Gyrofluid Model Research Articles

Effect of rotation on negative triangularity plasmas in DIII-D

Abstract At the DIII-D tokamak, plasmas with negative triangularity (NT) have been found to have similar energy confinement times as H-mode plasmas with positive triangularity. These NT plasmas also have a stable edge that inhibits H-mode, lacks dangerous edge transients, and has naturally low impurity confinement. For these reasons, NT plasmas have the potential to be a transformative reactor scenario. To determine the importance of strong co-current neutral beam torque for NT performance at DIII-D, scans of neutral beam torque at constant neutral beam power have been performed. These scans have shown that the energy confinement time for a basic, inductive NT scenario ( q 95 ≈ 2.8 ) decreases by 16% when torque is reduced to reactor levels. This reduction in confinement can be replicated with gyrofluid modeling that isolates the role of E × B shear in the change in transport. In a separate set of discharges with lower plasma current ( q 95 ≈ 4.2 ), no significant correlation between confinement time and rotation was found. Throughout this investigation, excellent MHD stability was observed, even with very low toroidal rotation. Further, low impurity confinement was found at multiple rotation levels. Throughout the campaign, rotation near the edge was counter-current, consistent with the measurement of counter-current intrinsic edge rotation, and these observations agree with NT results from the TCV tokamak.

Gyrofluid simulations of turbulence and reconnection in space plasmas

A Hamiltonian two-field gyrofluid model is used to investigate the dynamics of an electron-ion collisionless plasma subject to a strong ambient magnetic field, within a spectral range extending from the magnetohydrodynamic (MHD) scales to the electron skin depth. This model isolates Alfvén, Kinetic Alfvén and Inertial Kinetic Alfvén waves that play a central role in space plasmas, and extends standard reduced fluid models to broader ranges of the plasma parameters. Recent numerical results are reviewed, including (i) the reconnection-mediated MHD turbulence developing from the collision of counter-propagating Alfvén wave packets, (ii) the specific features of the cascade dynamics in strongly imbalanced turbulence, including a possible link between the existence of a spectral transition range and the presence of co-propagating wave interactions at sub-ion scales, for which new simulations are reported, (iii) the influence of the ion-to-electron temperature ratio in two-dimensional collisionless magnetic reconnection. The role of electron finite Larmor radius corrections is pointed out and the extension of the present model to a four-field gyrofluid model is discussed. Such an extended model accurately describes electron finite Larmor radius effects at small or moderate values of the electron beta parameter, and also retains the coupling to slow magnetosonic waves.

Effects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence

A full-F, isothermal, electromagnetic, gyro-fluid model is used to simulate plasma turbulence in a COMPASS-sized, diverted tokamak. A parameter scan covering three orders of magnitude of plasma resistivity and two values for the ion to electron temperature ratio with otherwise fixed parameters is setup and analysed. Two transport regimes for high and low plasma resistivities are revealed. Beyond a critical resistivity the mass and energy confinement reduces with increasing resistivity. Further, for high plasma resistivity the direction of parallel acceleration is swapped compared to low resistivity.Three-dimensional visualisations using ray tracing techniques are displayed and discussed. The field-alignment of turbulent fluctuations in density and parallel current becomes evident. Relative density fluctuation amplitudes increase from below 1% in the core to 15% in the edge and up to 40% in the scrape-off layer.Finally, the integration of exact conservation laws over the closed field line region allows for an identification of numerical errors within the simulations. The electron force balance and energy conservation show relative errors on the order of 10−3 while the particle conservation and ion momentum balance show errors on the order of 10−2.All simulations are performed with a new version of the FELTOR code, which is fully parallelized on GPUs. Each simulation covers a couple of milliseconds of turbulence.

Influence of ion-to-electron temperature ratio on tearing instability and resulting subion-scale turbulence in a low- β e collisionless plasma

A two-field gyrofluid model including ion finite Larmor radius (FLR) corrections, magnetic fluctuations along the ambient field, and electron inertia is used to study two-dimensional reconnection in a low βe collisionless plasma, in a plane perpendicular to the ambient field. Both moderate and large values of the ion-to-electron temperature ratio τ are considered. The linear growth rate of the tearing instability is computed for various values of τ, confirming the convergence to reduced electron magnetohydrodynamics predictions in the large τ limit. Comparisons with analytical estimates in several limit cases are also presented. The nonlinear dynamics leads to a fully developed turbulent regime that appears to be sensitive to the value of the parameter τ. For τ = 100, strong large-scale velocity shears trigger Kelvin–Helmholtz instability, leading to the propagation of the turbulence through the separatrices, together with the formation of eddies of size of the order of the electron skin depth. In the τ = 1 regime, the vortices are significantly smaller and their accurate description requires that electron FLR effects be taken into account.

Spectrum of kinetic-Alfvén-wave turbulence: intermittency or tearing mediation?

ABSTRACT We investigate the spectral properties of the electromagnetic fluctuations of sub-ion scale turbulence in weakly collisional, low-beta plasmas using a two-field isothermal gyrofluid model. The numerical results strongly support a description of the turbulence as a critically balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by previous studies to include intermittency effects. The measured universal index of the energy spectra from systems with different flux-unfreezing mechanisms excludes the role of tearing mediation in determining the spectra. The fluctuations remain isotropic in the plane perpendicular to the strong background magnetic fields as they cascade to smaller scales, which explains the absence of tearing mediation. The calculation of high-order, multipoint structure functions of magnetic fluctuations suggests that the intermittent structures have a quasi-2D, sheet-type morphology. These results are useful for explaining recent observations of the spectrum and structure of magnetic and density fluctuations in the solar wind at sub-proton scales, and are relevant for modelling the energy dissipation in a broad range of astrophysical systems.

Investigation of the collisionless plasmoid instability based on gyrofluid and gyrokinetic integrated approach

In this work, the development of two-dimensional current sheets with respect to tearing modes, in collisionless plasmas with a strong guide field, is analysed. During their nonlinear evolution, these thin current sheets can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. We carry out a detailed study of the effect of a finite $\beta _e$ , which also implies finite electron Larmor radius effects, on the collisionless plasmoid instability. This study is conducted through a comparison of gyrofluid and gyrokinetic simulations. The comparison shows in general a good capability of the gyrofluid models in predicting the plasmoid instability observed with gyrokinetic simulations. We show that the effects of $\beta _e$ promotes the plasmoid growth. The effect of the closure applied during the derivation of the gyrofluid model is also studied through the comparison among the variations of the different contributions to the total energy.

Kinetic effects on geodesic acoustic modes and Stringer spin-up driven by a poloidally asymmetric particle source

The impact of the poloidally inhomogeneous particle source on the onset of Stringer spin-up (SSU) and geodesic acoustic mode (GAM) is investigated. Using a gyrofluid model with Hammet–Perkins closure, it was found that Landau damping stabilizes both waves and subsequently makes a threshold. To capture the full effects of Landau damping, a gyrokinetic model is adopted and results are compared with those from the gyrofluid model. Both models predicted the same value of the threshold for SSU, while for the case of GAM, the gyrofluid model overestimates the threshold value. Considering maximal throughput of the ITER pellet fueling system, the source intensity is calculated at a similar or slightly lower level compared to the source threshold for SSU.

Global gyrofluid simulations of turbulence in tokamak plasmas

We develop a tokamak plasma turbulence simulation code based on a fluid model using the BOUT++ framework. The model corresponds to a global extension of the local gyrofluid model (Beer and Hammett, 1996 [11]), where external sources and neoclassical equilibrium flows are included but some higher-order kinetic effect terms are ignored for the global nonlinear simulation. Hyper-viscous damping terms are introduced to compensate for the stabilizing effect of the missing kinetic terms. With an appropriate hyper-viscosity, we obtain reasonable linear and nonlinear results on ion temperature gradient modes compared to global gyrokinetic simulations. We perform global flux-driven simulations with self-consistently evolving profiles with external heat sources/sinks. A spectral analysis of heat flux in flux-driven turbulence exhibits a broad 1/f (f is the frequency) spectrum observed in gyrokinetic simulations, indicating the prevalence of self-organized criticality-like heat avalanches. We also investigate the effect of an externally imposed vorticity source on turbulence suppression and transport barrier formation. It is shown that internal transport barrier can form even for a monotonic safety factor profile when a sufficiently strong vorticity source is applied.

Non-trace full-F gyro-fluid interchange impurity advection

A full-F isothermal gyro-fluid model and code (which is based on the full distribution function F compared to only small fluctuations) is extended to handle self-consistent coupling of multiple quasi-neutral ion species via the polarisation equation in the long wavelength approximation. The numerical model is used to determine two-dimensional interchange driven ‘blob’ transport in a plasma with intrinsic impurity content for a range of impurity parameters. With the same model, the self-consistent advective interaction of a main plasma species blob with a non-trace impurity cloud is studied. For homogeneous impurity distributions an increased effective mass reduces blob transport, whereas it is found that localised impurity clouds can lead either to acceleration or slowing down of blob propagation depending on the alignment of the impurity density gradient during the acceleration phase of the main ion species blob.

Analysis of the ECH effect on EPM/AE stability in Heliotron J plasma using a Landau closure model

The aim of the present study is to analyze the effect of the electron cyclotron heating (ECH) on the linear stability of Alfvén eigenmodes (AEs) and energetic particle modes (EPMs) triggered by energetic ions in Heliotron J plasma. The analysis is performed using the FAR3d code that solves a reduced MHD model to describe the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The simulations reproduce the AE/EPM stability trends observed in the experiments as the electron temperature (T e ) increases, modifying the thermal plasma β, EP β and EP slowing-down time. Particularly, the EPM and Global AE are stabilized in the low-bumpiness (LB) configuration due to an enhancement of the continuum, finite Larmor radius and e-i Landau damping effects as the thermal β increases. On the other hand, a larger ECH injection power cannot stabilize the AE/EPM in medium-bumpiness and high-bumpiness (HB) configurations because the damping effects are weaker compared to the LB case, unable to balance the further destabilization induced by an enhanced EP resonance as the EP slowing-down time and EP β increases with T e .

Long-wavelength closures for collisional and neutral interaction terms in gyro-fluid models

A collisional gyro-fluid model is presented. The goal of the model is edge and scrape-off layer turbulence. The emphasize in the model derivation heavily lies on ”implementability” with today’s numerical methods. This translates to an avoidance of infinite sums, strongly coupled equations in time and intricate elliptic operator functions. The resulting model contains the four moments density, parallel momentum, perpendicular pressure and parallel energy and is closed by a polarisation equation and parallel Ampere law. The central ingredient is a collisional long-wavelength closure that relies on a drift-fluid gyro-fluid correspondence principle. In this way the extensive literature on fluid collisions can be incorporated into the model including sources, plasma-neutral interactions and scattering collisions. Even though this disregards the characteristic finite Larmor radius terms in the collisional terms the resulting model is at least as accurate as the corresponding drift-fluid model in these terms. Furthermore, the model does enjoy the benefits of an underlying variational principle in an energy-momentum theorem and an inherent symmetry in moment equations with regards to multiple ion species. Consistent particle drifts as well as finite Larmor radius corrections and high amplitude effects in the advection and polarization terms are further characteristics of the model. Extensions and improvements like short-wavelength expressions, a trans-collisional closure scheme for the low-collisionality regime or zeroth order potential must be added at a later stage.

Simulation of the TAEs’ saturation phase in the Large Helical Device: MHD burst

The aim of the present study is to analyze the saturation regime of the toroidal Alfven eigenmodes (TAE) in the Large Helical Device plasma, particularly the MHD burst. The linear and nonlinear evolution of the TAEs are simulated by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The linear simulations indicate the overlapping of 1/2 − 1/1, 2/3–2/4 and 3/5–3/6 TAEs in the inner-middle plasma region and frequency range of 45–75 kHz, triggered by EPs with an energy of T f = 45 keV and EP β = 0.022. The nonlinear simulations show that 2/3–2/4 and 3/4–3/5 TAEs are further destabilized due to the energy transfer from the 1/1–1/2 TAE, leading to broad TAE radial overlapping and triggering of the MHD burst. The energy of the 1/1–1/2 TAE is also nonlinearly transferred to the thermal plasma destabilizing the 0/0 and 0/1 modes, inducing the generation of shear flows and zonal currents, as well as large deformations in the thermal pressure and EP density radial profiles. The nonlinear simulation reproduces the same succession of instabilities and the same frequency range with respect to the experiment. The instability propagates outward during the bursting phase, showing a large decrease of the EP density profile between the middle-outer plasma, indicating the loss of part of the EP population that explains the decrease in the plasma heating efficiency observed during the MHD burst.

A gyro-fluid model of global geodesic acoustic modes supported by finite ion Larmor radius

A theory of global geodesic acoustic modes with short wavelengths based on the framework of an electrostatic gyro-fluid has been developed, in which the more thorough sorts of finite-ion-Larmor-radius effects are encompassed than in the two-fluid model (Wang et al 2021 Nucl. Fusion 61 106024), while the radial differential equation of the eigenmodes still comes up in a compact and analytically tractable form. By solving the corresponding boundary value problem numerically with typical equilibrium profiles, a multitude of global geodesic acoustic modes with quantized eigen-frequencies have been found. In particular, as the consequence of the plasma model improvement, we have obtained multiple edge-localized global geodesic acoustic modes with the features resembling those observed experimentally.

Understanding the core confinement in DIII-D super-H experiments by transport modeling

The DIII-D super-H (SH) scenario, which is characterized by a significantly higher pedestal pressure compared to standard high confinement mode (H mode) plasmas, typically exhibits two phases in its temporal dynamics. The early hot ion (SH–HI) phase has higher core ion temperatures and normalized confinement factor (H 98(y,2) ∼ 2) than the later ‘standard’ SH phase, which has similar pedestal pressure characteristics to the SH–HI phase but a lower confinement factor (H 98(y,2) ∼ 1.2) as well as lower pedestal T i/T e ratio. However, beyond the pedestal differences, it is also observed that in the core plasma T i is more peaked and has a significantly larger normalized gradient scale length a/L Ti in the SH–HI phase than in the SH phase. This paper identifies the physics responsible for the different core profiles via gyrokinetic and gyrofluid modeling. It is found that the ion temperature gradient (ITG) mode dominates the core transport for both phases. Absent flow shear effects, the ITG critical gradient (a/L Ti,crit) is shown to be far smaller in the SH–HI phase than the SH phase. The lower a/L Ti,crit in the SH–HI phase is shown to be mainly induced by the hollow carbon (impurity) density profile, which is strongly destabilizing relative to the nearly flat carbon density profile in the SH phase. Differences in the T i/T e ratio between these phases are found to have a minor impact. However, the significantly stronger flow shearing in the SH–HI phase relative to the SH phase enables the achievement of higher core a/L Ti values and is therefore mainly responsible for the higher core T i values observed in the early SH–HI phase. Predictive transport modeling shows that the confinement in the lower-rotation SH phase could be elevated significantly if a peaked impurity density profile can be achieved, and potential applications to the performance improvement of future reactors are discussed.

Direct kinetic Alfvén wave energy cascade in the presence of imbalance

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections and parallel magnetic field fluctuations is used to study direct turbulent cascades from the magnetohydrodynamic to the sub-ion scales. For moderate energy imbalance and weak enough magnetic fluctuations, the spectrum of the transverse magnetic field and that of the most energetic wave display a steep transition zone near the ion scale, while the parallel transfer (and thus the parallel dissipation) remains weak. In this regime, the perpendicular flux of generalized cross-helicity displays a significant decay past the ion scale, while the perpendicular energy flux remains almost constant. A phenomenological model suggests that the interactions between co-propagative waves present at the sub-ion scales can play a central role in the development of a transition zone in the presence of a helicity barrier.

Conservation of currents in reduced full-F electromagnetic kinetic and fluid models

In this paper, we present an analysis of the conservation of currents in a full-F electromagnetic gyro-kinetic model in the long-wavelength limit. This equation corresponds to what is usually called the ‘vorticity equation’, which is not strictly correct as it cannot be formulated as the curl of a velocity equation. In the paper, we will therefore use the term ‘current conservation equation’ instead. Our results are relevant to reduced plasma descriptions like gyro-kinetic, drift-kinetic, gyro-fluid and drift-fluid models for tokamaks and stellarators. The equation describes the change of the polarization charge density (often called ‘vorticity’) in terms of the polarization stress due to the flow, external sources and three currents: the parallel current, the curvature current and a current related to the magnetic field fluctuations. We compare this equation with previous drift- and gyro-fluid equations and find general agreement, except in the vorticity source terms where previous drift-fluid models fail to capture the heating and density sources. We discuss the role of currents in the dynamics of diamagnetic and flow shear. The possible connection between these currents with phenomena observed in experiments that influence the radial electric field in the edge of tokamak plasmas, like resonant magnetic perturbations, and different magnetic field configurations and shapes, is presented.

Deconvolving the roles of E × B shear and pedestal structure in the energy confinement quality of super H-mode experiments

Analysis of ‘super H-mode’ experiments on DIII-D has put forward that high plasma toroidal rotation, not high pedestal, plays the essential role in achieving energy confinement quality H 98y2 ≫ 1 (Ding et al 2020 Nucl. Fusion 60 034001). Recently, super H-mode experiments with variable input torque have confirmed that high rotation shear discharges have very high levels of H 98y2 (>1.5), independent of the pedestal height, and that high pedestal discharges with low rotation shear have levels of H 98y2 only slightly above 1 (⩽1.2). Although some increase in stored energy with higher pedestal occurs, the energy confinement quality mainly depends on the toroidal rotation shear, which varies according to different levels of injected neutral beam torque per particle. Quasi-linear gyrofluid modeling achieves a good match of the experiment when including the E × B shear; without including plasma rotation, the modeling predicts a confinement quality consistent with the empirical observation of H 98y2 ∼ 1.2 at low rotation. Nonlinear gyrokinetic transport modeling shows that the effect of E × B turbulence stabilization is far larger than other mechanisms, such as the so-called hot-ion stabilization (T i/T e) effect. Consistent with these experimental and modeling results are previous simulations of the ITER baseline scenario using a super H-mode pedestal solution (Solomon et al 2016 Phys. Plasmas 23 056105), which showed the potential to exceed the Q = 10 target if the pedestal density could be increased above the Greenwald limit. A close look at these simulations reveals that the predicted energy confinement quality is below 1 even at the highest pedestal pressure. The improvement in Q at higher pedestal density is due to the improved fusion power generation at the higher core density associated with higher pedestal density, not to an improved energy confinement quality.

Gyrofluid analysis of electron β e effects on collisionless reconnection

The linear and nonlinear evolutions of the tearing instability in a collisionless plasma with a strong guide field are analysed on the basis of a two-field Hamiltonian gyrofluid model. The model is valid for a low ion temperature and a finite $\beta _e$ . The finite $\beta _e$ effect implies a magnetic perturbation along the guide field direction, and electron finite Larmor radius effects. A Hamiltonian derivation of the model is presented. A new dispersion relation of the tearing instability is derived for the case $\beta _e=0$ and tested against numerical simulations. For $\beta _e \ll 1$ the equilibrium electron temperature is seen to enhance the linear growth rate, whereas we observe a stabilizing role when electron finite Larmor radius effects become more relevant. In the nonlinear phase, stall phases and faster than exponential phases are observed, similarly to what occurs in the presence of ion finite Larmor radius effects. Energy transfers are analysed and the conservation laws associated with the Casimir invariants of the model are also discussed. Numerical simulations seem to indicate that finite $\beta _e$ effects do not produce qualitative modifications in the structures of the Lagrangian invariants associated with Casimirs of the model.

Theoretical analysis of the saturation phase of the 1/1 energetic-ion-driven resistive interchange mode

The aim of the present study is to analyze the saturation regime of the energetic-ion-driven resistive interchange mode (EIC) in the LHD plasma. A set of nonlinear simulations are performed by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The hellically trapped EP component is introduced through a modification of the averaged drift velocity operator to include their precessional drift. The nonlinear simulation results show similar 1/1 EIC saturation phases with respect to the experimental observations, reproducing the enhancement of the n/m = 1/1 resistive interchange modes (RIC) amplitude and width as the EP β increases, the EP β threshold for the 1/1 EIC excitation, the further destabilization of the 1/1 EIC as the population of the helically trapped EP increases and the triggering of burst events. The frequency of the 1/1 EIC calculated during the burst event is 9.4 kHz and the 2/2 and 3/3 overtones are destabilized, consistent with the frequency range and the complex mode structure measured in the experiment. In addition, the simulation shows the inward propagation of the 1/1 EIC due to the nonlinear destabilization of the 3/4 and 2/3 energetic particle modes, leading to the partial overlapping between resonances during the burst event. Finally, the analysis of the 1/1 EIC stabilization phase shows the excitation of the 1/1 RIC as soon as the flattening induced by the 1/1 EIC in the pressure profile vanishes, leading to the retrieval of the pressure gradient at the plasma periphery and the overcoming of the RIC stability limit.

Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport

A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρ tor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρ or = 0.4 where the fast ion population and normalized plasma pressure β = 2μ 0 nT/B 2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρ tor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.