Neoclassical and gyrokinetic analysis of time-dependent helium transport experiments on MAST
S. S. Henderson, L. Garzotti, F. J. Casson, D. Dickinson, M. F. J. Fox, M. O'Mullane, A. Patel, C. M. Roach, H. P. Summers, M. Valovic, the MAST team
备注：
22 pages, 12 figures. This is an author-created, un-copyedited version of an article accepted for publication in Nuclear Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it
发表信息：
Nuclear Fusion, Vol.54, No.9, September 2014, pp.093013
Time-dependent helium gas puff experiments have been performed on the Mega Ampere Spherical Tokamak (MAST) during a two point plasma current scan in L-mode and a confinement scan at 900 kA. An evaluation of the He II spectrum line induced by charge exchange suggests anomalous rates of diffusion and inward convection in the outer regions of both L-mode plasmas. Similar rates of diffusion are found in the H-mode plasma, however these rates are consistent with neoclassical predictions. The anomalous inward pinch found in the core of L-mode plasmas is also not apparent in the H-mode core. Linear gyrokinetic simulations of one flux surface in L-mode using the gs2 and gkw codes find that equilibrium flow shear is sufficient to stabilise ITG modes, consistent with BES observations, and suggest that collisionless TEMs may dominate the anomalous helium particle transport. A quasilinear estimate of the dimensionless peaking factor associated with TEMs is in good agreement with experiment. Collisionless TEMs are more stable in H-mode because the electron density gradient is flatter. The steepness of this gradient is therefore pivotal in determining the inward neoclassical particle pinch and the particle flux associated with TEM turbulence.
The purpose of this document is to find an analytical solution for the gyrokinetic equation under specific, simplificative hypotheses. The case I am considering is that of a collisional plasma in the presence of a chain of magnetic islands. The presence of the magnetic islands causes the onset of perturbative fields, in particular an electrostatic field, with a gradient length-scale comparable with the island's width. When the island's width w becomes comparable with the ion Larmor radius rho_i , the drift-kinetic equation is inadequate to treat the transport and the calculation of the neoclas…
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…
Intrinsic toroidal rotation in a tokamak can be driven by turbulent momentum transport due to neoclassical flow effects breaking a symmetry of turbulence. In this paper we categorize the contributions due to neoclassical effects to the turbulent momentum transport, and evaluate each contribution using gyrokinetic simulations. We find that the relative importance of each contribution changes with collisionality. For low collisionality, the dominant contributions come from neoclassical particle and parallel flows. For moderate collisionality, there are non- negligible contributions due to neocla…
Self-consistent simulations of neoclassical and electrostatic turbulent transport in a DIII-D H-mode edge plasma under resonant magnetic perturbations (RMPs) have been performed using the global total-f gyrokinetic particle-in-cell code XGC, in order to study density-pump out and electron heat confinement. The RMP field is imported from the extended magneto-hydrodynamics (MHD) code M3D-C1, taking into account the linear two-fluid plasma response. With both neoclassical and turbulence physics considered together, the XGC simulation reproduces two key features of experimentally observed edge tra…
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…
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…
Carbon and nitrogen impurity transport coefficients are determined from gas puff experiments carried out during repeat L-mode discharges on the Mega-Amp Spherical Tokamak (MAST) and compared against a previous analysis of helium impurity transport on MAST. The impurity density profiles are measured on the low-field side of the plasma, therefore this paper focuses on light impurities where the impact of poloidal asymmetries on impurity transport is predicted to be negligible. A weak screening of carbon and nitrogen is found in the plasma core, whereas the helium density profile is peaked over t…
Boundary plasma physics plays an important role in tokamak confinement, but is difficult to simulate in a gyrokinetic code due to the scale-inseparable nonlocal multi-physics in magnetic separatrix and open magnetic field geometry. Neutral particles are also an important part of the boundary plasma physics. In the present paper, noble electrostatic gyrokinetic techniques to simulate the flux-driven, low-beta electrostatic boundary plasma is reported. Gyrokinetic ions and drift-kinetic electrons are utilized without scale-separation between the neoclassical and turbulence dynamics. It is found …
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in a gyrokinetic simulation carried out in a realistic tokamak edge geometry. The results show that turbulent Reynolds stress driven sheared ExB flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just…
The kinetic effects of electrons are important to long wavelength magnetohydrodynamic(MHD)instabilities and short wavelength drift-Alfvenic instabilities responsible for turbulence transport in magnetized plasmas, since the non-adiabatic electron can interact with, modify and drive the low frequency instabilities. A novel conservative split weight scheme is proposed for the electromagnetic simulation with drift kinetic electrons in tokamak plasmas, which shows great computational advantages that there is no numerical constrain of electron skin depth on the perpendicular grid size without sacri…
This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium d…
Gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are delta-f simulations in which the slowly varying radial profiles of density and temperature are assumed to be constant for turbulence saturation times, and only the turbulent electromagnetic fluctuations are calculated. New massive simulations are being built to self-consistently determine the radial profiles of density and temperature. However, these new codes have failed to realize that modern gyrokinetic formulations, composed of a gyrokinet…
The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, document…
Development and validation of a local neoclassical transport module in NLT with applications to EAST-relevant impurity transport and trapped-electron-mode stability
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences（中国科学院合肥物质科学研究院等离子体物理研究所）；University of Science and Technology of China（中国科学技术大学）
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）
Observations of ion-scale (k_y*rho_i <= 1) density turbulence of relative amplitude dn_e/n_e <= 0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial x 4 poloidal channel) imaging Beam Emission Spectroscopy (BES) diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport b…
In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators -- while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources -- are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein…
Non-linear, radially global, turbulence simulations of ASDEX Upgrade (AUG) plasmas are performed and the nonlinear generated intrinsic flow shows agreement with the intrinsic flow gradients measured in the core of Ohmic L-mode plasmas at nominal parameters. Simulations utilising the kinetic electron model show hollow intrinsic flow profiles as seen in a predominant number of experiments performed at similar plasma parameters. In addition, significantly larger flow gradients are seen than in a previous flux-tube analysis (Hornsby et al {\it Nucl. Fusion} (2017)). Adiabatic electron model simula…
Neoclassical and turbulent heavy impurity transport in tokamak core plasmas are determined by main ion temperature, density and toroidal rotation profiles. Thus, in order to understand and prevent experimental behaviour of W accumulation, flux-driven integrated modelling of main ion heat and particle transport over multiple confinement times is a vital prerequisite. For the first time, the quasilinear gyrokinetic code QuaLiKiz has been applied for successful predictions of core kinetic profiles in an ASDEX Upgrade H-mode discharge in the turbulence dominated region within the integrated modell…
Pedestal profiles that span the ELM cycle have been obtained and used to test the idea that the pedestal pressure gradient in MAST is limited by the onset of Kinetic Ballooning Modes (KBMs). During the inter-ELM period of a regularly type I ELM-ing discharge on MAST, the pressure pedestal height and width increase together while the pressure gradient increases by only 15 % during the ELM cycle. Stability analyses show that the pedestal region over which infinite-n ballooning modes are unstable also broadens during the ELM cycle. To test the relationship between the width of the region that is …
Tokamak plasmas rotate even without external injection of momentum. A Doppler backscattering system installed at MAST has allowed this intrinsic rotation to be studied in Ohmic L-mode and H-mode plasmas, including the first observation of intrinsic rotation reversals in a spherical tokamak. Experimental results are compared to a novel 1D model, which captures the collisionality dependence of the radial transport of toroidal angular momentum due to the effect of neoclassical flows on turbulent fluctuations. The model is able to accurately reproduce the change in sign of core toroidal rotation, …
Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the po…
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 the Wendelstein 7-X magnetic confinement experiment, a reduction of turbulent density fluctuations as well as anomalous impurity diffusion is associated with a peaking of the plasma density profile. These effects correlate with improved confinement and appear largely due to a reduction of anomalous transport as the change in neoclassical transport is small. The observed decrease of turbulent heat flux with increased density gradients is in agreement with nonlinear gyrokinetic simulations, and has been attributed to the unique geometry of W7-X that limits the severity of trapped electron mod…
The flow shear associated with the differential toroidal rotation of tokamak plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by the up-down symmetry of the magnetic equilibrium. Using experimental Beam-Emission-Spectroscopy (BES) measurements and gyrokinetic simulations, this symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself as a tilt of the spatial correlation function and a finite skew in the distribution of the fluctuating density field. The tilt is a statistical expression of the "shearing" of the turbulent structures by the mean flow…
The global total-$f$ gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas, implements a continuum grid to perform the dissipative operations, such as plasma collisions. To transfer the distribution function between marker particles and a rectangular velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large in special conditions. In the present work we update XGC to use a novel mapping tech…
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…
We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial…
Reactor grade plasmas are likely to be fuelled by pellet injection. This technique transiently perturbs the profiles, driving the density profile hollow and flattening the edge temperature profile. After the pellet perturbation, the density and temperature profiles relax towards their quasi-steady-state shape. Microinstabilities influence plasma confinement and will play a role in determining the evolution of the profiles in pellet fuelled plasmas. In this paper we present the microstability analysis of pellet fuelled H-mode MAST plasmas. Taking advantage of the unique capabilities of the MAST…
We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate…
