Turbulent Particle Flux Research Articles

Prediction of urban ultrafine particle emission fluxes using generalized additive models

Ultrafine particles (UFP) are abundant in urban atmospheres. To assess the strength and temporal variation of urban UFP emission sources, information on the surface-atmosphere exchange, i.e. the turbulent vertical flux of particles, is vital. A three-year time series of UFP emission fluxes (FUFP) observed at an urban site in Berlin, Germany, using the eddy covariance technique was utilized to develop and evaluate generalized additive models (GAM) for FUFP. GAM allow to account for non-linear relationships between response and predictor variables. Two separate models for summer and winter were developed. The predictors that most strongly influenced modelled FUFP in the summer model were traffic activity, friction velocity, land use, air temperature and PM10 concentration, whereas the winter model additionally incorporated relative humidity. The GAM were evaluated by ten-fold cross-validation for the first two study years, and by predicting the third year based on the model trained with observational data of the first two years. The coefficients of determination of the two validation methods were R2 = 0.52 (uncertainty of −47 to 88% for FUFP) and R2 = 0.48 (−45 to 82% for FUFP) for the winter model, whereas the summer model yielded R2 = 0.48 and 0.44 (uncertainty of −51 to 102%). GAM were shown to successfully capture the non-linear relationships between predictor variables and FUFP for the three-year data set at this urban site.

Stability and transport of gyrokinetic critical pedestals

A gyrokinetic threshold model for pedestal width–height scaling prediction is applied to multiple devices. A shaping and aspect ratio scan is performed on National Spherical Torus Experiment (NSTX) equilibria, finding Δped=0.92A1.04κ−1.240.38δβθ,ped1.05 for the wide-pedestal branch with pedestal width Δped , aspect ratio A, elongation κ, triangularity δ, and normalized pedestal height βθ,ped . The width–transport scaling is found to vary significantly if the pedestal height is varied either with a fixed density or fixed temperature, showing how fueling and heating sources affect the pedestal density and temperature profiles for the kinetic-ballooning-mode (KBM) limited profiles. For an NSTX equilibrium, at fixed density, the wide branch is Δped=0.028(qe/Γe−1.7)1.5∼ηe1.5 and at fixed temperature Δped=0.31(qe/Γe−4.7)0.85 ∼ηe0.85 , where qe and Γe are turbulent electron heat and particle fluxes and ηe=∇ln⁡Te/∇ln⁡ne for an electron temperature Te and density ne . Pedestals close to the KBM limit are shown to have modified turbulent transport coefficients compared to the strongly driven KBMs. The role of flow shear is studied as a width–height scaling constraint and pedestal saturation mechanism for a standard and lithiated wide pedestal discharge. Finally, the stability, transport, and flow shear constraints are combined and examined for an NSTX experiment.

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Divertor turbulent transport in the single null and snowflake in the TCV tokamak

The relative importance of divertor radial turbulent particle fluxes is considered by comparing it against the fluxes in the main-chamber outer midplane (OMP) in a variety of conditions and divertor geometries in the tokamak à configuration variable. Within the first power falloff length, the radial turbulent fluxes in the leg of the outer divertor are consistently found to be small, and about 1/5th the magnitude measured at the OMP. In a low-density single null divertor, magnetic shear is found to play a strong role in isolating the main-chamber turbulence from the divertor. The snowflake divertor is purported to have turbulence-enhancing properties in the volume between the two X-points but was instead found to further reduce the divertor turbulent fluxes compared to the single null. Depending on the collisionality, the electric field fluctuations and radial turbulent fluxes were higher near the X-point than at the outer midplane, which is likely due to the binormal compression of the flux bundles consistent with analytical models of the resistive X-point mode. Density and potential fluctuation amplitudes decrease monotonically with distance from the OMP with a slope that depends on collisionality.

Analysis of Turbulent Particle Fluxes in Reduced MHD Simulation

Analysis of Turbulent Particle Fluxes in Reduced MHD Simulation

Radially inward particle transport driven by low-frequency instability in cylindrical magnetized plasma

Net radially inward turbulent particle flux was observed in a linear plasma device, the linear experimental advanced device (LEAD). The amplitude of the inward particle flux is comparable with outward particle flux. The inward particle flux peak value locates in the outer E r shear layer. Cross-phase evolution dominates the radial evolution of particle flux from outward to inward. In the frequency domain, a 1 kHz mode contributes most of the inward particle flux. Frequency-resolved energy transfer analysis infers that this mode obtains energy nonlinearly from very low frequency fluctuations below 0.5 kHz. Moreover, turbulence spreading could also transfer energy to the position where the inward flux peak locates from nearby positions, and thus acts as a nonlocal, nonlinear drive for the 1 kHz mode.

Edge turbulence transport during ELM suppression with n = 4 resonant magnetic perturbation on EAST

The edge turbulence characteristics and the induced radial transport have been investigated in edge localized mode (ELM) suppression by using the 4 resonant magnetic perturbation coils on EAST, with 3.6 and the electron collisionality 0.5. During ELM suppression, the edge turbulence is enhanced dramatically, as measured by the reciprocating probe and the poloidal correlation reflectometry. In the near SOL, the low frequency turbulence (<30 kHz) has a large fluctuation level and propagates along the ion diamagnetic drift direction with a speed of 0.35 km s−1 in the plasma frame; an electromagnetic mode around 120 kHz with a small (∼0.15 cm−1) appears when the ELM is suppressed; weak broadband turbulence between 40–120 kHz propagates in the electron diamagnetic drift direction with a velocity of 3.4 km s−1 in the plasma frame. During the ELM suppression, the radial turbulent particle flux, calculated in both the time and frequency domains, is much higher (can be up to five times) than that in the inter-ELM phase. Furthermore, the low frequency turbulence (<30 kHz) dominates the cross-field particle transport. The 120 kHz electromagnetic mode also contributes to outward particle flux, which is relatively small. A set of CGYRO simulations are performed to illustrate the nature of the 120 kHz electromagnetic mode and the low frequency turbulence, suggesting that the former is the micro-tearing mode and the latter is the ion temperature gradient mode. The bispectral analysis suggests a strong three-wave coupling between the low frequency and high frequency turbulence (>250 kHz), which could be beneficial to form the observed turbulent transport. The estimated upstream cross-field particle flux is consistent with the total particle flux deposited on divertor targets, demonstrating that the enhanced radial turbulent particle transport is an important mechanism for particle exhaust in ELM suppression.

Gyrokinetic Turbulent Transport Simulations on Steady Burning Condition in D-T-He Plasmas

Ion temperature gradient (ITG) and trapped electron modes (TEM) driven turbulent transport in an ITER-like plasma is investigated by means of multi-species gyrokinetic Vlasov simulations with D, T, He, and real-mass kinetic electrons including their inter-species collisions. Beyond the conventional zero-dimensional power balance analysis presuming the global energy and particle confinement times, gyrokinetic-simulation-based evaluation of a steady burning condition with He-ash exhaust and D-T fuel inward pinch is demonstrated. It is clarified that a significant imbalance appears in the turbulent particle Žflux for the fuel ions of D and T, depending on the D-T density ratio and the He-ash accumulation. Then several profile regimes to satisfy Reiter’s steady burning condition are, for the first time, identified by the gyrokinetic simulation. Also, the impacts of zonal Žflows and nonthermal He-ash on the optimal profile regimes are examined.

A self‐consistent mean‐field model for turbulent particle and heat transport in 2D interchange‐dominated electrostatic ExB turbulence in a sheath‐limited scrape‐off layer

AbstractIn this paper, a self‐consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange‐dominated electrostatic ExB drift turbulence in sheath‐limited scrape‐off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy (). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for through the interchange source. A series decomposition of the sheath term in the equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath‐driven conducting‐wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self‐saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean‐field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

Limit cycle oscillations, response time, and the time-dependent solution to the Lotka–Volterra predator–prey model

In this work, the time-dependent solution for the Lotka–Volterra predator–prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit cycle oscillations and also for the response time between predator and prey population. These results are applied to the predator–prey interaction of zonal density corrugations and turbulent particle flux in gyrokinetic simulations of the collisionless trapped-electron mode turbulence. In the turbulence simulations, the response time is shown to increase when approaching the linear threshold, and the same trend is observed in the Lotka–Volterra model.

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

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

Turbulent transport in the scrape-off layer of Wendelstein 7-X

Turbulent transport is widely considered to be the main driver for cross-field transport in the scrape-off layer (SOL) of toroidal magnetized plasmas. Here, reciprocating Langmuir probes are employed to measure both the plasma profiles and the turbulent particle transport in the SOL of the Wendelstein 7-X stellarator. The relation between turbulent radial particle flux Γr and the local pressure gradient is often approximately linear across the entire SOL width, indicating that radial turbulence spreading is absent. This observation holds across a wide range of magnetic configurations and different plasma heating and density scenarios. The magnitude of the turbulent transport for a given gradient reveals a dependence on the magnetic configuration and the position in the SOL, which we relate to the cross-spectral characteristics of multi-tip floating potential measurements. Magnetic islands can add further complexity due to non-monotonic SOL profiles and the breaking of the transport-gradient relation. Finally, anomalous diffusion coefficients are determined from the probe measurements.

Evolution of Heavy Ion Beam Probing from the Origins to Study of Symmetric Structures in Fusion Plasmas

The overview discusses development of the unique fusion plasma diagnostics—Heavy Ion Beam Probing (HIBP) in application to toroidal magnetic plasma devices. The basis of the HIBP measurements of the plasma electric potential and processing of experimental data are considered. Diagnostic systems for probing plasma in tokamaks TM-4, TJ-1, TUMAN-3M and T-10, stellarators WEGA, TJ-II and Uragan-2M are presented. Promising results of the HIBP projects for various existing modern machines, such as TCV, TCABR, MAST, COMPASS, GLOBUS-M2, T-15 MD and W7-X and the international fusion tokamak reactor ITER are given. Results from two machines with similar size and plasma parameters, but with different types of the magnetic con-figuration: axisymmetric tokamak T-10 and helically symmetric stellarator TJ-II are compared. The results of studies of stationary potential profiles and oscillations in the form of quasimonochromatic and broadband fluctuations, turbulent particle flux, fluctuations of density and poloidal magnetic field are presented. The properties of symmetric structures—zonal flows and geodesic acoustic modes of plasma oscillations as well as Alfvén Eigenmodes excited by fast particles from neutral beam injection heating are described. General trends in the behavior of electric potential and turbulence in magnetized fusion plasmas are revealed.

Energy and flux budget closure theory for passive scalar in stably stratified turbulence

The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification, and it implies that turbulence is maintained by the velocity shear at any stratification. In a steady-state, expressions for the turbulent flux of the passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are derived, and universal flux Richardson number dependencies of the components of this tensor are obtained. The diagonal component in the vertical direction of the turbulent diffusion tensor is suppressed by strong stratification, while the diagonal components in the horizontal directions are not suppressed, but they are dominant in comparison with the other components of the turbulent diffusion tensor. This implies that any initially created strongly inhomogeneous particle cloud is evolved into a thin pancake in a horizontal plane with very slow increase in its thickness in the vertical direction. The turbulent Schmidt number (the ratio of the eddy viscosity and the vertical turbulent diffusivity of the passive scalar) linearly increases with the gradient Richardson number. The physics of such a behavior is related to the buoyancy force that causes a correlation between fluctuations of the potential temperature and the particle number density. This correlation that is proportional to the product of the vertical turbulent particle flux and the vertical gradient of the mean potential temperature reduces the vertical turbulent particle flux. Considering the applications of these results to the atmospheric boundary-layer turbulence, the theoretical relationships are derived, which allows us to determine the turbulent diffusion tensor as a function of the vertical coordinate measured in the units of the local Obukhov length scale. The obtained relations are potentially useful in modeling applications of particle dispersion in the atmospheric boundary-layer turbulence and free atmosphere turbulence.

Review of hydrogen isotope effects on H-mode confinement in JT-60U

Hydrogen isotope effects on H-mode confinement in JT-60U are reviewed. The thermal energy confinement time becomes longer in deuterium by a factor of ∼1.4 than in hydrogen at a given absorbed power. When the absorbed power is fixed, the values of electron and ion temperature become evidently higher in deuterium than in hydrogen throughout the entire range of minor radius whereas the electron density profiles are nearly the same. Hence, the effective heat diffusivity becomes relatively lower in deuterium than in hydrogen. When the thermal stored energy is fixed, identical profiles for the electron density, electron temperature, and ion temperature are obtained for hydrogen and deuterium plasmas, whereas the required power clearly increases for hydrogen, which results in reduction of heat diffusivity for deuterium. The inverse of the ion-temperature-gradient (ITG) scale length required for a given ion heat diffusivity increased by a factor of approximately 1.2 for deuterium compared with that for hydrogen. Similar density profiles are formed for the hydrogen and deuterium plasmas despite the higher turbulent particle flux for the hydrogen case, suggesting that turbulent particle transport is more suppressed in the deuterium plasmas. The gyrokinetic calculation indicates that the stabilization effect of e-i collisionality on the TEM is more significant for deuterium plasmas and causes the difference in the quasilinear diffusivity between the two cases. The edge-core interplay leading to the overall H-mode confinement is also addressed where the effect of the hydrogen isotopic composition was involved. The correlation between edge pedestal pressure and global poloidal beta holds true consistently regardless of the difference in the isotopic composition. A higher value of global poloidal beta was obtained for deuterium because of its smaller ITG scale length and because of the additional stored energy in the thermal and fast ion components, the latter due to an increase of slowing down time with an increase of isotopic mass.

Asymmetry between deuterium and tritium turbulent particle flows

The asymmetry between deuterium (D) and tritium (T) turbulent particle fluxes in mixed D–T plasmas is studied with numerical simulations of nonlinear gyrokinetic turbulence in ion temperature gradient-dominated and trapped electron mode-dominated regimes. At 50–50 D–T concentration, the asymmetry, or flow separation, between D and T fluxes is such that the tritium is better confined than the deuterium in both regimes. To supplement the nonlinear simulations, an analytic quasilinear theory of the particle flux symmetry breaking is developed and is valid for general electron dynamics. This theory correctly predicts the numerically computed deviation in the ion density fraction (from 50–50), or ion density gradient (from the electron gradient), required to restore equal deuterium and tritium fluxes.

Bispectral analysis of broadband turbulence and geodesic acoustic modes in the T-10 tokamak

Local fluctuations of electrostatic potential, poloidal electric field, magnetic potential and electron density are simultaneously measured in the T-10 tokamak by a heavy ion beam probe (HIBP) having a five-slit energy analyser, which allows an estimate of the turbulent particle flux and $\boldsymbol {E}\times \boldsymbol {B}$ rotation velocity in the off-minor-axis gradient zone of the toroidal plasma column. The high spatial and temporal resolution of the modern multichannel HIBP makes it an effective tool to study plasma oscillations. Motivated by previous work that has documented time-resolved interactions between measured plasma parameters using correlation analysis (coherence of $E_{\textrm {pol}}$ and density $n_e$ , and cross-phase), a new result from bicorrelation analysis (bicoherence of magnetic potential $A_\zeta$ and density $n_e$ , and biphase) is reported for documenting the evidence of wave–wave coupling and energy transfer associated with the interaction between geodesic acoustic modes (GAM) and broadband, quasi-coherent modes.

Bayesian approach to parameter estimation and model validation for nuclear fusion reactor mean-field edge turbulence modelling

This paper presents a Bayesian approach to infer about two mean-field plasma turbulence models, a first based on the turbulent kinetic energy k ⊥, and a second based on k ⊥ and the turbulent enstrophy ζ ⊥. These models contain several closure terms with unknown constants that have to be determined through fitting to reference data from turbulence simulations or experiments. In this paper, we compare two techniques to solve the Bayesian inference problem: the Laplace approximation and the adaptive Metropolis–Hastings (AMH) algorithm. Our Bayesian inference allows for parameter uncertainty quantification, identification of parameter cross-correlations and model comparison through the Bayesian evidence. Our results indicate that while a diffusive k ⊥–ζ ⊥ scaling for the anomalous diffusion coefficient provides a better approximation to the turbulent particle flux when based on exact turbulence simulation data, at present large modelling uncertainties and parameter cross-correlations in the full k ⊥–ζ ⊥ model make it less performant than the more simple k ⊥ model. For the cases studied here, the cross-correlations can be removed by a reparameterization of the k ⊥–ζ ⊥ model with fewer parameters. The results can form the basis for further development of the turbulence models.

50 YEARS OF HOT PLASMA DIAGNOSTIC WITH HEAVY ION BEAM PROBING (HIBP) AT THE KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY

An overview describes the evolution of HIBP diagnostics from the origins till today. The progress in the beam technology is presented by examples of HIBPs in tokamaks and stellarators. At the beginning, HIBP provided timeaveraged measurements of plasma potential in single space location, then it evolves to time-resolved measurements of radial distributions and finally it becomes a multi-purpose diagnostics to study the temporal evolution of 2D distributions of potential and turbulence, including the long-range potential correlations with dual HIBP. Highlights in plasma potential profile evolution, a link between potential, density and confinement, geodesic acoustic modes, steady and chirping Alfvén eigenmodes, turbulent particle flux are presented.

Dynamics of enhanced neoclassical particle transport of tracer impurity ions in ion temperature gradient driven turbulence

Tracer impurity transport in ion temperature gradient-driven (ITG) turbulence is investigated using a global full-f gyrokinetic simulation including kinetic electrons, bulk ions, and low to medium Z tracer impurities, where Z is the charge number. It is found that in addition to turbulent particle transport, enhanced neoclassical particle transport due to a new synergy effect between turbulent and neoclassical transports makes a significant contribution to tracer impurity transport. Bursty excitation of the ITG mode generates non-ambipolar turbulent particle fluxes of electrons and bulk ions, leading to a fast growth of the radial electric field following the ambipolar condition. The divergence of E × B flows compresses up-down asymmetric density perturbations, which are subject to transport induced by the magnetic drift. The enhanced neoclassical particle transport depends on the ion mass because the magnitude of up-down asymmetric density perturbation is determined by a competition between the E × B compression effect and the return current given by the parallel streaming motion. This mechanism does not work for the temperature and, thus, selectively enhances only particle transport.