoretical understanding, and open questions on this emerging topic. [ABSTRACT FROM AUTHOR]

The recent progress in high-temperature superconductor technologies has led to the design and construction of SPARC, a compact tokamak device expected to reach plasma breakeven with up to 25 MW of external ion cyclotron resonant heating (ICRH) power. This manuscript presents local (flux-tube) and radially global gyrokinetic GENE (Jenko et al 2000 Phys. Plasmas 7 1904) simulations for a reduced-field and current H-mode SPARC scenario showing that supra-thermal particles—generated via ICRH—strongly suppress ion-scale turbulent transport by triggering a fast ion-induced anomalous transport barrier. The trigger mechanism is identified as a wave-particle resonant interaction between the fast particle population and plasma micro-instabilities (Di Siena et al 2021 Phys. Rev. Lett. 125 025002). By performing a series of global simulations employing different profiles for the thermal ions, we show that the fusion gain of this SPARC scenario could be substantially enhanced by up to ∼80% by exploiting this fast ion stabilizing mechanism. A study is also presented to further optimize the energetic particle profiles, thus possibly leading experimentally to an even more significant fusion gain. [ABSTRACT FROM AUTHOR]

Global electromagnetic gyrokinetic simulations are performed with the particle-in-cell code ORB5 for an ITER pre-fusion-power-operation plasma scenario, with half-field (2.65 T) and half-current (7.5 MA). We report on a ‘multi-scale‘ analysis of the discharge, considering eigenmodes and instabilities across three scale-lengths (n < 35, 45 < n < 70, n > 100). Although the scenario will nominally have neutral beam heating with particles injected with 1 MeV, AlfvĂ©n eigenmodes are investigated in the absence of such source, and reversed shear, toroidal and elliptical AlfvĂ©n eigenmodes are found with weak damping for moderately low toroidal mode numbers (10 â©˝ n â©˝ 35). At higher toroidal mode numbers (40 â©˝ n â©˝ 70), unstable AlfvĂ©nic modes have been observed close to rational surfaces and are labelled as beta-induced AlfvĂ©n eigenmodes (BAEs)/AlfvĂ©nic ion temperature gradient modes, since their frequency is associated with the BAE gap and they are driven by the bulk plasma on the AlfvĂ©nic continuum. These modes are unstable in the absence of energetic particles (EPs), and adding a species of EPs (with an isotropic 1 MeV slowing down distribution) has negligible impact on their growth rate. At higher toroidal mode numbers (n âŞ... 200), low frequency microscale instabilities are observed. [ABSTRACT FROM AUTHOR]

The excitation of toroidicity-induced Alfvén eigenmodes (TAEs) using prescribed external electromagnetic perturbations (hereafter ‘antenna’) acting on a confined toroidal plasma, as well as its nonlinear couplings to other modes in the system, is studied. The antenna is described by an electrostatic potential resembling the target TAE mode structure along with its corresponding parallel electromagnetic potential computed from Ohm’s law. Numerically stable long-time linear simulations are achieved by integrating the antenna within the framework of a mixed representation and pullback scheme (Mishchenko et al 2019 Comput. Phys. Commun. 238 194). By decomposing the plasma electromagnetic potential into symplectic and Hamiltonian parts and using Ohm’s law, the destabilizing contribution of the potential gradient parallel to the magnetic field is cancelled in the equations of motion. Besides evaluating the frequencies and the growth/damping rates of excited modes compared to referenced TAEs, we study the interaction of antenna-driven modes with fast particles and indicate their margins of instability. Furthermore, we show the first nonlinear simulations in the presence of a TAE-like antenna exciting other TAE modes, as well as global Alfvén eigenmodes with different toroidal wave numbers from that of the antenna. [ABSTRACT FROM AUTHOR]

Gyrokinetic simulations are among the main tools to predict turbulent transport in the core of fusion devices. Unlike the core, the plasma edge and scrape‐off layer are characterized by lower temperature and higher collisionality. To allow for realistic gyrokinetic modelling of edge and scrape‐off layer turbulence, it is crucial to include collisional effects into the simulations. In this work, we present a full‐f, gyro‐averaged, multi‐species, Lenard‐Bernstein/Dougherty (LBD) collision operator, for the use in the gyrokinetic turbulence code GENE‐X. The operator accounts for exact particle density, momentum, and energy conservation, with collision frequencies chosen such that the momentum or temperature relaxation rates of the Boltzmann collision operator are recovered. We provide a conservative second‐order finite‐volume implementation of the operator and present a thorough verification. Due to the excellent conservation properties of the finite‐volume implementation, it is possible to use a coarser velocity space grid, save computational resources and, as a consequence, perform simulations of larger fusion devices. [ABSTRACT FROM AUTHOR]

Continuum gyrokinetic simulations of electrostatic ion scale turbulence are presented for the case of a diverted (single‐null) tokamak geometry. The simulation model, implemented in the finite‐volume code COGENT, solves the long‐wavelength limit of the full‐F gyrokinetic equation for ion species coupled to a vorticity equation for electrostatic potential variations, where a fluid model is used for an electron response. The model describes the ion scale ion temperature gradient (ITG) and resistive drift modes as well as neoclassical ion physics effects. Different turbulence regimes are observed depending on the plasma profiles, and the roles of a self‐consistent background electric field and an X‐point geometry are explored. In particular, increasing the pedestal density gradient and the corresponding radial electric field is demonstrated to suppress the ITG turbulence, whereas the same edge plasma background can still be destabilized by the resistive modes when the plasma resistivity is increased. The effects of X‐point geometry are assessed by comparing cross‐separatrix simulations with counterpart calculations performed for a toroidal annulus geometry. For the simulation parameters considered, similar global behaviour is observed in both cases, whereas strong local suppression of turbulence fluctuations is demonstrated near the X‐point for the case of a single‐null geometry. [ABSTRACT FROM AUTHOR]

We present the first nonlinear, gyrokinetic, surface-global simulations of a Wendelstein 7-X-like stellarator with kinetic electrons. As a first application, we investigate the interplay between Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) driven turbulence in a Full-Flux-Surface (FFS) approach, as well as the effect of a neoclassical radial electric field, something that escapes the capabilities of flux-tube simulations. We find that even in this more complex setup, ITG turbulence is stabilised through a finite density gradient while TEM turbulence remains relatively weak. Furthermore, we show that the effect of the radial electric field itself is small in comparison with the variation of the gradients. Nevertheless, we observe that for some of the cases shown here, there is not only quantitative but also qualitative disagreement between flux-tube and FFS simulations, in contrast to earlier studies with an adiabatic electron model. These results emphasise the potential importance of retaining geometrical variations on the flux-surface when describing stellarator turbulence under realistic conditions.

Flux-tube (local) gyrokinetic codes are widely used to simulate drift-wave turbulence in magnetic confinement devices. While a large number of studies show that flux-tube codes provide an excellent approximation for turbulent transport in medium-large devices, it still needs to be determined whether they are sufficient for modeling supra-thermal particle effects on core turbulence. This is called into question given the large temperature of energetic particles (EPs), which makes them hardly confined on a single flux-surface, but also due to the radially broad mode structure of EP-driven modes. The primary focus of this manuscript is to assess the range of validity of flux-tube codes in modeling fast ion effects by comparing radially global turbulence simulations with flux-tube results at different radial locations for realistic JET parameters using the gyrokinetic code GENE. To extend our study to a broad range of different plasma scenarios, this comparison is made for four different plasma regimes, which differ only by the profile of the ratio between the plasma kinetic and magnetic pressure. The latter is artificially rescaled to address the (i) electrostatic limit and regimes with (ii) marginally stable, (iii) weakly unstable and (iv) strongly unstable fast ion modes. These EP-driven modes are identified as Alfvénic ion temperature gradient modes (AITG)/kinetic beta-induced Alfvén eigenmodes (KBAE) via linear ORB5 and LIGKA simulations. It is found that the local flux-tube simulations can recover well the global results only in the electrostatic and marginally stable cases. When the AITG/KBAE becomes linearly unstable, the local approximation fails to correctly model the radially broad fast ion mode structure and the consequent global zonal patterns. According to this study, global turbulence simulations are likely required in regimes with linearly unstable AITG/KBAEs. In conditions with different fast ion-driven modes, these results might change.

We present herein the results of a linear gyrokinetic analysis of electromagnetic microinstabilites in the conceptual high $-\beta,$ reactor-scale, tight-aspect-ratio tokamak Spherical Tokamak for Energy Production, https://step.ukaea.uk . We examine a range of flux surfaces between the deep core and the pedestal top for two candidate flat-top operating points of the prototype device. Local linear gyrokinetic analysis is performed to determine the type of microinstabilities that arise under these reactor-relevant conditions. We find that the equilibria are dominated at ion binormal scales by a hybrid version of the kinetic ballooning mode (KBM) instability that has significant linear drive contributions from the ion temperature gradient and from trapped electrons, while collisional microtearing modes (MTMs) are sub-dominantly also unstable at similar binormal scales. The hybrid -KBM and MTM exhibit very different radial scales. We study the sensitivity of these instabilities to physics parameters, and discuss potential mechanisms for mitigating them. The results of this investigation are compared to a small set of similar conceptual reactor designs in the literature. A detailed benchmark of the linear results is performed using three gyrokinetic codes; alongside extensive resolution testing and sensitivity to numerical parameters providing confidence in the results of our calculations, and paving the way for detailed nonlinear studies in a companion article.

The recent progress in high-temperature superconductor technologies has led to the design and construction of SPARC, a compact tokamak device expected to reach plasma breakeven with up to 25 MW of external ion cyclotron resonant heating (ICRH) power. This manuscript presents local (flux-tube) and radially global gyrokinetic GENE (Jenko et al 2000 Phys. Plasmas 7 1904) simulations for a reduced-field and current H-mode SPARC scenario showing that supra-thermal particles—generated via ICRH—strongly suppress ion-scale turbulent transport by triggering a fast ion-induced anomalous transport barrier. The trigger mechanism is identified as a wave-particle resonant interaction between the fast particle population and plasma micro-instabilities (Di Siena et al 2021 Phys. Rev. Lett. 125 025002). By performing a series of global simulations employing different profiles for the thermal ions, we show that the fusion gain of this SPARC scenario could be substantially enhanced by up to ∼80% by exploiting this fast ion stabilizing mechanism. A study is also presented to further optimize the energetic particle profiles, thus possibly leading experimentally to an even more significant fusion gain.

The derivation of an intermediate-scale gyrokinetic-electron theory in nonuniform tokamak plasmas (Chen et al 2021 Nucl. Fusion 61 https://doi.org/10.1088/1741-4326/abf81a ) has shown that a Navier–Stokes type nonlinearity couples electron-temperature-gradient (ETG) modes and zonal flow (ZF) modes with wavelengths much shorter than the ion gyroradius but much longer than the electron gyroradius. This intermediate-scale ETG-ZF coupling is typically stronger than the Hasegawa–Mima type nonlinearity characteristic of the fluid approximation and is predicted to lead to relevant ZF generation and ETG mode regulation. Electron-scale, continuum, gyrokinetic simulation results are presented here which include both single-mode ETG and full-spectrum ETG turbulence. The ZF generation due to single ETG modes is investigated and the single-mode intermediate-scale results are found to be in agreement with theory. The full-spectrum results are then presented and explained qualitatively in terms of the single-mode results. It is found that the ETG-driven ZFs regulate intermediate-scale electron heat flux transport to levels in the predicted range.

We present a comparative transport analysis of the isotope mass dependence in the pedestal of two pairs of deuterium/hydrogen type I ELMy H-mode discharges in JET with ITER-like wall, one characterized by the same input power, the other one by the same stored energy. The investigation, carried out using the gyrokinetic code GENE, focuses on the steep profile region of the pedestal. While large wavenumber modes mainly contribute to the electron heat flux and are scarcely influenced by the main gas isotope, an effect of the ion mass in agreement with the experimental (so called anti-gyro-Bohm) scaling is revealed in the low wavenumber range. In this context, the major role played by the ${E\!\times\!B}$ shear in regulating the ion-temperature-gradient turbulence is analyzed in some detail. The competing level of turbulent and neoclassical transport is quantified to shed light on the experimental features of the pedestal profiles at different ion mass, with the particle transport found to be consistent with a higher pedestal top density for increasing isotope masses, and the heat transport shown to match the roughly unaltered observed temperature profiles.

Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations.

In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators—while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources—are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein 7-X stellarator, where the central ion temperature was ‘clamped’ to $T_\textrm i \approx 1.5$ keV regardless of the external heating power. By performing first-principles based simulations, we provide key evidence to understand this effect, namely the inefficient thermal coupling between electrons and ions in a turbulence-dominated regime, which is exacerbated by the large $T_\textrm e/T_\textrm i$ ratios, and show that a more efficient ion heat source, such as direct ion heating, will increase the on-axis ion temperature. This work paves the way towards the use of high-fidelity models for the development of the next generation of stellarators, in which neoclassical and turbulent transport are optimized simultaneously.

We present a gyrokinetic theory of self-generated E × B vortex flows in a magnetic island in a collisionless tokamak plasma with a background vortex flow. We find that the long-term evolution of the self-generated vortex flows can be classified into two regimes by the background vortex flow potential Φ, with an asymptotic criterion given by $e\Phi_\mathrm{cr}/T = \epsilon w/r$ , where T is temperature, ε is the inverse aspect ratio and r is the radial coordinate. We find that the background vortex flow above the criterion significantly weakens the toroidal precession-induced long-term damping and structure change of the self-generated vortex flows. That is, the finite background vortex flow is beneficial to maintain the self-generated vortex flows, favorable to an internal transport barrier formation. Our result indicates that the island boundary region is a prominent location for triggering the transition to an enhanced confinement state of the magnetic island.

Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma β and having increased vertical stability. To understand the confinement properties that might be expected in the conceptual design for a high β ST fusion reactor, a 1 GW ST plasma equilibrium was analysed using local linear gyrokinetics to determine the type of micro-instabilities that arise. Kinetic ballooning modes and micro-tearing modes 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 θ 0 = 0.0. This work identifies the most important micro-instabilities expected to generate turbulent transport in high β 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. [ABSTRACT FROM AUTHOR]

The evidence of a large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. Given the large variety of possible stellarator configurations, in the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, a numerical cross-device comparison is presented, where the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-gradient (ITG) turbulence are obtained. The simulations have been performed for the helias W7-X, the heliotron LHD, the heliac TJ-II and the quasi-axisymmetric stellarator NCSX at the radial position r / a = 0.75. The results show that, although the size of D and V can differ across the four devices, inward convection is found for all of them. For W7-X, TJ-II and NCSX the two coefficients are comparable and the turbulent peaking factor is surprisingly similar. In LHD, appreciably weaker diffusive and convective impurity transport and significantly larger turbulent peaking factor, in comparison with the other three stellarators, are predicted. All this suggests that ITG turbulence, although not strongly, would lead to negative impurity density gradients in stellarators. Then, considering mixed ITG/trapped electron mode (TEM) turbulence for the specific case of W7-X, it has been quantitatively assessed to what degree pellet fueled reduced turbulence scenarios feature reduced turbulent transport of impurities as well. The results for trace iron impurities show that, although their turbulent transport is not entirely suppressed, a significant reduction of the convection and a stronger decrease of the diffusion term are found. Although the diffusion is still above neoclassical levels, the neoclassical convection would gain under such conditions a greater specific weight on the dynamics of impurities in comparison with standard ECRH scenarios without pellet fueling. [ABSTRACT FROM AUTHOR]

We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of potentials. As a benchmark, we perform linear as well as nonlinear simulations of the kinetic Alfvén wave; demonstrating physics in agreement with the analytical theories. [ABSTRACT FROM AUTHOR]

We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe strongly magnetized plasmas. The low-rank approximation is based on a decomposition into variables parallel and perpendicular to the magnetic field, as suggested by the physics of the underlying problem. We show that the resulting scheme exactly recovers the dispersion relation even with rank 1. We then perform a simulation of kinetic shear Alfvén waves and show that using the proposed dynamical low-rank algorithm a drastic reduction (multiple orders of magnitude) in both computational time and memory consumption can be achieved. We also compare the performance of robust first and second-order projector splitting, BUG (also called unconventional), and augmented BUG integrators as well as a FFT-based spectral and Lax–Wendroff discretization. • First dynamical low-rank framework for strongly magnetized plasmas. • Drastic reduction in the memory and computational cost due to a decomposition motivated by the underlying physical problem. • We show that exact dispersion relation is recovered with rank 1. • We provide a comparison of novel robust integrators and two space/time discretization strategies. [ABSTRACT FROM AUTHOR]

COGENT is an Eulerian gyrokinetic code being developed for edge plasma modelling. The code is distinguished by the use of a high‐order finite‐volume (conservative) discretization combined with mapped multi‐block grid technology. Our recent work is focused on the development of a 5D full‐F COGENT version. A numerical algorithm utilizing locally a field‐aligned multi‐block coordinate system is implemented to facilitate simulations of highly anisotropic microturbulence in the presence of a strong magnetic shear. In this approach, the toroidal direction is divided into blocks such that, within each block, the cells are field‐aligned and a non‐matching (non‐conformal) grid interface is allowed at the block boundaries. Here we report on details of the numerical implementation and present preliminary results of verification studies performed for the case of the ion temperature gradient (ITG) instability in a sheared toroidal annulus geometry. [ABSTRACT FROM AUTHOR]

Applying gyrokinetic simulations in theoretical turbulence and transport studies for the plasma edge and scrape‐off layer (SOL) presents significant challenges. To particularly account for steep density and temperature gradients in the SOL, the "full‐f" code PICLS was developed. PICLS is a gyrokinetic particle‐in‐cell (PIC) code, is based on an electrostatic model with a linearized field equation, and uses kinetic electrons. In previously published results, we applied PICLS to the well‐studied 1D parallel transport problem during an edge‐localized mode (ELM) in the SOL without collisions. As an extension to this collision‐less case and in preparation for 3D simulations, in this work, a collisional model will be introduced. The implemented Lenard–Bernstein collision operator and its Langevin discretization will be shown. Conservation properties of the collision operator, as well as a comparison of the collisional and non‐collisional case, will be discussed. [ABSTRACT FROM AUTHOR]