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Flow shear induced fluctuation suppression in finite aspect ratio shaped tokamak plasma
Abstract
The suppression of turbulence by the E×B flow shear and parallel flow shear is studied in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis previously utilized in a high aspect ratio tokamak plasma [Phys. Plasmas 1, 2940 (1994)]. The result shows that only the E×B flow shear is responsible for the suppression of flute‐like fluctuations. This suppression occurs regardless of the plasma rotation direction and is, therefore, relevant for the very high (VH) mode plasma core as well as for the high (H) mode plasma edge. Experimentally observed in–out asymmetry of fluctuation reduction behavior can be addressed in the context of flux expansion and magnetic field pitch variation on a given flux surface. The adverse effect of neutral particles on confinement improvement is also discussed in the context of the charge exchange induced parallel momentum damping. © 1995 American Institute of Physics.
... This is precisely the aim of this paper, which illustrates magnetic geometry dependent features of the mean E × B shearing rate contrasting the effects of positive and negative triangularities. It is well known that magnetic geometry plays a role in shearing physics [33]. Here, we focus on the interplay of NT configuration with mean E × B shearing. ...
... Shaping parameters related to Triangularity δ how triangular the shape is Triangularity gradient S δ radial variation of triangularity Shafranov shift gradient R 0 radial varition of shift of magnetic axis from geometric axis Elongation κ how elongated the shape is Elongation gradient S κ radial variation of elongation Squareness σ how square the shape is Squareness gradient S σ radial variation of squareness The rest of the paper is organized as follows. The dependencies of the shearing rate on different geometric parameters is calculated in Section 2. The results are discussed and conclusions are given in Section 3. A c c e p t e d M a n u s c r i p t Geometric dependencies of the mean E×B shearing rate in negative triangularity tokamaks5 2. Flux surface geometry dependence of mean ExB shearing rate The Hahm-Burrell formula for the mean E ×B shearing rate [33], ignoring mean parallel flow shear, is obtained from a 2-point correlation calculation for an axisymmetric toroidal system and reads as ...
... Mean E ×B shear is well known to reduce turbulent transport and improve confinement, even in L-mode discharges [44]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d M a n u s c r i p t flux surface shape dependent features of the mean E×B shearing rate, which are relevant to L-H transition physics in different plasma shapes. The Hahm and Burrell formula (1) for the mean E × B shearing rate [33] for an axisymmetric toroidal system is analyzed for negative and positive triangularity flux surface shapes, including the effects of updown asymmetry, using the locally parametrized equilibrium model of Miller et al [34]. ...
This paper presents a comparative study of the poloidal distribution of mean ExB shearing rate for positive triangularity(PT) and negative triangularity(NT) tokamaks. The effects of flux surface up-down asymmetry due to asymmetric upper and lower triangularities is also considered. Both direct eddy straining and effects on Shafranov shift feedback loops are examined. Shafranov shift increases the shearing rate at all poloidal angles for all triangularities, due to flux surface compression. The maximum shearing rate bifurcates at a critical triangularity δ crit (≤0). Thus, the shearing rate is maximal off the outboard mid-plane for NT, while it is maximal on the outboard mid-plane for PT. For up-down asymmetric triangularity, the usual up-down symmetry of the shearing rate is broken. The shearing rate at the out board mid-plane is lower for NT than for PT suggesting that the shearing efficiency in NT is reduced. Implications for turbulence stabilization and confinement improvement in high-β p NT and ITB discharges are discussed.
... The enhanced energy confinement of tokamak H-mode plasmas [1] is believed to result from E × B shear flow suppression of ion scale turbulence (k y ρ i ∼ O (1), where k y is the wave number perpendicular to the flux surfaces and to the magnetic field B and ρ i is the ion Larmor radius) [2] within a localized edge transport barrier (ETB) referred to as the pedestal, which forms just inside the last-closed flux surface (LCFS). The radial electric field within the ETB is proportional to the ion pressure gradient E r ∼ p i /(enB) (where = d/dr and r is the minor radius) [3] and p is maintained by the residual, conducted heat flux q cond across the pedestal remaining after accounting for radiation and energy losses due to edge-localized modes (ELMs) 1 [4]. ...
... The predictive EPED model [5] for the total pressure at the pedestal top p ped assumes that the pressure pedestal width p is determined by the stability of kinetic ballooning modes (KBMs), which limit p , yielding the relation p ∝ β 1/2 p , where β p is the pedestal pressure normalized to the energy density of the poloidal magnetic field. 2 The pedestal height is determined by increasing p ped until the MHD stability limit set by peeling-ballooning instabilities [6] is reached, above which an ELM would be triggered. To determine the electron temperature at the pedestal top T e,ped , which is required as a boundary condition for modelling the core temperature profiles, it is hence necessary to assume a prescribed pedestal density n e,ped . ...
... As the turbulent heat transport is stiff, i.e. approximately q e ∝ (R/L T e − R/L T e ,cr ) 3 , we may expect the temperature gradient T e to adjust such that the absolute electron heat flux q e remains constant across the pedestal (as would be expected with minimal sources and sinks in the pedestal), with the resulting profiles ensuring that the locally gyro-Bohm normalized heat flux Q e follows approximately contours of constant η e not far above the threshold η e,cr for the onset of turbulence. In other words, when η e − η e,cr > O(1), i.e. at values of η e ∼ O (2) where Q e ∼ O(1), the absolute heat flux increases rapidly with R/L T e , hence clamping the experimental (R/L n e , R/L T e ) loci to contours of approximately constant η e ∼ O (2). It is shown in §3 how this property, embodied in equation (2.4), can be used to predict the temperature profile for a prescribed density profile and boundary conditions at the separatrix. ...
A predictive model for the electron temperature profile of the H-mode pedestal is described, and its results are compared with the pedestal structure of JET-ILW plasmas. The model is based on a scaling for the gyro-Bohm normalized, turbulent electron heat flux q e / q e , gB resulting from electron temperature gradient (ETG) turbulence, derived from results of nonlinear gyrokinetic (GK) calculations for the steep gradient region. By using the local temperature gradient scale length L T e in the normalization, the dependence of q e / q e , gB on the normalized gradients R / L T e and R / L n e can be represented by a unified scaling with the parameter η e = L n e / L T e , to which the linear stability of ETG turbulence is sensitive when the density gradient is sufficiently steep. For a prescribed density profile, the value of R / L T e determined from this scaling, required to maintain a constant electron heat flux q e across the pedestal, is used to calculate the temperature profile. Reasonable agreement with measurements is found for different cases, the model providing an explanation of the relative widths and shifts of the T e and n e profiles, as well as highlighting the importance of the separatrix boundary conditions. Other cases showing disagreement indicate conditions where other branches of turbulence might dominate.
This article is part of a discussion meeting issue ‘H-mode transition and pedestal studies in fusion plasmas’.
... Plasma rotation will play a major role in future fusion devices as it is one of the key elements for the suppression of different plasma instabilities [1][2][3][4][5][6][7]. The nature of the edge flow, and how it couples to the plasma core, is important for accurately modelling the rotation profile in present and future devices from first principles. ...
... The second possible explanation could be that impurity sources and radial flows might not be negligible [28] . This assumption was made to get equation (3) from equation (1). The third possible explanation is that the method based on the FSA of the parallel flow is simplifying the poloidal dependence of the parallel flow as it is only considering HFS and LFS midplane profiles to evaluate the FSA. ...
Impurity profiles have been measured with the edge high field side (HFS) and low field side (LFS) charge exchange recombination spectroscopy suite at ASDEX Upgrade enabling the study of the poloidal structure of the edge parallel flow in H-mode, L-mode and I-mode. In H-mode, asymmetries in the impurity density, toroidal and poloidal rotations are found. In I-mode, only toroidal rotation asymmetries have been measured while in L-mode no asymmetries have been observed. The measured parallel flow can be divided in two components, the Pfirsch–Schlüter (PS) flow and the symmetric flow. Two different methods have been followed to determine both contributions to the parallel flow. The first method is based on the calculation of the PS flow at the HFS and LFS from the radial electric field. The second method directly provides the symmetric flow from the flux surface average (FSA) of the parallel flow. In H-mode, the methods provide different results, while in L-mode and I-mode they agree. The differences observed in H-mode between the two methods could be explained by the existence of asymmetries in the impurity density, by the non-negligible particle sources and radial losses, or by the approximations made in the calculation of the FSA of the parallel flow from measurements in two poloidal positions (midplane HFS and LFS) only.
... Indeed, zonal flows are known to dominate the saturation of instabilities arising at microscopic and mesoscopic scales such as drift waves [7] and Alfvén eigenmodes (AEs) [8,9]. The radial electric field shear of zonal flows can suppress turbulent transport [10], resulting in the formation of an internal transport barrier (ITB) that greatly enhances plasma confinement [11]. An outstanding issue is whether zonal flows can play a similar role in saturating macroscopic MHD modes, which may affect turbulent transport through cross-scale interactions common in fusion [12] and astrophysical plasmas [13]. ...
... Since the shearing rate generated by the fishbone is larger than the TEM growth rate and the ratio of TEM radial to poloidal wavelength is much larger than one, the effective shearing rate of the fishbone-induced zonal flows is much larger than the TEM growth rate. Therefore, the zonal flows generated by the fishbone could suppress the turbulence [10], confirming the speculated role of fishbones in the formation of ITBs [19]. Evidence of microturbulence suppression is obtained experimentally in DIII-D with the ion temperature measurement using the charge exchange recombination spectroscopy (CXRS) diagnostic [40]. ...
Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments.
... The E Â B shearing rate x EÂB is the radial derivative of the advecting zonal flow velocity 17,18 and quantifies the zonal flow induced shearing of turbulent structures. 17,19,20 Consistent with Ref. 2, the turbulence level is quantified by the turbulent heat conduction coefficient v, which is normalized by ...
... The E Â B shearing rate x EÂB is the radial derivative of the advecting zonal flow velocity 17,18 and quantifies the zonal flow induced shearing of turbulent structures. 17,19,20 Consistent with Ref. 2, the turbulence level is quantified by the turbulent heat conduction coefficient v, which is normalized by ...
The radial size convergence of the E×B staircase pattern is addressed in local gradient-driven flux tube simulations of ion temperature gradient (ITG)-driven turbulence. It is shown that a mesoscale pattern size of ∼57–76 ρ is inherent to ITG-driven turbulence with Cyclone Base Case parameters in the local limit.
... Similar results have been observed for the ITG mode in toroidal plasma and field-reversed configurations. 27,28 The E r shear is calculated from a two-point nonlinear analy- 27,40 where Dw and Df are the turbulence correlation lengths in radial and toroidal direction, respectively, and B p is the poloidal magnetic field. For an isotropic turbulence eddy (DR $ RDf) near equatorial plane, then the shearing rate can be simplified to the radial variation of the toroidal rotation frequency: ...
... This result is obtained because the ratio of the correlation lengths of the ambient turbulence in the radial and toroidal directions increases with the increasing of the toroidal mode numbers, leading to an increase in the effective E Â B shearing rate. 40 Figure 2(b) shows that the real frequency also decreases as x s increases, but the changes in x are considerably smaller than that in c because E r ¼ 0 is located on the diagnostic surface to minimize the Doppler frequency shift. ...
Global gyrokinetic particle simulations show that the radial electric field ( E r ) shear can suppress the kinetic ballooning mode (KBM) in a toroidal plasma. The linear KBM growth rate reaches a maximum when the toroidal rotation induced by the ion diamagnetic shear is canceled by the E × B flow shear. High toroidal-mode-number (high- n) KBMs are more sensitive to the E r shear than low- n KBMs. Nonlinear simulations find that both the E r shear and a self-generated zonal flow can reduce the nonlinear KBM saturation level with smaller particle and ion heat transport. Meanwhile, the zonal flow can weaken the suppressing effects of the E r shear on KBM nonlinear saturation amplitude. The radial correlation length of the turbulence is reduced by the E r shear and the zonal flow.
... The gyrokinetic-Maxwell equations used here assume negligible plasma rotation. In reality, sheared rotation in tokamak plasmas does exist and can stabilise microinstabilities [26]. To gauge the magnitude of this effect, we estimate the Hahm-Burrel shearing rate |ω HB | [26] by calculating the E × B flow arising from the diamagnetic flow in the equilibrium. ...
... In reality, sheared rotation in tokamak plasmas does exist and can stabilise microinstabilities [26]. To gauge the magnitude of this effect, we estimate the Hahm-Burrel shearing rate |ω HB | [26] by calculating the E × B flow arising from the diamagnetic flow in the equilibrium. That is, we estimate the E × B flow shear from the balance of electric field and pressure gradient forces in the equilibrium, in the absence of externally driven rotation (as expected for reactorgrade tokamak plasmas). ...
To be economically competitive, spherical tokamak (ST) power plant designs require a high β (plasma pressure/magnetic pressure) and sufficiently low turbulent transport to enable steady-state operation. A novel approach to tokamak optimisation is for the plasma to have negative triangularity, with experimental results indicating this reduces transport. However, negative triangularity is known to close access to the “second stability” region for ballooning modes, and thus impose a hard β limit. Second stability access is particularly important in ST power plant design, and this raises the question as to whether negative triangularity is feasible. A linear gyrokinetic study of three hypothetical high β ST equilibria is performed, with similar size and fusion power in the range 500-800MW. By closing the second stability window, the negative triangularity case becomes strongly unstable to long-wavelength kinetic ballooning modes (KBMs) across the plasma, likely driving unacceptably high transport. By contrast, positive triangularity can completely avoid the ideal ballooning unstable region whilst having reactor-relevant β, provided the on-axis safety factor is sufficiently high. Nevertheless, the dominant instability at long wavelength still appears to be the KBM, though it could be stabilised by flow shear.
... A rich body of literature demonstrates the significance of radially sheared zonal flows (ZFs), i.e., toroidally symmetric plasma flows due to the E Â B-drift, for both the nonlinear saturation [1][2][3][4] as well as the nonlinear stabilization [5][6][7][8] of microturbulence in tokamak plasmas. The underlying process is mediated by the E Â B nonlinearity and can be understood either as resulting from the deformation or equivalently tilting of turbulent structures through the advection by the sheared ZFs, 6,9,10 or as a ZF mediated spectral transfer of energy to larger radial wave vectors. [2][3][4] As a consequence of ZF shearing, turbulent structures exhibit an anisotropy or equivalently a tilt in position space; a property robustly observed in experiments [11][12][13] and simulations. ...
... 1,10 A metric that characterizes the strength of this shearing process is the E Â B shearing rate x EÂB , i.e., the radial derivative of the advecting ZF velocity. 9,14 Shear stabilization of microturbulence is then often expressed in the form of the empirical Waltz rule x EÂB $ c, 7,14 where c denotes the maximum linear growth rate of the underlying microinstabilities. Gyrokinetic studies support this condition. ...
Microturbulence close to marginality with inclusion of electron dynamics and in the electrostatic limit [A. Weikl et al., Phys. Plasmas 25, 072305 (2018)] is revisited. In such states the E × B shearing rate ωE×B, i.e., the second radial derivative of the zonal electrostatic potential, a quantity often applied to study zonal flow structure formation, has been found to be dominated by radial fine scale features. Those features are significantly different from the mesoscale E × B staircase structures [G. Dif-Pradalier et al., Phys. Rev. E 82, 025401(R) (2010)] normally occurring close to the threshold. Instead of the E × B shearing rate, here, zonal flow structure formation is studied through the zonal flow shear induced tilt of turbulent structures, which is measured by director field methods. In contrast to dominant fine scale features in ωE×B, mesoscale zonal flow pattern formation on two disparate scales is identified: (i) A zonal flow with radial scale of the boxsize develops, (ii) superposed by zonal flow corrugations in form of shear layers emerging in the vicinity of lowest order rational layers. This mesoscale zonal flow pattern exhibits properties of E × B staircases: (i) A shearing rate of ∼10−1 vth,i/R0 (vth,i is the ion thermal velocity and R0 is the major radius), comparable to typical growth rates, can be attributed to both components of the mesoscale pattern. (ii) Avalanche-like turbulent transport events organize spatially on the same mesoscales. (iii) Shear stabilization by a background E × B shear flow requires values of the background shearing rate exceeding those connected to the mesoscale pattern. In conclusion, this work demonstrates that E × B staircases do develop, even when the E × B shearing rate ωE×B is dominated by radial fine scale features. The E × B shearing rate ωE×B, therefore, fails to estimate the shear provided by zonal flows when fine scale structures dominate its radial profile.
... Using this quench rule, γ − ω E×B , turbulence is completely suppressed when ω E×B exceeds γ. The flow shear rate integrated into the MMM was originally formulated by Hahm and Burrell [22] for general toroidal geometry as: ...
The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM’s ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.
... Tokamak plasmas, influenced by externally applied torque from neutral beam injection (NBI) heating, commonly exhibit strong toroidal rotation and, consequently, substantial toroidal plasma momentum. The rotation plays an important role in characterizing plasma performance as it influences the transport of plasma impurities [1][2][3][4][5], stabilizes turbulence, and enhances confinement [6][7][8][9][10][11]. Moreover, rotation contributes to mitigating and preventing harmful magnetohydrodynamic (MHD) events [12][13][14][15][16][17], such as locked modes, which can cause severe damage on (future) fusion devices. ...
This study employs the established momentum transport analysis at ASDEX Upgrade [Zimmermann et al., Nucl. Fusion 63, 124003 (2023)] to investigate the parametric variations of the momentum transport coefficients in the core of H-mode plasmas. These experimental results are compared to a comprehensive database of gyrokinetic calculations. Generally, good agreement between predicted and measured diffusive and convective transport coefficients is found. The predicted and measured Prandtl numbers correlate most dominantly with the magnetically trapped particle fraction. The experimentally inferred pinch numbers strongly depend on the logarithmic density gradient and magnetic shear, consistent with the theoretical predictions of the Coriolis pinch. The intrinsic torque from residual stress in the inner core is small, scales with the local logarithmic density gradient, and the data indicate a possible sign reversal. In the outer periphery of the core, the intrinsic torque is always co-current-directed and scales with the pressure gradient. This is consistent with prior experimental findings and global, non-linear gyrokinetic predictions. It suggests that profile shearing effects generate the intrinsic torque in the inner core. Toward the outer core, most likely, effects from E×B-shearing become more influential. These results offer the first comprehensive picture of this transport channel in the core plasma and contribute to validating the corresponding theoretical understanding. The derived scaling laws are used to construct a reduced momentum transport model, which has been validated against an additional dataset. This demonstrates that the model captures the essential contributions to momentum transport in the core of H-mode plasmas.
... Optimization of EFC also controls the edge transport barrier (ETB) formation and H-mode transition, triggered by a zonal flow and E × B shear [49][50][51] in tokamaks, while maintaining the n = 1 field at low density 52 without locking and disruption. Figure 5a, d compare the n = 1 EFC to access and to avoid the H-mode transition. ...
A tokamak relies on the axisymmetric magnetic fields to confine fusion plasmas and aims to deliver sustainable and clean energy. However, misalignments arise inevitably in the tokamak construction, leading to small asymmetries in the magnetic field known as error fields (EFs). The EFs have been a major concern in the tokamak approaches because small EFs, even less than 0.1%, can drive a plasma disruption. Meanwhile, the EFs in the tokamak can be favorably used for controlling plasma instabilities, such as edge-localized modes (ELMs). Here we show an optimization that tailors the EFs to maintain an edge 3D response for ELM control with a minimized core 3D response to avoid plasma disruption and unnecessary confinement degradation. We design and demonstrate such an edge-localized 3D response in the KSTAR facility, benefiting from its unique flexibility to change many degrees of freedom in the 3D coil space for the various fusion plasma regimes. This favorable control of the tokamak EF represents a notable advance for designing intrinsically 3D tokamaks to optimize stability and confinement for next-step fusion reactors.
... Prior research has investigated the connection between the L-H transition and the radial electric field [1,2]. The E × B flow shear resulting from the radial electric field has the potential to mitigate turbulent transport and enhance plasma confinement [3,4]. In the double transport barrier experiment, the internal radial electric field enhances confinement performance within the plasma's central region, leading to internal transport [5]. ...
The radial electric field plays an important role in plasma confinement in tokamaks and can be generated through neutral beam injection. In this study, we propose a model for calculating the radial electric field resulting from tangential local neutral beamlet injection, aiming to externally control and improve plasma confinement. The NEOE code has been developed to analyze this problem. The charge separation is primarily caused by the redistribution and loss of beam ions due to magnetic gradient and curvature drift as well as collision effects, and it is maintained through continuous beamlet injection. The electric field is calculated using Poisson's equation, taking into account both classical and neoclassical polarization effects. The results demonstrate that despite the high losses and low heating efficiency associated with localized beamlets, they are capable of generating a significant radial electric field characterized by a steep gradient. This presents opportunities for external control of the electric field, potentially enhancing plasma confinement.
... The radial electric field can change the linear growth rate of the drift-wave instability. It can break the turbulent eddies into finer eddies and the radial correlation length decreases, reducing the turbulence [28,29]. The advancements in the neoclassical transport codes such as NTSS [30], SFINCS [31], FORTEC-3D [32] and PETA [33] have allowed an accurate description of neoclassical transport and hence have made it possible to calculate the ambipolar radial electric field in stellarators. ...
Global gyrokinetic simulations of electrostatic microturbulent transport for discharge # 166256 of the LHD stellarator in the presence of boron impurity show the co-existence of the ion temperature gradient (ITG) turbulence and trapped electron mode (TEM) turbulence before and during boron powder injection. ITG turbulence dominates in the core, whereas TEM dominates near the edge, consistent with the experimental observations. Linear TEM frequency increases from ∼ 80 kHz to ∼ 100 kHz during boron injection, and ITG frequency decreases from ∼ 20 kHz to ∼ 13 kHz, consistent with the experiments. The poloidal wave number spectrum is broad for both ITG (0 − 0.5 mm ⁻¹ ) and TEM (0 − 0.25 mm ⁻¹ ). The nonlinear simulations with boron impurity show a reduction in the heat conductivity compared to the case without boron. The comparison of the nonlinear transport before and during boron injection shows that the ion heat transport is substantially reduced in the region where the TEM is dominant. However, the average electron heat transport throughout the radial domain and the average ion heat transport in the region where the ITG is dominant are similar. The simulations with boron show the effective heat conductivity values qualitatively agree with the estimate obtained from the experiment.
... Understanding momentum transport is crucial to reliably predict the plasma rotation profiles in fusion devices. Rotation is known to influence impurity transport [1][2][3][4][5], contribute to the avoidance of MHD instabilities [6][7][8][9][10][11], and affect turbulence through E × B shearing [12][13][14]. Understanding the sources, sinks, and transport of momentum is necessary to reliably predict the rotation profiles in future machines and its impact upon the stability and confinement of those plasmas. ...
Advanced momentum transport analysis is used to study matched hydrogen (H) and deuterium (D) plasmas in the core of ASDEX Upgrade. The aim is to validate gyrokinetic theory and assess a possible isotope dependence. The methodology extracts momentum diffusion, convection, and intrinsic torque as a function of time from experiments employing neutral beam injection (NBI) modulation. H and D plasma scenarios with comparable ion heat fluxes, NBI torque, electron densities, and several dimensionless parameters were designed to highlight any mass dependency. Linear gyrokinetic simulations predict that, for similar background gradients, the Prandtl and pinch numbers should be similar for H and D. This was confirmed by the experimental momentum transport analyses. The assessed intrinsic torques were found to be similar between H and D, co-current directed and located near the outermost region of the plasma core. The strength of the intrinsic torque is correlated with the amplitude of the plasma pressure gradient in the pedestal. Finally, a robust error analysis demonstrates the uniqueness of the parameters obtained together with their uncertainties. Neglecting the intrinsic torque, or its time dependence, systematically distorts the assessed momentum diffusion and convection. This is the first method to separate all three transport mechanisms from experimental data by retaining their time dependencies, that is found to match, quantitatively, the gyrokinetic predictions for Prandtl and pinch numbers, within experimental uncertainties.
... 29,30 Tokamak experiments feature several ion-mass-dependent effects 3,26 that can lead to a reversal of the gyro-Bohm mass scaling. E  B shear stabilization (either via bulk rotation 34 or zonal flows 35,36 ), collisional trapped electron mode (TEM) stabilization, 37 and electromagnetic effects at high beta 38 are a few examples. Additionally, global full-f gyrokinetic simulations of ITG-dominated plasmas have shown the pervasiveness of a Bohm-like q à i scaling in energy confinement of both electron and ion-heated L-mode plasmas. ...
Design and operation of future tokamak fusion reactors using a deuterium–tritium 50:50 mix requires a solid understanding of how energy confinement properties change with ion mass. This study looks at how turbulence and energy transport change in L-mode plasmas in the ASDEX Upgrade tokamak when changing ion species between hydrogen and deuterium. For this purpose, both experimental turbulence measurements and modeling are employed. Local measurements of ion-scale (with wavevector of fluctuations perpendicular to the B-field k⊥< 2 cm−1, k⊥ρs< 0.2, where ρs is the ion sound Larmor radius using the deuterium ion mass) electron temperature fluctuations have been performed in the outer core (normalized toroidal flux ρTor=0.65−0.8) using a multi-channel correlation electron cyclotron emission diagnostic. Lower root mean square perpendicular fluctuation amplitudes and radial correlation lengths have been measured in hydrogen vs deuterium. Measurements of the cross-phase angle between a normal-incidence reflectometer and an ECE signal were made to infer the cross-phase angle between density and temperature fluctuations. The magnitude of the cross-phase angle was found larger (more out-of-phase) in hydrogen than in deuterium. TRANSP power balance simulations show a larger ion heat flux in hydrogen where the electron-ion heat exchange term is found to play an important role. These experimental observations were used as the basis of a validation study of both quasilinear gyrofluid trapped gyro-Landau fluid-SAT2 and nonlinear gyrokinetic GENE codes. Linear solvers indicate that, at long wavelengths (k⊥ρs<1), energy transport in the deuterium discharge is dominated by a mixed ion-temperature-gradient (ITG) and trapped-electron mode turbulence while in hydrogen transport is exclusively and more strongly driven by ITG turbulence. The Ricci validation metric has been used to quantify the agreement between experiments and simulations taking into account both experimental and simulation uncertainties as well as four different observables across different levels of the primacy hierarchy.
... 4 Oft-quoted and probably well-understood aspect of the problem is the ExB shearing of turbulence, which reduces the radial size and amplitude of turbulence eddies. [5][6][7][8] Incomplete damping of zonal flows in collisionless limit, which turns out to influence the turbulence level and transport is quantified by the Rosenbluth-Hinton residual zonal flow level. 9 Since the posed problem is conceptually clear and simple, it has been further extended to broader wavelength regimes. ...
Fast ions' effects on turbulence-driven zonal flow generation are investigated in the context of a simple reduced model based on the Hasegawa–Mima equation. Fast ions' much higher characteristic frequency of parallel motion in comparison with the drift wave's phase velocity along the magnetic field facilitates a derivation of the reduced model equations. Nonlinear mode coupling analyses show that the threshold amplitude of drift wave required for the zonal flow modulational instability is significantly reduced, making its generation easier. This occurs as both a down-shift of the drift wave's frequency and a reduction of dispersion in the presence of the fast ions cause a decrease in the mismatch between the primary drift wave frequency and the zonal flow modulated sideband drift wave's characteristic frequency. This finding could be a common nonlinear physics mechanism behind numerous recent results on tokamak plasma confinement enhancement caused by the fast ions.
... The E r well with its large gradients produces a large rotational shearing rate ω E×B , which is the leading candidate to enable the H-mode regime. An example of the Hahm-Burrell E × B shearing rate [11] is shown in figure 1(b). The underlying theoretical hypothesis is that this shear reduces or eliminates turbulence in the pedestal, thus reducing turbulent-driven transport and enabling the formation of the observed gradients. ...
This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling- ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.
... In figure 17(b) two E r profiles outside (α = 0 π, blue) and [40]) profiles are plotted. Not only is the E r well deeper in the region of the fluctuation gap, but also narrower. ...
We study localized edge turbulence in the ASDEX Upgrade tokamak that appears if resonant magnetic perturbations (RMP) are applied to suppress edge localized modes (ELMs) in the high confinement mode. The concomitant density fluctuations are detected by microwave reflectometry at the outboard midplane. Two modes can be distinguished, (i) a broadband fluctuation below a threshold of the RMP field amplitude, and (ii) a narrow-band quasi-coherent mode (QCM) above the threshold. The broadband fluctuation is toroidally spread out but disappears at the toroidal position of maximum E×B shear in the gradient region. Temporal and spatial correlation along field lines of the midplane density fluctuation and the divertor particle flux suggests that this mode is producing significant particle transport across the gradient region and into the divertor, hence contributing to the plasma density reduction that is often observed when applying RMP fields (the so-called “pump-out” effect). The QCM is also toroidally localized, its radial extent grows with increasing RMP field amplitude, and leads to further increased divertor particle flux compared to the broadband mode. Our observations suggest that both modes not only play an important role in keeping the plasma density stationary in the absence of ELMs but also to reduce the plasma pressure such that the plasma edge becomes stable against ELMs.
... Indeed, zonal flows are known to dominate the saturation of instabilities arising at microscopic and mesoscopic scales such as drift-waves [7] and Alfvén eigenmodes (AEs) [8] [9]. The radial electric field shear of zonal flows can suppress turbulent transport [10], resulting in the formation of an internal transport barrier (ITB) that greatly enhances plasma confinement [11]. An outstanding issue is whether zonal flows can play a similar role in saturating macroscopic MHD modes, which may affect turbulent transport through cross-scale interactions common in fusion [12] and astrophysical plasmas [13]. ...
Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space with mode down-chirping. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the suppression of the microturbulence by fishbone-induced zonal flows is likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments.
... Toroidal rotation plays a key role in the confinement properties of tokamak plasmas. Indeed, numerous experiments have highlighted the link between plasma rotation and improved plasma performance [21,26,[89][90][91]. On most medium size tokamaks, rotation is controllable using the external torque exerted by tangential neutral beam injection. ...
Understanding the self-generation of flows in tokamak plasmas is of prime importance.Indeed, the control of flows by external momentum injection in future reactors will be challenging, if not impossible.However, flows play a major role in the stability and performance of a fusion plasma.In this thesis, the self-generation of the perpendicular field line flow, associated with the radial electric field, is studied in two experimentally relevant contexts.The way this field is established is a major issue, as it is involved in the formation and sustainment of transport barriers that appear spontaneously in high power discharges, significantly reducing turbulent transport.In a first step, the effect of a 3D perturbation of the magnetic field such as the one caused by the modulation arising from the finite number of toroidal coils, also called ``ripple", is studied. Such a perturbation impacts the toroidal velocity of the plasma, itself generated spontaneously by the turbulence.Until now, the competition and synergy between these two contributions had not been studied numerically and theoretically.However, numerous experimental studies on different tokamaks have shown that these two effects drastically impact the toroidal velocity of the plasma.Using a theoretical model and simulations performed with the gyrokinetic code GYSELA, the competition has been observed and quantified.An expression of the critical ripple amplitude for which turbulence becomes subdominant in the control of the toroidal rotation has been defined and validated with these simulations.Preliminary studies show that this threshold could be reached in ITER.The synergy between turbulence and ripple has also been evaluated.The dominant effect is the impact of the ripple on the Reynolds tensor through the modification of the radial electric field radial shear.In a second step, recent experiments on the WEST tokamak showing that the radial electric field is sensitive to the winding rate of the magnetic field lines, called ``safety factor", are numerically investigated with gyrokinetic simulations.As observed experimentally, these simulations show that the radial electric field increases as the safety factor and the turbulent intensity decrease.However, collisional effects appear to be negligible for the establishment of the radial electric field, highlighting the undeniable role of turbulence.The main effect comes from the transfer of turbulent energy varying with the safety factor, which favors either very low frequency flows called ``zonal flows", or higher frequency flows called ``GAMs".
... In inhomogeneous turbulence, the nonlinearities also produce turbulent diffusivities D ej that spread fluctuation intensity radially. The E  B shear suppression terms incorporate the toroidal form of the shearing rate, 28 x EÂB ¼ ðr=qÞ@=@r½ðq=rÞE r =B / q is the safety factor, E r is the radial electric field, and B / is the toroidal magnetic field. The shear suppression coefficients are a 2 j ¼ ðD jr =rD jh Þ 2 c À1 j , where D jr and D jh are radial and poloidal correlation lengths. ...
The initiation, termination, and control of internal transport barriers associated with E × B flow shear near local minima of magnetic shear are examined for burning plasmas to determine if the positive feedback loops between profiles, instability, transport, and flow shear operate in regimes with fusion self-heating. A five-field transport model for the evolution of profiles of density, ion and electron temperature, ion and electron fluctuations, and radial electric field is utilized to examine the efficacy of controls associated with external inputs of heat and particles, including neutral beam injection, RF, pellets, and gas puffing. The response of the plasma to these inputs is studied in the presence of self-heating. The latter is affected by the external inputs and their modification of profiles and is, therefore, not an external control. Provided sufficient external power is applied, internal transport barriers can be created and controlled, both in ion and electron channels. Barrier control is sensitive to the locations of power deposition and pellet ablation, as well as temporal sequencing of external inputs.
... EDWM uses a toroidal slab geometry, and the E Â B-shearing rate is taken into account as a reduction in the linear growth rate in the Hahm-Burrell formalism. 29 As EDWM uses an eigenvalue solver, all unstable modes not just the most unstable, account for the total flux. ...
The verification of a new saturation rule applied to the quasi-linear fluid model EDWM (extended drift wave model) and the calibration of several other features are presented. As one of the computationally fastest first-principle-based core transport models, EDWM can include an arbitrary number of ions and charge states. This feature is especially important for experimental devices with plasma-facing components made of heavy elements, such as the upcoming ITER device. As a quasi-linear model, EDWM solves a linear dispersion relation to obtain the instabilities driving the turbulence and combines the linear description with an estimation of the saturation level of the electrostatic potential to determine the fluxes. A new saturation rule at the characteristic length combined with a spectral filter for the poloidal wavenumber dependency is developed. The shape of the filter has been fitted against the poloidal wavenumber dependency of the electrostatic potential from non-linear gyrokinetic simulations. Additionally, EDWM's collision frequency and safety factor dependencies, as well as the electron heat flux level, have been calibrated against gyrokinetic and gyrofluid results. Finally, the saturation level has been normalized against non-linear gyrokinetic simulations and later validated against experimental measured fluxes from 12 discharges at JET.
... In this section, the results of the CTEM-induced current are demonstrated. It is known that the zonal flow shear plays an important role in the turbulence mitigation [31,32], the intrinsic rotation of bulk ions [2] and the current generation [12]. In our simulations, two cases with different electron temperature gradient (R 0 /L Te = 5, 10) are performed to take into account the zonal flow shearing effects on the current generation and its connection with the fine structure of the current density [13]. ...
The spatial structure and amplitude of the current induced by the collisionless trapped electron mode (CTEM) turbulence are investigated by the gyrokinetic simulations. It is shown that the barely passing electrons play a crucial role in determining the magnitude and the direction of the current density. Two characteristic radial scales of the current density are found. The fine structure (a few ion Larmor radii) of the turbulence-induced current is observed near the rational surfaces. Further, the mesoscale structure (tens of ion Larmor radii) of the turbulence-induced current related to the zonal flow shear is confirmed, especially for the high toroidal mode number (n) CTEM. For the strongly driven CTEM, the zonal flow shear effect on the turbulence-induced current is significant, while it is not visible for the weakly driven CTEM. The magnitude of the CTEM turbulence-induced current is featured with moderate local magnitude comparable to the bootstrap current near the rational surfaces, which is shown by the nonlinear simulations with multi-n modes.
... Sufficient rotation can provide stability against neoclassical tearing modes [7,8], resistive wall modes [9][10][11], and locked mode instabilities [12]. By the velocity shear, rotation can stabilize turbulence and influence the confinement [13][14][15][16][17]. Despite this relevance, there is currently no fully validated predictive model for the plasma rotation. ...
The prediction of the plasma rotation is of high interest for fusion research due to the effects of the rotation upon MHD instabilities, impurities, and turbulent transport in general. In this work, an analysis method was studied and validated to reliably extract momentum transport coefficients from NBI modulation experiments. To this end, a set of discharges was created with similar background profiles for the ion and electron temperatures, the heat fluxes, the electron density, and the plasma rotation that, therefore, should exhibit similar momentum transport coefficients. In these discharges, a range of temporal perturbations were imposed by modulating and varying the power deposition of the NBI, ECRH, and ICRH. The transport model including diffusion, convection, and residual stress was implemented within the ASTRA code. The Prandtl number Pr = χ φ /χ i was assessed via the GKW code. A convective Coriolis pinch was fitted and the intrinsic torque from the residual stress was estimated. The obtained transport coefficients agree within error bars for sufficiently small imposed temperature perturbations, as would be expected, from the similar background profiles. This successful validation of the methodology opens the door to study the parametric dependence of the diffusive and convective momentum transport of the main ions of the plasma as well as the turbulent intrinsic torque in a future work.
This paper provides a comprehensive review of the TRANSP code, a sophisticated tool for interpretive and predictive analysis of tokamak plasmas, detailing its major capabilities and features. It describes the equations for particle, power, and momentum balance analysis, as well as the poloidal field diffusion equations. The paper outlines the spatial and time grids used in TRANSP and details the equilibrium assumptions and solvers. Various models for heating and current drive, including updates to the NUBEAM model, are discussed. The handling of large-scale events such as sawtooth crashes and pellet injections is examined, along with the predictive capabilities for advancing plasma profiles. The integration of TRANSP with the ITER Integrated Modeling and Analysis Suite (IMAS) is highlighted, demonstrating enhanced data access and analysis capabilities. Additionally, the paper discusses best practices and continuous integration techniques to enhance TRANSP's robustness. The suite of TRANSP tools, designed for efficient data analysis and simulation, further supports the optimization of tokamak operations and coupling with other tokamak codes. Continuous development and support ensure that TRANSP remains a major code for the analysis of experimental data for controlled thermonuclear fusion, maintaining its critical role in supporting the optimization of tokamak operations and advancing fusion research.
A symmetry-breaking in rotational spatial pattern of quasi-periodic solitary oscillations is revealed with tomography measurement of plasma emission, simultaneously with background asymmetry in stationary plasma structure. Although the oscillatory pattern deformation is a natural course in the presence of asymmetry, elaborate analyses identify existence unfeatured nonlinear effects of the background asymmetry, i.e., its nonlinear couplings with harmonic modes of rotational symmetry, to produce non-harmonic mode to break the symmetry and cause the oscillatory pattern to be chaotic. The findings suggest the unrecognized fundamental process for plasmas to be turbulent.
The concept and theory of potential vorticity in drift wave turbulence are extended to the case of an inhomogeneous magnetic field. A one-field magnetic potential vorticity conserving equation is derived via the use of conservative gyrokinetics. The similarity between the corresponding systems for drift wave turbulence and shallow water theory is discussed in detail. Zonal flow physics in an inhomogeneous magnetic field is discussed. In particular, a Charney–Drazin type nonacceleration theorem is derived from the novel system, which conserves magnetic potential vorticity. Extensions of the turbulent equipartition theory to the transport of magnetic potential vorticity are proposed.
We present a gyrokinetic theory of an E $$\times$$ × B vortex flow in a magnetic island self-generated from turbulence in a collisionless tokamak plasma. We have found that after fast collisionless damping, the self-generated vortex flow arrives at a residual level higher than the Rosenbluth-Hinton level predicted in the tokamak geometry. In the longer term, the residual vortex flow undergoes further damping with a deformation toward a zonal-vortex mixture, making open streamlines near the X-points that reduce the isolated region of the island. It is due to the helical symmetry breaking by the toroidal precession, expected to be stronger in higher-temperature plasmas and in lower aspect ratio tokamaks. A strong enough background vortex flow can significantly suppress the toroidicity-induced damping and deformation of the self-generated vortex flow, proposing that the island boundary is a key location for the bifurcation of the confinement state.
Plasma transport driven by turbulence ultimately determines the energy confinement performance of controlled fusion devices regardless of their confinement schemes and configurations. A large variety of plasma instabilities have been proposed for driving turbulence responsible for anomalous plasma transport beyond classical/neoclassical transport due to collisions. Although ion-scale turbulence usually dominates due to its large eddy size and saturation level, electron-scale turbulence has been recognized to be important in regions where ion-scale turbulence is suppressed (e.g., in internal transport barrier and in spherical tokamak H-mode plasmas) or is close to marginality. Electron-scale turbulence has been shown to nonlinearly interact with ion-scale turbulence, which modifies the dynamics of both and affects the resulting plasma transport, particularly when ion-scale instability is weakly driven. In this review paper, we focus on electron-scale turbulence that is believed to operate in magnetically confinement fusion devices and aim to provide a review of theoretical, numerical, and experimental developments in understanding electron-scale turbulence and its role in driving anomalous plasma turbulence. In particular, we focus on the electrostatic electron temperature gradient (ETG) mode which is the most widely recognized plasma instability underlying electron-scale turbulence observed in magnetically confined plasmas. We note that there are other less studied instabilities that might be responsible for observed electron-scale turbulence, most notably ubiquitous mode, and short-wavelength ion temperature gradient (SWITG) mode, which will be briefly touched on in this review.
We extend the bounce-averaged kinetic (BK) electron model to be applicable in general tokamak magnetic geometries and implement it on the global δf particle-in-cell gyrokinetic code gKPSP. We perform a benchmark study of the updated BK model against the gyrokinetic electron model in flux-tube codes, CGYRO and GENE. From the comparisons among the simulations based on the local parameters of a KSTAR L-mode plasma, we confirm a reasonable agreement among the linear results from the different codes. In the nonlinear gKPSP simulation with a narrow plasma gradient region whose width comparable to the mode correlation length, ion and electron heat fluxes are compatible with those calculated by CGYRO. However, with an unstable region sufficiently wider than the mode correlation length, gKPSP predicts 2–3 times larger turbulent heat fluxes. Taking into account the differences between the flux-tube and global simulations, the overall agreement is encouraging for further validation and development of the BK electron model. In global simulations using a wide range of the experimental plasma profiles, we find an intricate coupling of turbulence spreading and a zonal flow in determining the radial profiles of turbulent heat fluxes, which has not been reported to date.
In magnetic fusion plasmas, a transport barrier is essential to improve the plasma confinement. The key physics behind the formation of a transport barrier is the suppression of the micro-scale turbulent transport. On the other hand, long-range transport events, such as avalanches, has been recognized to play significant roles for global profile formations. In this study, we observed the impact of the avalanche-type of transport on the formation of a transport barrier for the first time. The avalanches are found to inhibit the formation of the internal transport barrier (ITB) observed in JT-60U tokamak. We found that (1) ITBs do not form in the presence of avalanches but form under the disappearance of avalanches, (2) the surface integral of avalanche-driven heat fluxe is comparable to the time rate change of stored energy retained at the ITB onset, (3) the mean E × B flow shear is accelerated via the ion temperature gradient that is not sustained under the existence of avalanches, and (4) after the ITB formation, avalanches are damped inside the ITB, while they remain outside the ITB.
A new approach to infer the momentum transport in tokamak core plasmas via perturbation experiments is presented. For the first time, the analysis self-consistently includes all momentum transport components and their time dependencies, which are essential to separate the momentum fluxes and closely match the experiment. The quantitative agreement between the experimentally inferred transport coefficients and the gyrokinetic predictions provides an unprecedented validation. This work shows that the new methodology and gyrokinetic predictions can now be utilized on the route to physics-based prediction of momentum transport in future reactor plasmas.
This memorial note for Professor Sanae-I Itoh presents her specific achievements in physics research alongside her wider record of accomplishment in the field of magnetically confined plasmas. The topics include bifurcation phenomena (e.g., H-mode and improved confinement modes), turbulence-generated structures (e.g., zonal flows and streamers), and fundamental concepts and processes in plasma turbulence (e.g. nonlinear couplings and energy transfer. The note focuses initially on results obtained through her integration of theory, simulation, and experiment, particularly those arising from a low temperature plasma facility at Kyushu University. We then describe contemporary challenges in plasma turbulence which Sanae addressed with great interest, and consider some of the perspectives that were opened by her achievements.
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 eΦcr/T = ϵw/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.
A tokamak relies on the axisymmetric magnetic fields to confine fusion plasmas and aims to deliver sustainable and clean energy. However, misalignments arise inevitably in the tokamak construction, leading to small asymmetries in the magnetic field known as error fields (EFs). The EFs have been a major concern in the tokamak approaches because a small level EFs, even less than 0.1 %, can drive a plasma disruption. Contrary to conventional wisdom, we report that the EFs in a tokamak can be favorably used for controlling plasma instabilities, such as edge-localized modes (ELMs), while maintaining a hot fusion plasma at a temperature of 100 million kelvin. A novel optimization tailors the EFs to maintain an edge 3D response for ELM control with a minimized core 3D response to avoid plasma disruption and unnecessary degradation. We design and demonstrate such an edge-localized 3D response at the Korean Superconducting Tokamak Advanced Research facility, benefiting from its unique flexibility to change many degrees of freedom in the 3D coil space for the various fusion plasma regimes. This favorable control of the tokamak EF represents a notable advance for designing intrinsically 3D tokamaks to optimize stability and confinement for the next-step fusion reactors.
Global gyrokinetic particle simulations show that equilibrium radial electric field (Er) shear reduces the linear growth rate, ion heat conductivity, and nonlinear turbulence amplitude for both the ion temperature gradient (ITG) and kinetic ballooning mode (KBM) microturbulence with tilting the poloidal mode structure. Increase in the magnetic shear enhances the stabilizing performance of the Er shear on linear growth rate for ITG case but has no effect on that for KBM case. The radial correlation length of the ITG turbulence is decreased by increasing the magnetic shear in a weak ion diamagnetic flow shear condition with low β, leading to a reduction in effective ExB shearing rate, which weakens the suppression performance of the Er shear on ITG turbulence amplitude. In contrast, under a larger ion diamagnetic flow shear for higher β, increase in magnetic shear strengthens the suppression performance of the Er shear on KBM turbulence amplitude due to increase in the effective shearing rate by increasing the radial correlation length of the turbulence.
New H-mode regimes with high confinement, low core impurity accumulation, and small edge-localized mode perturbations have been obtained in magnetically confined plasmas at the Joint European Torus tokamak. Such regimes are achieved by means of optimized particle fueling conditions at high input power, current, and magnetic field, which lead to a self-organized state with a strong increase in rotation and ion temperature and a decrease in the edge density. An interplay between core and edge plasma regions leads to reduced turbulence levels and outward impurity convection. These results pave the way to an attractive alternative to the standard plasmas considered for fusion energy generation in a tokamak with a metallic wall environment such as the ones expected in ITER.
Linear and nonlinear simulations are carried out for the edge coherent mode (ECM) using the global gyrokinetic code GEM based on the EAST experimental parameters. The linear simulation results show that ECM is an electrostatic mode with dominant toroidal mode number n=18 and frequency about 48kHz, and propagates along the direction of electron diamagnetic drift, which are consistent with the experimental results. In addition, the density and electron temperature gradients destabilize the mode, while the collision stabilizes the mode. The nonlinear simulation results show that the saturated particle and heat fluxes induced by ECM are mainly due to the perturbed electrostatic ExB drift, and the fluxes of electrons and ions are almost equal. The ECM drives significant outward particle and heat fluxes, thus greatly promoting the maintenance of the long pulse H-mode. The Fourier decomposition of fluxes and potentials demonstrate that the intermediate-n modes of n=14, 18 grow fastest in the linear phase, while in the nonlinear saturation phase, the low-n modes such as n=4, 6 dominate and the fluxes are mainly contributed by the mode of n=10. It is found that zonal flow is not the dominant saturation mechanism of the turbulence. The inverse spectral cascade of turbulence is inevitably observed in the nonlinear saturation process, indicating that it is a more universal turbulence saturation mechanism. It is also found that radial electric field can greatly reduce the turbulence intensity and transport level. From the analyses of frequency and transport channels, it can be concluded that ECM appears to be the collisionless trapped electron mode (CTEM).
The fishbone instabilities and internal transport barriers (ITBs) are frequently and sequentially observed in tokamak plasmas. Recently, the relationship between fishbone and ITB was numerically studied mainly on the basis of experimental results (Z. X. Liu et al., 2020 Nucl. Fusion 60 122001). It was identified that a radial electric field can be generated by fishbone itself, which may act as a trigger of ITB formation. To gain a deeper understanding of this subject, in this work, we further demonstrate the multiple interactions between fishbone instability and ITB in Experimental Advanced Superconducting Tokamak (EAST) experiment (discharge #56933) using hybrid kinetic-MHD code M3D-K. In the multiple-n simulations, it is found that the zonal electric field can be induced in the nonlinear stage of fishbone, leading to a relatively large E×B zonal flow that is sufficient to suppress the dominant microinstability before ITB formation, which should account for the trigger of ITB. After the ITB is triggered, the equilibrium pressure gradient increases and the fast ions from the neutral beam injection accumulate in ITB region. Then, the linear simulations are performed to analyze the effect of ITB formation on fishbone instability. It is shown that due to the change of the pressure gradient during ITB expansion, the change of bootstrap current density profile modifies the q profile, and then stabilizes the fishbone mode. Additionally, the accumulation of the fast ions leads to a broadening of fast ion distribution around the ITB region, which also has a stabilizing effect on the fishbone mode.
We carry out several numerical simulations to illustrate how the radial electric field ( E r ) impacts the edge magnetohydrodynamic (MHD) instabilities. The analyses reveal that E r -shear ([Formula: see text], here the prime denotes the derivative with respect to the radial direction) tends to stabilize the kink[Formula: see text]Peeling–Ballooning modes by dephasing the perturbed radial velocity ([Formula: see text]) and displacement ([Formula: see text]). However, E r -curvature ([Formula: see text]) tends to destabilize the kink/peeling modes by inducing a phase lock between [Formula: see text] and [Formula: see text]. More specifically, the ratio between them could be measured to quantify their relative competition strength. Consequently, the shape of E r is crucial to the shape of linear growth rate spectrum [Formula: see text] (here n is the toroidal mode number), which further determines the nonlinear dynamics. On the one hand, relatively larger E r -curvature causes narrower [Formula: see text], leading to larger nonlinear energy loss fraction. On the other hand, relatively larger E r -shear has the opposite effect.
Global nonlinear gyrokinetic simulation of the ion-temperature-gradient (ITG) modes clearly demonstrates the nonlinear phase-space resonance, which can be well understood by the nonlinear frequency chirping due to the nonlinear poloidal acceleration of resonant particles by the large-scale structure of radial electric field rather than the widely discussed local shearing effects of the zonal flows. The nonlinear radial restructure of a single-n ITG mode generates multiple Child-Ballooning-Modes.
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.
In absence of external torque, plasma rotation in tokamaks results from a balance between collisional magnetic braking and turbulent drive. The outcome of this competition and cooperation is essential to determine the plasma flow. A reduced model, supported by gyrokinetic simulations, is first used to explain and quantify the competition only. The ripple amplitude above which magnetic drag overcomes turbulent viscosity is obtained. The synergetic impact of ripple on the turbulent toroidal Reynolds stress is explored. Simulations show that the main effect comes from an enhancement of the radial electric field shear by the ripple, which in turn impacts the residual stress.
The impact of the parallel flow shear on the tokamak plasma stability and turbulent transport driven by the ion temperature gradient (ITG) modes is analyzed by means of local gyrokinetic numerical analyses. It is shown that the parallel flow shear increases the ITG growth rate in the linear regime, and induce a broadening and shift of the radial spectrum. Then, the different effects of the finite parallel shear on the ITG turbulence characteristics are deeply analyzed in the nonlinear regime. These studies highlight that a reduction of the thermal-ion turbulent heat flux is induced by a complex mechanism involving the nonlinear generation of an enhanced zonal flow activity. Indeed, the turbulent sources of the zonal flows are increased by the introduction of the finite parallel flow shear in the system, beneficially acting on the saturation level of the ITG turbulence. The study has been carried out for the Waltz standard case below the critical threshold of the destabilization of the parallel velocity gradient instability, and then generalized to a selected pulse of a recent JET scenario with substantial toroidal rotation in the edge plasma region. It is, thus, suggested that the investigated complex mechanism triggered by the finite parallel flow shear reducing the ITG turbulent heat fluxes could be complementary to the well-established perpendicular flow shear in region with sufficiently large plasma toroidal rotation.
Nonlinear multiscale gyrokinetic simulations of a Joint European Torus edge pedestal are used to show that electron-temperature-gradient (ETG) turbulence has a rich three-dimensional structure, varying strongly according to the local magnetic-field configuration. In the plane normal to the magnetic field, the steep pedestal electron temperature gradient gives rise to anisotropic turbulence with a radial (normal) wavelength much shorter than in the binormal direction. In the parallel direction, the location and parallel extent of the turbulence are determined by the variation in the magnetic drifts and finite-Larmor-radius (FLR) effects. The magnetic drift and FLR topographies have a perpendicular-wavelength dependence, which permits turbulence intensity maxima near the flux-surface top and bottom at longer binormal scales, but constrains turbulence to the outboard midplane at shorter electron-gyroradius binormal scales. Our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport -- in our case by $\sim$40 \% -- through multiscale interactions.
In this work, we have investigated the influences of magnetic island (MI) on electrostatic toroidal ion temperature gradient (ITG) mode, where the ions are described by gyro-kinetic equations including MI, and adiabatic approximation is used for electrons. The eigen-equation for short-wavelength toroidal ITG mode in Fourier-ballooning representation is derived, and the corresponding eigen-value as well as mode structure are solved. Both the flattening effects of MI on plasma pressure and MI-scale shear flow are considered. It is found that when only considering the flattening effects of MI, ITG mode can be stabilized as compared to the case without MI. While, the effective drive of toroidal ITG mode could be enhanced by including MI-scale flow, which indicates the dominant destabilizing by MI-scale flow over the stabilizing by flattening profile and results in higher growth rate than the case without MI. It is also found that the total flow shearing may prevent the ITG turbulence spreading from X-point of MI but not strong enough to prevent spreading from the seperatrix across O-point of larger MI via comparison between the flow shearing rate and the linear growth rate. Furthermore, the corresponding width of lowest-order mode structure in ballooning angle is slightly widened (narrowed) for the case without (with) MI-scale flow, as compared to the case without MI. Besides, the shifted even symmetry in ballooning angle is not qualitatively influenced by the presence of MI. The mode structure is radially asymmetric, but is symmetric with respect to the phase of MI at the O-point.
Mitigation of deleterious heat flux from edge-localized modes (ELMs) on fusion reactors is often attempted with 3D perturbations of the confining magnetic fields. However, the established technique of resonant magnetic perturbations (RMPs) also degrades plasma performance, complicating implementation on future fusion reactors. In this paper, we introduce an adaptive real-time control scheme on the KSTAR tokamak as a viable approach to achieve an ELM-free state and simultaneously recover high-confinement (β N ~1.91, β p ~1.53, and H 98 ~0.9), demonstrating successful handling of a volatile complex system through adaptive measures. We show that, by exploiting a salient hysteresis process to adaptively minimize the RMP strength, stable ELM suppression can be achieved while actively encouraging confinement recovery. This is made possible by a self-organized transport response in the plasma edge which reinforces the confinement improvement through a widening of the ion temperature pedestal and promotes control stability, in contrast to the deteriorating effect on performance observed in standard RMP experiments. These results establish the real-time approach as an up-and-coming solution towards an optimized ELM-free state, which is an important step for the operation of ITER and reactor-grade tokamak plasmas.
Interaction between a magnetic island and turbulence has been intensively studied in recent years with advance of plasma diagnostics in various plasma experiment devices such as LHD, J-TEXT, TJ-II, DIII-D, KSTAR, and HL-2A. Simultaneous measurements of plasma turbulence and pressure and flow profiles have provided a comprehensive understanding of their interaction. Experiments found that plasma turbulence becomes strongly inhomogeneous around a magnetic island due to the combined effect of the pressure gradient (driver) and flow shear (regulator) modifications by the island. Those experimental observations are consistent with gyrokinetic simulations results obtained using GKW, GTC, GENE, and gKPSP, and imply the limitation of conventional understanding of the island evolution. The effect of inhomogeneous and nonlinear characteristic of plasma turbulence would complicate the island evolution which depends on ambient transport physics. In addition, more complex turbulence phenomena which can affect the island stability in fusion plasmas as well as the underlying magnetic reconnection process have been suggested from theoretical and numerical studies. Some of them whose experimental evidences are being accumulated from both fusion and laboratory plasmas are introduced; turbulence spreading, nonlinear mode coupling, turbulence driven flow, and turbulent magnetic reconnection. They can either suppress or facilitate the island growth. Since turbulence spreading and turbulent magnetic reconnection can be a universal feature of magnetized plasmas, their observations would provide general physical insights into the island turbulence dynamics.
We explore the inboard-limited internal transport barrier (ITB) as an alternative advanced operation scenario for KSTAR. This paper presents in detail the progress of the ITB experiment at KSTAR. In an earlier study, the ITB formed in both ion and electron thermal channels, and an early neutral-beam injection (NBI) power of over 4 to 5 MW under a limited L-mode was crucial to ITB access. In the present study, we access the ITB experimentally with about 3 MW of NBI power by using the upper single null (USN), which is an unfavorable H-mode condition with a higher L–H power threshold. Finding an ITB access condition with a lower heating power should allow for a more efficient control of the heat flux and for maintaining stable plasma performance. The key control parameters of the experiment are the vertical position and the location of outboard striking point of the plasma. The shape-control attempts to divert the plasma to a vertically shifted USN with a marginal touch of the inboard limiter so that the plasma can remain in the L-mode at the boundary, while the striking-point control maintains the ITB performance for a longer period of time.
We report a discovery of a fusion plasma regime suitable for commercial fusion reactor where the ion temperature was sustained above 100 million degree about 20 s for the first time. Nuclear fusion as a promising technology for replacing carbon-dependent energy sources has currently many issues to be resolved to enable its large-scale use as a sustainable energy source. State-of-the-art fusion reactors cannot yet achieve the high levels of fusion performance, high temperature, and absence of instabilities required for steady-state operation for a long period of time on the order of hundreds of seconds. This is a pressing challenge within the field, as the development of methods that would enable such capabilities is essential for the successful construction of commercial fusion reactor. Here, a new plasma confinement regime called fast ion roled enhancement (FIRE) mode is presented. This mode is realized at Korea Superconducting Tokamak Advanced Research (KSTAR) and subsequently characterized to show that it meets most of the requirements for fusion reactor commercialization. Through a comparison to other well-known plasma confinement regimes, the favourable properties of FIRE mode are further elucidated and concluded that the novelty lies in the high fraction of fast ions, which acts to stabilize turbulence and achieve steady-state operation for up to 20 s by self-organization. We propose this mode as a promising path towards commercial fusion reactors.
A theory of resistive, density-gradient-driven turbulence is presented and compared with tokamak edge fluctuation measurements. In addition to linear driving, the theory accounts for relaxation of the density gradient through a nonlinear process associated with emission from localized density fluctuation elements. From a fluid model for isothermal electrons in toroidal geometry, equations are obtained and solved analytically, retaining both coherent and incoherent contributions. The effect of collisions on the density blobs is treated. A Reynolds number parameterizes the magnitude of the turbulent scattering relative to the collisional viscous diffusion. The analytic results indicate that the spectrum is characterized by linewidths which increase as a function of the Reynolds number and may reach Δω/ω≳1. Energy lies predominantly in the small wavenumbers (k⊥ &rgr;s∼0.1). For larger wavenumbers and frequency, the spectrum decays as k−17/6 and ω−2. The fluctuation level scales as 1/k⊥Ln and may reach −30% for parameters typical of the pretext edge. Particle diffusion is Bohm-like in magnitude but does not follow Bohm scaling, going instead as n2/3T1/6e. The density fluctuations exhibit nonadiabatic character caused by the incoherent mode coupling. An expression for the departure from adiabaticity is given.
A new operational regime has been observed in neutral-injection-heated ASDEX divertor discharges. This regime is characterized by high βp values comparable to the aspect ratio A(βp<~0.65A) and by confinement times close to those of Ohmic discharges. The high-βp regime develops at an injection power ≥1.9 MW, a mean density n¯e>~3×1013 cm−3, and a q(a) value ≥2.6. Beyond these limits or in discharges with material limiter, low βp values and reduced particle and energy confinement times are obtained compared to the Ohmic heating phase.
The impact of radially sheared poloidal flows on ambient edge turbulence in tokamaks is investigated analytically. In the regime where poloidal shearing exceeds turbulent radial scattering, a hybrid time scale weighted toward the former is found to govern the decorrelation process. The coupling between radial and poloidal decorrelation results in a suppression of the turbulence below its ambient value. The turbulence quench mechanism is found to be insensitive to the sign of either the radial electric field or its shear.
In a circular cross-section plasma bounded by a limiter, the H-mode transition is triggered by a rapid rampdown in plasma current during auxiliary heating, even in the case when the edge electron temperature gradually decreases prior to the transition. This result suggests that the transition is governed by the enhancement of the magnetic shear near the plasma edge, associated with the radial modification of the edge current-density profile.
The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry both numerically and analytically. For typical Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 51] and Texas Experimental Tokamak (TEXT) [Nucl. Technol. /Fusion 1, 479 (1981)] edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, j crit e , is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient. PACS numbers: 52.35.Kt, 52.35.Qz, 52.25.Gj, 52.55.Fa I.
Guideline for new subjects in this summary are the needs for next-step devices and for advanced tokamaks and stellarators. Improved wall conditioning allowed the power threshold to decrease and H-mode operation already under ohmic conditions becomes the typical case. Density-, helium exhaust-, and ELM control has been demonstrated for H-mode plasmas though still in a rather rudimentary form. Schemes of enhanced edge radiation can be reconciled with the H-mode specific edge conditions. Modelling of the SOL with ELMs has been started. There are several routes for further enhancements in confinement. As also the stability quality can thereby be improved, prospects of advanced tokamak operation with a large bootstrap current fraction in the H-mode seems favourable. As the advanced stellarator concept addresses primarily collisional transport and stability aspects, this line further improves its reactor prospects with the recently discovered H-mode in stellarators.
The thermal and particle diffusivities driven by resistive fluid turbulence in diverted tokamak edge plasmas are calculated. Diverted tokamak geometry is characterized by increased global shear near the separatrix and the tendency of field lines to linger near the x point. For resistive fluid turbulence, the dominant effect is increased global shear, which causes a reduction in the effective step size of the turbulent diffusion process and corresponding improvements in heat and particle confinement close to the separatrix. Stability of resistive kink modes resonant near separatrix is also ensured by the increased global shear. The relevance of these considerations to the L..-->..H transition and to the edge transport barrier in H-mode plasmas is discussed.
The mechanism for confinement improvement in the toroidal-rotation-induced very high mode (VH mode) may be the turbulence suppression due to the shear of the [ital toroidal] angular frequency associated with [ital parallel] flow. This explanation is in contrast to the plausible hypothesis that high-mode (H-mode) confinement improvement may be caused by the turbulence suppression due to the shear of the [ital poloidal] angular frequency associated with [bold E][times][bold B] and parallel flows. Here, [bold E] is the electric field and [bold B] is the magnetic field. A theory for VH mode, based on the rapid change of the radial gradient of the toroidal flow, is presented.
The poloidal momentum balance equation in tokamaks is shown to have bifurcated solutions; the poloidal flow velocity {ital U}{sub {ital p}} can suddenly become more positive when the ion collisionality decreases. The corresponding radial electric field {ital E}{sub {ital r}} becomes more negative, suppresses turbulent fluctuations, and improves plasma confinement. A heuristic argument is employed to illustrate the effects of {ital E}{sub {ital r}} on turbulent fluctuations. A more negative value of {ital E}{sub {ital r}} and/or a more positive value of {ital dE}{sub {ital r}} /{ital dr} can suppress the fluctuation amplitudes, if {ital dP}/{ital dr}{lt}0 (with {ital r} the local minor raidus and {ital P} the plasma pressure). The theory is employed to explain the L--H transition observed in tokamaks.
A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries. The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfve´n wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear-Alfve´n waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency.
A novel state of turbulent plasma characterized by small scale phase-space granulations called “clumps” is proposed. Clumps are produced when regions of different phase space density are mixed by the fluctuating electric field. They move along ballistic orbits and drive the turbulent field in a manner similar to that in which thermal fluctuations are driven by particle discreteness. In the coherent wave limit the clumps become the familiar trapped particle eddies of a Bernstein-Green-Kruskal mode. The turbulent state can exist in the absence of linear instability although it is more likely to occur in a linearly unstable plasma. The spectrum contains a ballistic portion as well as resonances at the wave (collective) frequencies. The discreteness of the clumps produces collision-like process. For example, the average distribution function satisfies a Fokker-Planck equation instead of a quasilinear diffusion equation.
The theory of ionization-driven drift wave turbulence is presented in the context of a quasilocal model. Linear analysis reveals that ionization effects can destabilize collisional drift waves and can possibly induce parallel shear flow instabilities, as well. Nonlinear analysis indicates that energy is transferred from large to small stable scales and converted to ion kinetic energy. Results indicate mode coupling effects are dominant. Large fluctuation levels, in excess of mixing length expectations, are predicted. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles that occurs in response to gas puffing.
The hypothesis of stabilization of turbulence by shear in the E×B drift speed successfully predicts the observed turbulence reduction and confinement improvement seen at the L (low)–H (high) transition; in addition, the observed levels of E×B shear significantly exceed the value theoretically required to stabilize turbulence. Furthermore, this same hypothesis is the best explanation to date for the further confinement improvement seen in the plasma core when the plasma goes from the H mode to the VH (very high) mode. Consequently, the most fundamental question for H‐mode studies now is: How is the electric field Er formed? The radial force balance equation relates Er to the main ion pressure gradient ∇Pi, poloidal rotation vθi, and toroidal rotation vϕi. In the plasma edge, observations show ∇Pi and vθi are the important terms at the L–H transition, with ∇Pi being the dominant, negative term throughout most of the H mode. In the plasma core, Er is primarily related to vϕi. There is a clear temporal and spatial correlation between the change in E×B shear and the region of local confinement improvement when the plasma goes from the H mode to the VH mode. Direct manipulation of the vϕi and E×B shear using the drag produced by a nonaxisymmetric magnetic perturbation has produced clear changes in local transport, consistent with the E×B shear stabilization hypothesis. The implications of these results for theories of the L–H and H–VH transitions will be discussed.
The enhanced decorrelation of fluctuations by the combined effects of the E×B flow (VE) shear, the parallel flow (V∥) shear, and the magnetic shear is studied in toroidal geometry. A two‐point nonlinear analysis previously utilized in a cylindrical model [Phys. Fluids B 2, 1 (1990)] shows that the reduction of the radial correlation length below its ambient turbulence value (Δr0) is characterized by the ratio between the shearing rate ωs and the ambient turbulence scattering rate ΔωT. The derived shearing rate is given by ω2s= (Δr0)2[(1/Δϕ2){(∂/∂r)(qVE/r)}2 +(1/Δη2){(∂/∂r)(V∥/qR)}2], where Δϕ and Δη are the correlation angles of the ambient turbulence along the toroidal and parallel directions. This result deviates significantly from the cylindrical result for high magnetic shear or for ballooning‐like fluctuations. For suppression of flute‐like fluctuations, only the radial shear of qVE/r contributes, and the radial shear of V∥/qR is irrelevant regardless of the plasma rotation direction.
High confinement mode ([ital H]-mode) discharges with peaked toroidal current density profile (high internal inductance, [ital l][sub [ital i]]) and improved confinement are obtained in the DIII-D tokamak by dynamically varying the current profile using a rapid elongation ramp technique. The confinement improvement increases with [ital l][sub [ital i]] and persists in the presence of edge-localized modes. The plasma toroidal rotation and the corresponding radial electric field component also increase with the peakedness of the current density profile.
Poloidal and toroidal rotation of the main ions (He[sup 2+]) and the impurity ions (C[sup 6+] and B[sup 5+]) in [ital H]-mode helium plasmas have been measured via charge exchange recombination spectroscopy in the DIII-D tokamak. It was discovered that the main ion poloidal rotation is in the [ital ion] [ital diamagnetic] [ital drift] direction while the impurity ion rotation is in the [ital electron] [ital diamagnetic] [ital drift] direction, in qualitative agreement with the neoclassical theory. The deduced radial electric field in the edge is of the same negative-well shape regardless of which ion species is used, validating the fundamental nature of the electric field in [ital L]-[ital H] transition phenomenology.
the radial shear of the angular rotation frequency· in perpendicular and parallel directions is given by a2 n
- Here
Here, the radial shear of the angular rotation frequency· in perpendicular and parallel directions is given by a2 n . ~ , = = - ( J ~ <1>0(1/1) and Phys. Plasmas, Vol. 2, No.5, May 1995
- M Thomas
M. Thomas, in Proceedings of the Fifteenth International Conference on
Plasma Physics and Controlled Nuclear Fusion Research, Seville, Spain,
September 1994 (International Atomic Energy Agency, Vienna, in press),
Paper No. lAEA-CN-60/A-2-I-5.
- Jot H Dupree
JOT. H. Dupree,Phys. Fluids IS, 334 (1972).
- Gt S Hahm
GT. S. Hahm, Phys. Plasmas 1, 2940 (1994).
- E Siller
- A Speth
- K H Stbler
- G Steuer
- O Yenus
- Z Vollmer
- Yu
Siller, E. Speth, A. Stbler, K. H. Steuer, G. yenus, O. Vollmer, and Z. Yu,
Phys. Rev. Lett. 49, 1408 (1982).
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