In this bachelor's thesis, isotope effects for pedestal instabilities have been studied based on an ASDEX Upgrade H-Mode scenario. This was done using the JOREK code for extended MHD simulations, including the ion diamagnetic drift and the establishment of ExB flows. Simulations with single toroidal harmonics were performed for multiple times during the build-up of the pedestal, to assess the evolution of the linear stability of modes occurring near the edge. When changing the average ion masses from 2.0 to 2.5 and 3.0, the variations were small, and MHD's momentum equation was shown to be the major cause for them. As a second step, simulations with multiple toroidal harmonics were performed to simulate an Edge Localized Mode (ELM) crash, again comparing between the average ion masses of 2.0, 2.5, and 3.0. The resulting variations of heat and particle losses were compared to JET results. The experimental differences between ion masses could not be reproduced. Together with the fact that the simulations' pedestal for an average ion mass of 2.5 and 3.0 was not matched to the experiment, this indicates that other effects, such as small-scale turbulences, must be included - for example, by adapting the simulations' transport coefficients - to explain the experimental differences.
Stronger impurity density in-out poloidal asymmetries than predicted by the most comprehensive neoclassical models have been measured in several tokamaks around the world during the last decade, calling into question the reduction of turbulence by sheared radial electric fields in H-mode tokamak pedestals. However, these pioneering theories neglect the impurity diamagnetic drift, or fail to retain it self-consistently; while recent measurements indicate that it can be of the same order as the ExB drift. We have developed the first self-consistent theoretical model retaining the impurity diamag…
Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher $β$ regimes, which leads to the flattening…
The spontaneous pedestal formation above a power threshold at the edge of magnetically confined plasma is modelled for the first time in flux driven three-dimensional fluid simulations of electromagnetic turbulence with the code EMEDGE3D. The role of the collisional friction between trapped and passing particles is shown to be the key ingredient for shearing the radial electric field, hence stabilizing the turbulence, rather than the Maxwell and Reynolds stresses. The isotope effect, observed in many tokamaks worldwide, is recovered in EMEDGE3D simulations: the power threshold for pedestal for…
Plasma equilibria reconstructed from the Mega-Amp Spherical Tokamak (MAST) have sufficient resolution to capture plasma evolution during the short period between edge-localized modes (ELMs). Immediately after the ELM steep gradients in pressure, P, and density, ne, form pedestals close to the separatrix, and they then expand into the core. Local gyrokinetic analysis over the ELM cycle reveals the dominant microinstabilities at perpendicular wavelengths of the order of the ion Larmor radius. These are kinetic ballooning modes (KBMs) in the pedestal and microtearing modes (MTMs) in the core clos…
The characteristic profile and magnitude are predicted in theory for the neoclassical toroidal viscosity (NTV) torque induced by plasma response to the resonant magnetic perturbation (RMP) in a tokamak with an edge pedestal. For a low-$β$ equilibrium, the NTV torque is dominated by the toroidal component with the same dominant toroidal mode number of RMP. The NTV torque profile is found to be localized, whose peak location is determined by profiles of both the equilibrium temperature (pressure) and the plasma response. In general, the peak of NTV torque profile is found to track the pedestal p…
In a tokamak pedestal, radial scale lengths can become comparable to the ion orbit width, invalidating conventional neoclassical calculations of flow and bootstrap current. In this work we illustrate a non-local approach that allows strong radial density variation while maintaining small departures from a Maxwellian distribution. Non-local effects alter the magnitude and poloidal variation of the flow and current. The approach is implemented in a new global delta-f continuum code using the full linearized Fokker-Planck collision operator. Arbitrary collisionality and aspect ratio are allowed a…
Global electromagnetic gyrokinetic simulations show the existence of near threshold conditions for both a high-$n$ kinetic ballooning mode (KBM) and an intermediate-$n$ kinetic version of peeling-ballooning mode (KPBM) in the edge pedestal of two DIII-D H-mode discharges. When the magnetic shear is reduced in a narrow region of steep pressure gradient, the KPBM is significantly stabilized, while the KBM is weakly destabilized and hence becomes the most-unstable mode. Collisions decrease the KBM's critical $β$ and increase the growth rate.
Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of Edge Lo- calised Modes, the inter-ELM pedestal, and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other are covered in detail. This framework is completely self-consistent; it is derived fr…
The structure of poloidal and toroidal flows of trace impurities in the edge pedestal of tokamak plasmas is studied analytically and numerically. Parallel momentum balance is analysed upon retaining the following terms: poloidal and toroidal centrifugal forces (inertia), pressure force, electric force, and the friction force. It is shown that, when the poloidal flow is such to produce a properly defined Mach number of order unity somewhere on the flux surface, shock fronts can form. The shock fronts can modify the predicted asymmetry structures in both the flow and the density profile along th…
Conventional radially-local neoclassical calculations become inadequate if the radial gradient scale lengths of the H-mode pedestal become as small as the poloidal ion gyroradius. Here, we describe a radially global $δf$ continuum code that generalizes neoclassical calculations to allow stronger gradients. As with conventional neoclassical calculations, the formulation is time-independent and requires only the solution of a single sparse linear system. We demonstrate precise agreement with an asymptotic analytic solution of the radially global kinetic equation in the appropriate limits of aspe…
Starting from expressions in Connor et al. (1988) [1], we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna and Callen (1984) [2] and by Nishimura et al (1998) [3], but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. JET. We discuss how this one-dimensional model fo…
In the pedestal of a tokamak, the sharp radial gradients of density and temperature can give rise to poloidal variation in the density of impurities. At the same time, the flow of the impurity species is modified relative to the conventional neoclassical result. In this paper, these changes to the density and flow of a collisional impurity species are calculated for the case when the main ions are in the plateau regime. In this regime it is found that the impurity density can be higher at either the inboard or outboard side. This finding differs from earlier results for banana- or Pfirsch-Schl…
Impurity-driven turbulence opens a pathway to ELM-free operation and enhanced pedestal stability in tokamaks
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；General Atomics（通用原子公司）；UCLA（加州大学洛杉矶分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Pedestal is the key to conventional high performance plasma scenarios in tokamaks. However, high fidelity simulations of pedestal plasmas are extremely challenging due to the multiple physical processes and scales that are encompassed by tokamak pedestals. The leading paradigm for predicting the pedestal top pressure is encompassed by EPED-like models. However, EPED does not predict the pedestal top density, $n_\text{e,ped}$, but requires it as an input. EUROPED employs simplified models, such as log-linear regression, to constrain $n_\text{e,ped}$ with tokamak machine control parameters in an…
Quasi-periodic Pedestal Burst Instabilities (PBIs), featuring alternative turbulence suppression and bursts, have been clearly identified by various edge diagnostics during I-mode to H-mode transition in the EAST Tokamak. The radial distribution of the phase perturbation caused by PBI shows that PBI is localized in the pedestal. Prior to each PBI, a significant increase of density gradient close to the pedestal top can be clearly distinguished, then the turbulence burst is generated, accompanied by the relaxation of the density profile, and then induces an outward particle flux. The relative d…
In some conditions, I-mode plasmas can feature pedestal relaxation events (PREs) that transiently enhance the energy reaching the divertor target plates. To shed light into their appearance, characteristics and energy reaching the divertor targets, a comparative study between two tokamaks $-$ Alcator C-Mod and ASDEX Upgrade $-$ is carried out. It is found that PREs appear only in a subset of I-mode discharges, mainly when the plasma is close to the H-mode transition. Also, the nature of the triggering instability is discussed by comparing measurements close to the separatrix in both devices. T…
The density dependence of edge-localized-mode (ELM) suppression and density pump-out (density reduction) by n = 2 resonant magnetic perturbations (RMPs) is consistent with the effects of narrow well-separated magnetic islands at the top and bottom of the H-mode pedestal in DIII-D low-collisionality plasmas. Nonlinear two-fluid MHD simulations for DIII-D ITER Similar Shape (ISS) discharges show that, at low collisionality, low pedestal density is required for resonant field penetration at the pedestal top, consistent with the ubiquitous low density requirement for ELM suppression in these DIII-…
In this paper, we develop the kinetic and hydrodynamic theories of the convective mesoscale flows driven by the spatially inhomogeneous electrostatic ion cyclotron parametric microturbulence in the pedestal plasma with a sheared poloidal flow. The developed kinetic theory predicts the generation of the sheared poloidal convective flow, and of the radial compressed flow with radial flow velocity gradient. The developed hydrodynamic theory of the convective flows reveals the radial compressed convective flow as the dominant factor in the formation of the steep pedestal density profile with densi…
Recently, theoretical analysis has identified plasma microinstabilities as the primary mechanism responsible for anomalous heat transport in tokamaks. In particular, the microtearing mode (MTM) has been credited with the production of intense electron heat fluxes, most notably through a thin self-organized boundary layer called the pedestal. Here we exploit a novel, time-dependent analysis to compile explicit experimental evidence that MTMs are active in the pedestal region. The expected frequency of pedestal MTMs, calculated as a function of time from plasma profile measurements, is shown in …
The local intrinsic parallel current density driven by electron drift wave (DW) turbulence including electromagnetic (EM) effects is analytically studied. The scalings of the ratios of intrinsic current density driven by residual turbulent flux and by turbulent source to the bootstrap current density with electron density and temperature are predicted to be $T_e^{3/4}T_i/n_e$ and $T_eT_i/n_e$, respectively. Based on the typical parameters in DIII-D pedestal region, the local intrinsic current density driven by both the residual turbulent flux and the turbulent source is negligible. However, de…
Ion orbit loss is considered important for generating the radially inward electric field $E_r$ in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code…
We present a numerical study of collisional transport in a tokamak pedestal in the presence of non-trace impurities, using the radially global $δf$ neoclassical solver PERFECT [M. Landreman et al. 2014 Plasma Phys. Control. Fusion 56 045005]. It is known that in a tokamak core with non-trace impurities present the radial impurity flux opposes the bulk ion flux to provide an ambipolar particle transport, with the electron transport being negligibly small. However, in a sharp density pedestal with sub-sonic ion flows the electron transport can be comparable to the ion and impurity flows. Further…
Microtearing modes (MTMs) are unstable in the shallow gradient region just inside the top of the pedestal in the spherical tokamak experiment MAST, and may play an important role in the pedestal evolution. The linear properties of these instabilities are compared with MTMs deeper inside the core, and further detailed investigations expose the basic drive mechanism. MTMs near the MAST pedestal top are not well described by existing theories. In particular the growth rate of the dominant edge MTM does not peak at a finite collision frequency, as frequently reported for MTMs further into the core…
Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor q95) in the DIII-D tokamak. However, wide q95 ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER Similar Shape (ISS) plasmas with n=3 RMPs, the range of q95 for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed q95 windows of ELM suppression and the dependence on plasma densit…
Poloidal asymmetries in the impurity density can be generated by radio frequency heating in the core and by neoclassical effects in the edge of tokamak plasmas. In a pedestal case study, using global neoclassical simulations we find that finite orbit width effects can generate significant poloidal variation in the electrostatic potential, which varies on a small radial scale. Gyrokinetic modeling shows that these poloidal asymmetries can be strong enough to significantly modify turbulent impurity peaking. In the pedestal the ExB drift in the radial electric field can give a larger contribution…
We present that a statistical method known as the Complexity-Entropy analysis is useful to characterize a state of plasma turbulence and flux in the resonant magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The RMP ELM suppression phase with the stochastic pedestal top temperature fluctuation can be distinguished from the natural ELM free phase with the chaotic fluctuation. It is discussed that the stochastic temperature fluctuation localized near the pedestal top can be originated from the narrow layer of the field penetration near the pedestal top. The forced magneti…
Nitrogen-induced ELM suppression and confinement improvement in the EAST tokamak with a full metal wall
School of the Gifted Young, University of Science and Technology of China（中国科学技术大学少年班）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院）；Southwestern Institute of Physics（西南物理研究所）
The plasma response to an externally generated, static, n=2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D discharge #158115 is investigated. In this particular discharge, the resonant amplitudes of the RMP are modulated in a cycloidal manner at a frequency of 1 Hz. Adopting the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of edge localized modes (ELMs), recent cylindrical, nonlinear, reduced-magnetohydrodynamical (MHD) simulations performed by Hu, Nazikian, et al., (2019) c…
Access conditions for full suppression of Edge Localised Modes (ELMs) by Magnetic Perturbations (MP) in low density high confinement mode (H-mode) plasmas are studied in the ASDEX Upgrade tokamak. The main empirical requirements for full ELM suppression in our experiments are: 1. The poloidal spectrum of the MP must be aligned for best plasma response from weakly stable kink-modes, which amplify the perturbation, 2. The plasma edge density must be below a critical value, $3.3 \times 10^{19}$~m$^{-3}$. The edge collisionality is in the range $ν^*_i = 0.15-0.42$ (ions) and $ν^*_e = 0.15-0.25$ (e…
The complete refuelling of the plasma density loss (pump-out) caused by mitigation of Edge Localised Modes (ELMs) is demonstrated on the ASDEX Upgrade tokamak. The plasma is refuelled by injection of frozen deuterium pellets and ELMs are mitigated by external resonant magnetic perturbations (RMPs). In this experiment relevant dimensionless parameters, such as relative pellet size, relative RMP amplitude and pedestal collisionality are kept at the ITER like values. Refuelling of density pump out requires a factor of two increase of nominal fuelling rate. Energy confinement and pedestal temperat…
The extended-MHD NIMROD code [C.R. Sovinec and J.R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H.R. Wilson et al. Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD model complexity is increased incrementally, resistive and first-order finite-Larmour radius effects are destabilizing and stabilizing, respectively. The full result is compared to local analytic calculations which are found to overpredict both the resistive destabilization and drift stabilization in comparison to the NIMROD computations.
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 dr…
Understanding the multi-scale neoclassical and turbulence physics in the edge region (pedestal + scrape-off layer) is required in order to reliably predict performance in future fusion devices. We explore turbulent characteristics in the edge region from a multiscale neoclassical and turbulent XGC1 gyrokinetic simulation in a DIII-D like tokamak geometry, here excluding neutrals and collisions. For an H-mode type plasma with steep pedestal, it is found that the electron density fluctuations increase towards the separatrix, and stay high well into the SOL, reaching a maximum value of $δn_e / \b…
Ion cyclotron emission (ICE) is detected during edge localised modes (ELMs) in the KSTAR tokamak at harmonics of the proton cyclotron frequency in the outer plasma edge. The emission typically chirps downward (occasionally upward) during ELM crashes, and is driven by confined 3MeV fusion-born protons that have large drift excursions from the plasma core. We exploit fully kinetic simulations at multiple plasma densities to match the time-evolving features of the chirping ICE. This yields a unique, very high time resolution diagnostic of the collapsing edge pedestal density.
Using a high-speed and broadband radio frequency (RF) (0.1-1 GHz) spectrum analyzer developed on the KSTAR tokamak, it is found that several distinct stages of RF emission appear at the pedestal collapse in high confinement discharges. Comparison with 2-D electron cyclotron emission (ECE) images has revealed that each stage is related to the instantaneous condition at the outboard mid-plane edge. First, high-harmonic ion cyclotron emissions (ICE) are intensified with the appearance of a non-modal filamentary perturbation in the edge within several tens of microseconds before the collapse. Then…
Modeling Temperature Profiles in the Pedestal of NSTX with Reduced Models
Institute for Fusion Studies, The University of Texas at Austin（德克萨斯大学奥斯汀分校聚变研究所）；ExoFusion；Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学研究所）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
In tokamak transport barriers, the radial scale of profile variations can be comparable to a typical ion orbit width, which makes the coupling of the distribution function across flux surfaces important in the collisional dynamics. We use the radially global steady-state neoclassical δf code Perfect to calculate poloidal and toroidal flows, and radial fluxes, in the pedestal. In particular, we have studied the changes in these quantities as the plasma composition is changed from a deuterium bulk species with a helium impurity to a helium bulk with a deuterium impurity, under specific profile s…
The diamagnetic drift effects on the low-$n$ magnetohydrodynamic instabilities at the high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation effects for stability, where $n$ is the toroidal mode number. The AEGIS (Adaptive EiGenfunction Independent Solutions) code [L. J. Zheng, M. T. Kotschenreuther, J. Comp. Phys. {\bf 211}, (2006)] is extended to include the diamagnetic drift effects. This can be viewed as the lowest order approximation of the finite Larmor radius effects in consideration of the pressure gradient steepn…
Hollow toroidal rotation profiles in strongly electron heated H-mode plasmas in the ASDEX Upgrade tokamak
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Department of Applied Physics and Applied Mathematics, Columbia University（哥伦比亚大学应用物理与应用数学系）；VTT（芬兰技术研究中心VTT）
Understanding turbulent transport physics in the tokamak edge and scrape-off layer (SOL) is critical to developing a successful fusion reactor. The dynamics in these regions plays a key role in achieving high fusion performance by determining the edge pedestal that suppresses turbulence in H-mode. Additionally, the survivability of a reactor is set by the heat load to the vessel walls, making it important to understand turbulent spreading of heat as it flows along open magnetic field lines in the SOL. Large-amplitude fluctuations, magnetic X-point geometry, and plasma interactions with materia…
Machine learning methods for modelling local, linear gyrokinetic simulations of MAST-U pedestal turbulence
VTT Technical Research Centre of Finland（芬兰技术研究中心）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Institute for Fusion Studies, University of Texas at Austin（德克萨斯大学奥斯汀分校聚变研究所）；UK Atomic Energy Authority（英国原子能管理局）
On the basis of three-dimensional nonlinear magnetohydrodynamic simulations, we propose a new dynamical process leading to the stochastization of magnetic fields during an edge pedestal collapse. Primary tearing modes are shown to grow by extracting kinetic energy of unstable ballooning modes, eventually leading to the island overlap. Secondary tearing modes, which are generated through a coherent nonlinear interaction between adjacent ballooning modes, play a key role in this process, mediating the energy transfer between primary ballooning and tearing modes. Explicit calculations of the para…
Instability to high toroidal mode number ($n$) ballooning modes has been proposed as the primary gradient-limiting mechanism for tokamak equilibria with negative triangularity ($δ$) shaping, preventing access to strong H-mode regimes when $δ\ll0$. To understand how this mechanism extrapolates to reactor conditions, we model the infinite-$n$ ballooning stability as a function of internal profiles and equilibrium shape using a combination of the CHEASE and BALOO codes. While the critical $δ$ required for avoiding $2^\mathrm{nd}$ stability to high-$n$ modes is observed to depend in a complicated …
