Magnetic Flutter Research Articles

Theoretical and global simulation analysis of collisional microtearing modes

Microtearing modes (MTMs) are suggested as a candidate for anomalous thermal transport in tokamak H-mode discharges. This study investigates MTMs in tokamak plasmas, employing simulations in the BOUT++ framework. It simplifies and linearizes the governing equations in detailed linear simulations. The study meticulously evaluates various conductivity models under diverse plasma conditions and collision regimes. The research thoroughly assesses different conductivity models across a range of plasma conditions and collision regimes. A unified dispersion relation that includes both MTM and Drift-Alfvén Wave (DAW) instabilities is derived, showing that DAW and MTM instabilities occur at varying distances from the rational surface. Specifically, MTMs become unstable near the rational surface but stabilize farther away, while drift-Alfvén instability appears farther from the rational surface. The study also re-derives MTM dispersion relations using Ohm's law and the vorticity equation, providing a thorough analysis of electromagnetic and electrostatic interactions in tokamaks. Global simulations demonstrate an inverse correlation between MTM growth rates and collisionality, and a direct correlation with temperature gradients. The nonalignment of the rational surface with the peak ω*e stabilizes the MTMs. Nonlinear simulations highlight electron temperature relaxation as the primary saturation mechanism for MTMs, with magnetic flutter identified as the dominant mode of electron thermal transport.

Magnetic flutter effect on validated edge turbulence simulations

Small magnetic fluctuations ( B1/B0∼10−4 ) are intrinsically present in a magnetic confinement plasma due to turbulent currents. While the perpendicular transport of particles and heat is typically dominated by fluctuations of the electric field, the parallel stream of plasma is affected by fluttering magnetic field lines. In particular through electrons, this indirectly impacts the turbulence dynamics. Even in low beta conditions, we find that E × B turbulent transport can be reduced by more than a factor 2 when magnetic flutter is included in our validated edge turbulence simulations of L-mode ASDEX Upgrade. The primary reason for this is the stabilization of drift-Alfvén-waves, which reduces the phase shifts of density and temperature fluctuations with respect to potential fluctuations. This stabilization can be qualitatively explained by linear analytical theory and appreciably reinforced by the flutter nonlinearity. As a secondary effect, the steeper temperature gradients and thus higher η i increase the impact of the ion-temperature-gradient mode on overall turbulent transport. With increasing beta, the stabilizing effect on E × B turbulence increases, balancing the destabilization by induction, until direct electromagnetic perpendicular transport is triggered. We conclude that including flutter is crucial for predictive edge turbulence simulations.

Landau-fluid simulations of edge-SOL turbulence with GRILLIX

The Landau-fluid closure for parallel heat fluxes is implemented in the edge turbulence fluid code GRILLIX, replacing the previously used collisional Braginskii closure (with limiters). This extends the validity of the model toward lower collisionality, introduces non-local effects, and leads to a more realistic and self-consistent limiting of heat fluxes. Turbulence simulations comparing the Landau-fluid with the Braginskii closure in realistic divertor geometry are carried out. Clear differences between the simulations are observed, most pronounced a spurious up-down ion temperature asymmetry emerges for a strongly limited Braginskii case. For the Landau-fluid case, we demonstrate the presence and relevance of non-local heat fluxes in full-scale turbulence simulations and show that this behavior could only hardly be reproduced with simple flux-limited models. The implementation of the Landau-fluid closure within the flux-coordinate independent approach employed by GRILLIX results in a set of 3D elliptic problems, where magnetic flutter can be incorporated naturally. On reusing the existing solver in GRILLIX, only a moderate additional computational effort is necessary for the higher fidelity Landau-fluid closure.

Nonlinear microtearing modes in MAST and their stochastic layer formation

First nonlinear gyrokinetic simulations of microtearing modes in the core of a MAST case are performed on two surfaces of the high-collisionality discharge used in Valovič et al (2011 Nucl. Fusion 51 073045) to obtain the favorable energy confinement scaling with collisionality, . On the considered surfaces microtearing modes dominate linearly at binormal length scales of the order of the ion Larmor radius. While the effect of electron collision frequency is moderate in linear simulations, a strong dependence on this parameter is found in nonlinear simulations at , where r and a are the surface and tokamak minor radius, respectively. The dynamics of magnetic islands generated by microtearing modes is analysed, showing that the radial extent of the stochastic region caused by islands overlapping plays an important role in determining the saturation level of the microtearing mode driven heat flux. Local nonlinear gyrokinetic simulations show that the microtearing mode driven heat flux, , is largely dominated by magnetic flutter and depends strongly on the magnetic shear, . Comparing two surfaces, and , reveals that is negligible at (), with the electron temperature gradient (ETG) driven heat flux, , comparable to the experimental electron heat flux, , while is significantly larger and comparable to and at (). Microtearing modes cause more experimentally significant transport in higher regions and may influence (together with ETG modes) the observed scaling of energy confinement time with collisionality (Valovič et al 2011 Nucl. Fusion 51 073045).

Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal-quench phase of tokamak disruptions, are numerically investigated with BOUT++’s flux-driven six-field electromagnetic turbulence model. Here, transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens the core temperature profile. Interesting features, such as surging of divertor heat load (up to 50 times) and broadening of heat-flux width (up to four times) on the outer-divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes in divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely, the E × B turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. First, an elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via the E × B convection, which causes the initial divertor heat-load burst, but it also induces amplified magnetic fluctuation . Once themagnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, reaches to 10−4 level that completely breaks magnetic flux surfaces such that stochastic field lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat-flux width broadening.

A comprehensive view on real-time magnetic resonance-guided flutter ablation image planes from an electrophysiological perspective.

A comprehensive view on real-time magnetic resonance-guided flutter ablation image planes from an electrophysiological perspective.

The ‘SXR—Pit’ paradox as an indicator of electron transport in tokamaks

A phenomenon is analyzed, which is observed at some laboratory-scale tokamaks and seems to be unexplained: a strong drop in the soft x-ray radiation (SXR) after it passed through the ‘thick’ Be foils (the pit in the SXR spectrum). This phenomenon becomes more pronounced as the foil thickness increases and the plasma electron density decreases. The explanation for this phenomenon is proposed, which involves the assumption that the Maxwellian electron velocity distribution becomes ‘depleted’ in the range of velocities that are 3–5 times higher than the thermal one. The anomalous electron heat transport along the weakly perturbed toroidal magnetic field of the tokamak (the ‘magnetic flutter’ model) seems to be the most probable reason for this depletion. Thus, the ‘SXR—Pit’ can be a new tool for studying the physical nature of the anomalous electron transport in tokamaks.

Turbulent transport driven by kinetic ballooning modes in the inner core of JET hybrid H-modes

Turbulent transport in the inner core of the high-β JET hybrid discharge 75225 is investigated extensively through linear and non-linear gyro-kinetic (GK) simulations using the GK code GKW in the local approximation limit. Compared to previous studies (Citrin et al 2015 Plasma Phys. Control. Fusion 57 014032; Garcia et al 2015 Nucl. Fusion 55 053007), the analysis has been extended towards the magnetic axis, ρ < 0.3, where the turbulence characteristics remain an open question. Understanding turbulent transport in this region is crucial to predict core profile peaking that in turn will impact the fusion reactions and the tungsten neoclassical transport, in present devices as well as in ITER. At ρ = 0.15, a linear stability analysis indicates that kinetic ballooning modes (KBMs) dominate, with an extended mode structure in ballooning space due to the low magnetic shear. The sensitivity of KBM stability to main plasma parameters is investigated. In the non-linear regime, the turbulence induced by these KBMs drives a significant ion and electron heat flux. Standard quasi-linear (QL) models are compared to the non-linear results. The standard reduced QL models work well for the E × B fluxes, but fail to capture magnetic flutter contribution to the electron heat flux induced by the non-linear excitation of low k θ ρ i micro-tearing modes that are linearly stable. An extension of the QL models is proposed allowing better capturing the magnetic flutter flux.

Quasilinear modeling of heat flux from microtearing turbulence

Microtearing (MT) turbulence affects plasma confinement and profile evolution in many different magnetic-confinement scenarios, ranging from tokamak core plasmas to the H-mode pedestal and from spherical tokamaks to reversed-field pinches. Thus, an urgent need exists to design and test reduced models of MT turbulence and transport. Here, a heuristic quasilinear model is composed and verified by comparing its predictions against nonlinear MT simulations. It is found to yield good predictions of magnetic flutter transport as key parameters are varied: the collision frequency, the electron temperature gradient, and the normalized plasma pressure.

Impact of Sheath Boundary Conditions and Magnetic Flutter on Evolution and Distribution of Transient Particle and Heat Fluxes in the Edge-Localized Mode Burst by Experimental Advanced Superconducting Tokamak Simulation**Supported by the National Key R&D Program of China under Grant Nos 2017YFE0301100, 2017YFE0301101, 2017YFE0301104 and 2014GB106001, the National Natural Science Foundation of China under Grant Nos 11275047, 11675217, 11505236 and 11405215,

To study the evolution and distribution of the transient particle and heat fluxes during the edge-localized modes (ELMs) burst on the experimental advanced superconducting tokamak (EAST), the BOUT++ six-field two-fluid model with sheath boundary conditions (SBCs) and magnetic flutter terms in the parallel thermal conduction is used to simulate the evolution of the profiles and growing process of the fluxes at divertor targets. Although SBCs hardly play a role in the linear phase, in the nonlinear phase both SBCs and magnetic flutter can change the dominant toroidal mode. SBCs are able to broaden the frequency distribution of the turbulence. The magnetic flutter increases the ELM size from 2.8% to 8.4%, and it doubles the amplitudes of the radial heat and particle transport coefficients at outer midplane (OMP), at around 1.0m2s−1. It is then able to increase the particle and heat flux at the divertor targets and to broaden the radial distribution of the parallel heat flux towards the targets.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Suppression of Ion-Scale Microtearing Modes by Electron-Scale Turbulence via Cross-Scale Nonlinear Interactions in Tokamak Plasmas

Gyrokinetic turbulence simulations are applied for the first time to the cross-scale interactions of microtearing modes (MTMs) and electron-temperature-gradient (ETG) modes. The investigation of the fluctuation response in a multiscale simulation including both types of instabilities indicates that MTMs are suppressed by ETG turbulence. A detailed analysis of nonlinear mode coupling reveals that radially localized current-sheet structures of MTMs are strongly distorted by fine-scale E×B flows of ETG turbulence. Consequently, electron heat transport caused by the magnetic flutter of MTMs is significantly reduced and ETG turbulence dominates electron heat transport.

Nonlinear fluid simulation of particle and heat fluxes during burst of ELMs on DIII-D with BOUT++ code

In order to study the distribution and evolution of the transient particle and heat fluxes during edge-localized mode (ELM) bursts, a BOUT++ six-field two-fluid model based on the Braginskii equations with non-ideal physics effects is used to simulate pedestal collapse in divertor geometry. The profiles from the DIII-D H-mode discharge #144382 with fast target heat flux measurements are used as the initial conditions for the simulations. A flux-limited parallel thermal conduction is used with three values of the flux-limiting coefficient , free streaming model with , sheath-limit with , and one value in between. The studies show that a 20 times increase in leads to ∼6 times increase in the heat flux amplitude to both the inner and outer targets, and the widths of the fluxes are also expanded. The sheath-limit model of flux-limiting coefficient is found to be the most appropriate one, which shows ELM sizes close to the measurements. The evolution of the density profile during the burst of ELMs of DIII-D discharge #144382 is simulated, and the collapse in width and depth of are reproduced at different time steps. The growing process of the profiles for the heat flux at divertor targets during the burst of ELMs measured by IRTV (infrared television) is also reproduced by this model. The widths of heat fluxes towards targets are a little narrower, and the peak amplitudes are twice the measurements possibly due to the lack of a model of divertor radiation which can effectively reduce the heat fluxes. The magnetic flutter combined with parallel thermal conduction is found to be able to increase the total heat loss by around 33% since the magnetic flutter terms provide the additional conductive heat transport in the radial direction. The heat flux profile at both the inner and outer targets is obviously broadened by magnetic flutter. The lobe structures near the X-point at LFS are both broadened and elongated due to the magnetic flutter.

Convective radial energy flux due to resonant magnetic perturbations and magnetic curvature at the tokamak plasma edge

With the resonant magnetic perturbations (RMPs) consolidating as an important tool to control the transport barrier relaxation, the mechanism on how they work is still a subject to be clearly understood. In this work, we investigate the equilibrium states in the presence of RMPs for a reduced MHD model using 3D electromagnetic fluid numerical code with a single harmonic RMP (single magnetic island chain) and multiple harmonics RMPs in cylindrical and toroidal geometry. Two different equilibrium states were found in the presence of the RMPs with different characteristics for each of the geometries used. For the cylindrical geometry in the presence of a single RMP, the equilibrium state is characterized by a strong convective radial thermal flux and the generation of a mean poloidal velocity shear. In contrast, for toroidal geometry, the thermal flux is dominated by the magnetic flutter. For multiple RMPs, the high amplitude of the convective flux and poloidal rotation are basically the same in cylindrical geometry, but in toroidal geometry the convective thermal flux and the poloidal rotation appear only with the islands overlapping of the linear coupling between neighbouring poloidal wavenumbers m, m – 1, and m + 1.

Pedestal Structure without and with 3D Fields

AbstractAchieving high pedestal pressures in H(high)‐mode plasmas confined in tokamaks is critical for obtaining fusion burning plasmas in ITER. Recent characterizations of quasi‐equilibrium plasma parameter profiles in low collisionality H‐mode pedestals in the DIII‐D tokamak are briefly summarized. Critical plasma transport properties (large radial electron heat flow, density pinch) that establish the transport barrier structure of the pedestal profiles are identified. The paleoclassical transport model, which naturally includes a density pinch, is shown to provide the minimum electron heat and density transport in the pedestal. Microinstabilities can provide additional plasma transport within and especially at the top of pedestals. Macroscopic peeling‐ballooning (P‐B) instabilities cause periodic edge localized modes (ELMs) that limit the temporal and spatial growth of the pedestal initially and between ELMs. Externally imposed 3D resonant magnetic perturbations (RMPs) in the pedestal have been used to stabilize P‐B modes and suppress ELMs. A magnetic flutter model of plasma transport induced by the 3D RMPs has been developed for low collisionality DIII‐D pedestals. Comparisons of it with data on ELM suppression by RMPs indicate it can provide a “diffusivity hill” at the pedestal top that can impede pedestal growth and thereby stabilize P‐B modes and suppress ELMs. Finally, transport equations for plasma density, electron and ion pressures and, most importantly, the plasma toroidal rotation frequency (and hence, via radial force balance, the radial electric field) in the presence of plasma transport due to collisional, paleoclassical, microturbulence‐induced and 3D field effects are presented. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The effect of magnetic flutter on residual flow

The hypothesis that stochastic magnetic fields disrupt zonal flows associated with ion temperature gradient turbulence saturation is investigated analytically with a residual flow calculation in the presence of magnetic flutter. The calculation starts from the time-asymptotic zero-beta residual flow of Rosenbluth and Hinton [Phys. Rev. Lett. 80, 724 (1998)] with the sudden application of an externally imposed, fixed magnetic field perturbation. The short-time electron response from radial charge loss due to magnetic flutter is calculated from the appropriate gyrokinetic equation. The potential evolution has quadratic behavior, with a zero crossing at finite time. The crossing time and its parametric dependencies are compared with numerical results from a gyrokinetic simulation of residual flow in the presence of magnetic flutter. The numerical and analytical results are in good agreement and support the hypothesis that the high-beta runaway of numerical simulations is a result of the disabling of zonal flows by finite-beta charge losses associated with magnetic flutter.

Progress in simulating turbulent electron thermal transport in NSTX

Nonlinear simulations based on multiple NSTX discharge scenarios have progressed to help differentiate unique instability mechanisms and to validate with experimental turbulence and transport data. First nonlinear gyrokinetic simulations of microtearing turbulence in a high-beta NSTX H-mode discharge predict experimental levels of electron thermal transport that are dominated by magnetic flutter and increase with collisionality, roughly consistent with energy confinement times in dimensionless collisionality scaling experiments. Electron temperature gradient (ETG) simulations predict significant electron thermal transport in some low- and high-beta discharges when ion scales are suppressed by E × B shear. Although the predicted transport in H-modes is insensitive to variation in collisionality (inconsistent with confinement scaling), it is sensitive to variations in other parameters, particularly density gradient stabilization. In reversed shear L-mode discharges that exhibit electron internal transport barriers, ETG transport has also been shown to be suppressed nonlinearly by strong negative magnetic shear, s ≪ 0. In many high-beta plasmas, instabilities which exhibit a stiff beta dependence characteristic of kinetic ballooning modes (KBMs) are sometimes found in the core region. However, they do not have a distinct finite beta threshold, instead transitioning gradually to a trapped electron mode (TEM) as beta is reduced to zero. Nonlinear simulations of this ‘hybrid’ TEM/KBM predict significant transport in all channels, with substantial contributions from compressional magnetic perturbations. As multiple instabilities are often unstable simultaneously in the same plasma discharge, even on the same flux surface, unique parametric dependencies are discussed which may be useful for distinguishing the different mechanisms experimentally.

Resonant-magnetic-perturbation-induced plasma transport in H-mode pedestals

Plasma toroidal rotation reduces reconnection of externally applied resonant magnetic perturbation (RMP) fields δB on rational (q = m/n) magnetic flux surfaces. Hence, it causes radial perturbations δBρm/n to be small there, and thus inhibits magnetic island formation and stochasticity in the edge of high (H-) mode confinement tokamak plasmas. However, electron collisional damping combined with the spatial magnetic flutter δBρm/n induced by RMPs in the vicinity of rational surfaces causes a radial electron heat diffusivity χeRMP∼(1/2)∑m,n[δB̂ρm/n(x)/B0]2χe∥eff(x) in which χe∥eff∼(vTe2/νe)/(1+x2/δ∥2) is an effective parallel electron thermal diffusivity. These effects are reduced by magnetic shear effects at a distance x from rational surfaces for |x|&amp;gt;δ∥ but amplified for δB̂ρm/n(x)&amp;gt;δB̂ρm/n(0). A kinetic, toroidal model of these RMP-flutter-induced plasma transport effects is developed and compared to a previously developed cylindrical model. The RMP-induced increases in plasma transport can be large enough to reduce plasma gradients in H-mode pedestals. Thus, they may contribute to suppressing edge localized modes in tokamak plasmas.

Resonant magnetic perturbation effects on pedestal structure and ELMs

The plasma transport processes by which externally applied resonant magnetic field perturbations (RMPs) mitigate or suppress edge-localized modes (ELMs) in low-collisionality tokamak H-mode plasmas are explored. Experimental data from DIII-D indicates the dominant RMP-induced transport occurs at the pedestal top where electron temperature gradient scale lengths increase up to 3 times more than density gradient scale lengths. The increases scale approximately with the square of the strength of the RMPs. Since flow screening is predicted to inhibit magnetic island formation and magnetic stochasticity, a plasma transport model that does not depend on stochasticity is apparently needed. Thus, a basic magnetic-flutter-based cylindrical screw-pinch model theory of plasma transport is developed. A key attribute of this new model is that while RMP-induced radial magnetic perturbations can be significantly reduced on rational surfaces by flow screening, they induce spatial magnetic flutter away from them and thereby can cause substantial radial plasma transport. The plasma transport predictions of this spatial flutter model are compared with the DIII-D transport data.

Role of singular layers in the plasma response to resonant magnetic perturbations

The response of an H-mode plasma to magnetic perturbations that are resonant in the edge is evaluated using a fluid model. With two exceptions, the plasma rotation suppresses the formation of magnetic islands, holding their widths to less than a tenth of those predicted by the vacuum approximation. The two exceptions are at the foot of the pedestal, where the plasma becomes more resistive, and at the surface where the perpendicular component of the electron velocity reverses. The perturbations exert a force on the plasma so as to brake the perpendicular component of the electron rotation. In the pedestal, the corresponding Maxwell stress drives the radial electric field in such a way as to accelerate ion rotation. Despite the suppression of the islands, the perturbations give rise to particle fluxes caused by magnetic flutter, with a negligible contribution from E × B convection. In the pedestal, the fluxes are such as to reduce the density.