Landau Fluid Model Research Articles

Study of the evolution of density and particle transport during density relaxation phase after pellet fueling on the EAST tokamak

Abstract The impact of pellet injection depth on particle transport characteristics and density profile evolution during the post-pellet density relaxation phase is investigated on the experimental advanced superconducting tokamak. Experiments were conducted under similar background plasma conditions and the results showed that variations in pellet deposition depths led to differences in density profiles despite comparable core fueling efficiencies. By computing the effective particle transport coefficients immediately after the pellet injection, it is found that the differences in density profiles are mainly due to significantly different transport velocities in the inner region of ρ < 0.4. The potential influence of pellets on electrostatic turbulence in this region is investigated using the trapped gyro Landau fluid model and CO 2 laser collective scattering diagnostics. The simulation suggests that the increase in transport coefficients following pellet injection is attributed to the destabilization of lower-k modes rather than the higher-k modes within the diagnostic measurement range.

Tokamak edge-SOL turbulence in H-mode conditions simulated with a global, electromagnetic, transcollisional drift-fluid model

Abstract The design of commercially feasible magnetic confinement fusion reactors strongly relies on the reduced turbulent transport in the plasma edge during operation in the high confinement mode (H-mode). We present first global turbulence simulations of the ASDEX Upgrade tokamak edge and scrape-off layer in ITER baseline H-mode conditions. Reasonable agreement with the experiment is obtained for outboard mid-plane measurements of plasma density, electron and ion temperature, as well as the radial electric field. The radial heat transport is underpredicted by roughly 1/3. These results were obtained with the GRILLIX code implementing a transcollisional, electromagnetic, global drift-fluid plasma model, coupled to diffusive neutrals. The transcollisional extensions include neoclassical corrections for the ion viscosity, as well as either a Landau-fluid or free-streaming limited model for the parallel heat conduction. Electromagnetic fluctuations are found to play a critical role in H-mode conditions. We investigate the structure of the significant E × B flow shear, finding both neoclassical components as well as zonal flows. But unlike in L-mode, geodesic acoustic modes are not observed. The turbulence mode structure is mostly that of drift-Alfvén waves. However, in the upper part of the pedestal, it is very weak and overshadowed by neoclassical transport. At the pedestal foot, on the other hand, we find instead the (electromagnetic) kinetic ballooning mode, most clearly just inside the separatrix. Our results pave the way towards predictive simulations of fusion reactors.

Effect of resonant magnetic perturbation on edge–core turbulence spreading in a tokamak plasma

Turbulence spreading from the edge to the core region of a tokamak with a resonant magnetic perturbation (RMP) is investigated using an electromagnetic Landau-fluid model in a toroidal geometry. As a RMP field with an appropriate amplitude is applied, long-wavelength fluctuations around the resonance surface can be excited due to forced magnetic reconnection. Strong shear flow at the magnetic island separatrix is observed, which can break the radially elongated vortex structures of the turbulent fluctuation. Inward turbulence spreading can be blocked by this shear flow, and the saturation level of turbulence intensity in the core region declines.

Energy transport analysis of NSTX plasmas with the TGLF turbulent and NEO neoclassical transport models

This work presents a study of plasma transport at low aspect ratio on the National Spherical Torus Experiment tokamak, where the turbulent and neoclassical energy fluxes calculated by the quasilinear Trapped Gyro Landau Fluid (TGLF) model and the multi species drift-kinetic Neoclassical solver (NEO) are validated against experimental data. The turbulent energy transport of two plasma discharges, one in the L-mode confinement regime and another in the H-mode regime, is dominated by electrostatic drift-wave instabilities, while the ion heat transport has a significant neoclassical contribution. The data analysis workflow is described in detail to understand how the variations of mapping and fitting of experimental data affect the power balance solution and subsequent flux-matching plasma profile predictions with the TGYRO solver. On average, the predicted plasma profiles are consistent with experimental data. However, the solutions are sensitive to various input parameters, including boundary conditions, and the electron-ion coupling. Linear gyrokinetic stability analysis demonstrates close agreement of the real frequencies of unstable modes between TGLF and CGYRO gyrokinetic simulations, but higher growth rates are predicted by TGLF, especially for the H-mode case. Estimates of the low-k modes’ contributions to the total flux are consistent with linear stability analysis and the E × B suppression of turbulence in TGLF simulations with the SAT1 saturation model, while the SAT2 saturation model over-predicts the low-k modes’ contribution in the H-mode case. Moreover, the results with SAT1 model are consistent with power balance analysis, which indicates only neoclassical ion energy fluxes inside ρ < 0.4 in the L-mode case and ρ⩽0.7 in the H-mode case. The presence of multi-scale turbulence and ion-scale driven zonal flow mixing effects are also observed in TGLF scans of the electron turbulent heat flux over a range of temperature gradients and the electron-ion temperature ratio, which could explain the strong model sensitivity to variations of input parameters.

Global Effects on Drift Wave Microturbulence in Tokamak Plasmas

Microturbulence excited by ion temperature gradient (ITG)-dominant and trapped electron mode (TEM)-dominant instabilities is investigated by employing an extended fluid code (ExFC) based on the so-called Landau fluid model, which includes the trapped electron dynamics. Firstly, the global effect is emphasized through direct comparison of ITG and TEM instability domains based on local and global simulations. The global effect makes differences in both linear instability and nonlinear transport, including the fluxes and the structure of zonal flow. The transitions among ITG, TEM, and ITG & TEM (ITG & TEM represents that ITG and TEM coexist with different wavelengths) instabilities/turbulence depend not only on the three key drive forces (R/L n, R/L Te, R/L Ti) but also on their global (profile) effects. Secondly, a lot of electrostatic linear gyro-fluid simulations are concluded to obtain a distribution of the instability.

Bifurcation of coherent vortex flow in a magnetic island through nonlinear parity instability

The topology of the vortex flow associated with the magnetic island plays a significant role in modulating the turbulent transport near the magnetic island. In this paper, self-consistent nonlinear simulations of multi-scale interactions among large scale tearing mode, vortex flow, and small scale ion temperature-gradient (ITG) mode are numerically investigated based on the five-field Landau-fluid model. We found that the coherent vortex flow in a magnetic island has different parities in the nonlinear quasi-steady state, and this can be described by a theoretical framework—nonlinear parity instability. In the ITG stable case, the structure of the vortex flow bifurcates from tearing parity to twisting parity, which is characterized by modulational parity instability, modeled by a four-wave nonlinear coupling process. In the ITG unstable case, the vortex flow stays in tearing parity without parity bifurcation, and the energy is transferred from the twisting parity modes to the tearing parity modes. The impact of the parity instability on the magnetic island width is discussed as well.

Electromagnetic drift wave instability in tokamak plasmas with strong pedestal gradient

The linear eigenmode characterizations and the nonlinear turbulence energy spreading of the drift waves in a tokamak plasma with strong pedestal gradient are numerically investigated based on an electromagnetic Landau fluid model. By the linear eigenmode analysis, it is found that the dominant instability in the low β regime is the ion-temperature-gradient (ITGc) mode and the electron drift wave instability (eDWI p ) in the core and edge region with strong density gradient, respectively. Multiple eigenstates of the eDWI p with different peak locations in the poloidal direction can be obtained by the eigenvalue problem solver. The dominant one is the high order eDWI p corresponding to the unconventional ballooning mode structure with multiple peaks in the poloidal position, in contrast to the conventional modes that peak at the outboard mid-plane, and has been verified through initial value simulation. In the high β regime, the dominant eigenmodes in the core and edge region are the conventional and unconventional kinetic ballooning modes respectively. In the nonlinear simulation, an inward turbulence spreading phenomenon during the quasi-saturation phase of the edge turbulence is clearly observed. The inward speed of the turbulence energy front in the high β regime is much faster than that in the low β regime. It is interestingly found that the speed of the turbulence energy front increases with the increase of the plasma β in the low β regime, while it is almost unchanged in the high β regime. It is identified that the turbulence spreading in the low and high β regimes are determined by the nonlinear dynamics and the linear toroidal coupling respectively.

MAS: a versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, multiscale analysis for plasma stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in terms of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal magnetohydrodynamic (MHD) model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfvén wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfvén eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear AE, the tunneling damping of toroidal AE, as well as the polarization characteristics of kinetic beta-induced AE and beta-induced Alfvén-acoustic eigenmode being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in the linear regime.

Role of secondary long wavelength fluctuation in nonlinear saturation of the kinetic ballooning mode in tokamak plasmas

Nonlinear saturation dynamics of electromagnetic turbulence and associated transport are investigated using a global simulation based on the Landau-fluid model in the finite β tokamak plasmas. The focus is on the kinetic ballooning mode (KBM), while a comparison to the β stabilized ion temperature gradient mode is carried out. Results show that the KBM turbulence creates relatively weaker zonal flows in finite β plasmas. Zonal current could be formed around the low order rational surfaces, but is too narrow and localized to affect the global transport level. It is found that the KBM turbulence is nonlinearly saturated in two sequential stages. The linear KBM instability is first saturated transiently at a low fluctuation level by weak zonal flows. Afterward, robust, linearly stable long wavelength fluctuations are nonlinearly excited and then interact feedback with primary unstable KBM components through the modulation process. As a result, the KBM is finally saturated with a down-shifted wavenumber spectrum. The suppression of turbulent transport by long wavelength fluctuations is identified as mainly resulting from the reduction of KBM turbulence intensity.

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model. The multi-mode turbulence here is composed of a shorter wavelength electromagnetic (EM) ion temperature gradient (ITG) mode and a Kelvin–Helmholtz (KH) instability with long wavelengths excited by externally imposed small-scale shear flows. For strong shear flow, a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution, which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities. It is identified that the intermittency phenomenon results from the zonal flow dynamics, which is mainly generated by the KH mode and back-reacts on it. It is demonstrated that the odd symmetric components of zonal flow (same symmetry as the external flow) make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first. Afterwards, the ITG intermittency follows due to nonlinear mode coupling. Parametric dependences of the features of the intermittency are elaborated. Finally, associated turbulent heat transport is evaluated.

Simulation prediction of micro-instability transition and associated particle transport in tokamak plasmas

Two reduced simulation approaches are exploited to predict the parametric boundary of dominant instability regime with global effects and the characteristics of corresponding turbulent particle fluxes in tokamak plasmas. One is usual numerical simulation of coexisting ion temperature gradient (ITG) mode and trapped electron mode (TEM) turbulence employing an extended fluid code (ExFC) based on the so-called Landau–Fluid model including the trapped electron dynamics. Here the density gradient (i.e. R/L n ) driven TEM (∇n-TEM) is emphasized. The other one is a surrogate turbulence transport model, taking a neural network (NN) based approach with speeding calculation. It is shown that the turbulent particle flux, particularly their directions depend on the type of micro-instability as ITG and/or TEM. On the other hand, the density gradient may govern the direction of the turbulent particle fluxes in general circumstances. Specifically, in the parameter regime explored here, the ITG and the electron temperature gradient driven TEM (∇T e-TEM) are destabilized for flat density profile, generally causing an inward particle flux, i.e. particle pinch. Contrarily, for steep density profile, the ∇n-TEM or coexisting ITG and TEM turbulence are dominant so that the particle always diffuses outwards. An empirical criterion is obtained to predict the dominant instability and the direction of particle flux for medium density gradients, involving the gradients of both ion and electron temperature as well as the density. These two transport models are applied to analyze the spontaneous excitation of a quasi-coherent mode in the turbulence modulation discharge by MHD magnetic island observed on tokamak HL-2A, clearly showing a dynamic transition from ITG to TEM. Furthermore, the ExFC-NN model can predict and speed up the analysis of the turbulence transport in tokamak experiments.

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework [1] has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.

Local and global properties of energy transfer in models of plasma turbulence

The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov–Maxwell simulations of collisionless plasmas, Hall magnetohydrodynamics and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer. This approach provides information on the structure of energy fluxes, under the assumption that the turbulent cascade transfers most of the energy that is then dissipated at small scales by various kinetic processes in these kinds of plasmas.

Multi-scale multi-mode nonlinear interaction in tokamak plasma turbulence with moderate small-scale shear flow

Effects of moderate small-scale shear flow, e.g., which may be created by the trapped electron mode, on electromagnetic (EM) ion-scale turbulence in tokamak plasmas are numerically investigated via a self-consistent Landau-fluid model. A modeling analysis is carried out in slab geometry to reveal the underlying mechanism of the multi-scale multi-mode nonlinear interaction. Results show that while a Kelvin–Helmholtz (KH) instability with long wavelengths may be excited by the shear flows to dominate the multi-scale EM fluctuation, shorter wavelength ion temperature gradient (ITG) modes experience multiple quasi-steady (QS) stages with enhanced fluctuation level through different driving and saturation mechanisms. One mechanism is the secondary ITG instability due to the decrease in flow stabilization modified by the zonal flow. Meanwhile, the other one is the modulational interaction between the EM ITG and KH modes through the nonlinear mode coupling. Moreover, the synergism of these two mechanisms may sustain the final QS state near the marginal KH instability threshold. Complex linear and nonlinear interactions among multiple modes and external flow, as well as self-generated zonal flow, result in a weak dependence of the final saturation level of the dominant EM ITG mode on the small-scale flow amplitude. The turbulent heat transport is visibly suppressed by weaker shear flow, but is almost not affected by stronger shear flows. The underlying mechanism is elaborated.

An introductory guide to fluid models with anisotropic temperatures. Part 1. CGL description and collisionless fluid hierarchy

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non-Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the fluid model of Chew–Goldberger–Low (CGL) in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the fourth-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the ‘normal’ closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the ‘normal’ closure, and beyond the fourth-order moment, Landau fluid closures are required.

Basic features of the multiscale interaction between tearing modes and slab ion-temperature-gradient modes**Project supported by the National Key R&D Program of China (Grant Nos. 2017YFE0301100 and 2017YFE0300500), the National Natural Science Foundation of China (Grant Nos. 11675038, 11775069, and 11305027), and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT17RC(4)54).

Nonlinear interaction between tearing modes (TM) and slab ion-temperature-gradient (ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumbers become broader during the transition phase from the ITG-dominated stage to TM-dominated stage. Accompanied with the fast growth of the magnetic island, the frequency of TM/ITG with long/short wavelength fluctuations in the electron/ion diamagnetic direction decreases/increases respectively. The decrease of TM frequency is identified to result from the effect of the profile flattening in the vicinity of the magnetic island, while the increase of the frequencies of ITG fluctuations is due to the eigenmode transition of ITG induced by the large scale zonal flow and zonal current related to TM. Roles of zonal current induced by the ITG fluctuations in the instability of TM are also analyzed. Finally, the electromagnetic transport features in the vicinity of the magnetic island are discussed.

Gyrofluid modeling of magnetosphere in feedback instability

Feedback instability occurs in a coupling system of the magnetosphere and the ionosphere, and is a theoretical model explaining spontaneous development of the quiet aurora. In this study, we extend a model of the magnetosphere in the feedback instability to the gyrofluid model. This extension makes it possible to properly discuss kinetic effects, such as the finite Larmor radius effect, the Landau damping, and the mirror force, on the feedback instability in a framework of a fluid model. The derived model is applied to linear stability analysis of the low-frequency feedback instability in the absence of the mirror force. An analytical expression of the parallel electron momentum diffusion coefficient associated with the electron Landau damping is obtained by considering a Landau-fluid closure model. It is found that high-wavenumber modes are strongly affected by the finite ion Larmor radius effect and the electron Landau damping. In particular, a stabilizing effect of the electron Landau damping is dominant and stronger for high-parallel-wavenumber modes. This result indicates that the lowest-parallel-wavenumber mode primarily grows during the spontaneous development of the quiet aurora.

Fluid simulations of plasma turbulence at ion scales: Comparison with Vlasov-Maxwell simulations

Comparisons are presented between a hybrid Vlasov-Maxwell (HVM) simulation of turbulence in a collisionless plasma and fluid reductions. These include Hall-magnetohydrodynamics (HMHD) and Landau fluid (LF) or finite Larmor radius-Landau fluid (FLR-LF) models that retain pressure anisotropy and low-frequency kinetic effects such as Landau damping and, for the last model, finite Larmor radius (FLR) corrections. The problem is considered in two space dimensions, when initial conditions involve moderate-amplitude perturbations of a homogeneous equilibrium plasma subject to an out-of-plane magnetic field. LF turns out to provide an accurate description of the velocity field up to the ion Larmor radius scale, and even to smaller scales for the magnetic field. Compressibility nevertheless appears significantly larger at the sub-ion scales in the fluid models than in the HVM simulation. High frequency kinetic effects, such as cyclotron resonances, not retained by fluid descriptions, could be at the origin of this discrepancy. A significant temperature anisotropy is generated, with a bias towards the perpendicular component, the more intense fluctuations being rather spread out and located in a broad vicinity of current sheets. Non-gyrotropic pressure tensor components are measured and are shown to reach a significant fraction of the total pressure fluctuations, with intense regions closely correlated with current sheets.

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolaï, and Busquet’s [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the helium gas-fill by a factor of ∼2 despite predicting the peak heat flux to within 16%.

Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.