Sawtooth Models Research Articles

Diagnosing fast ion redistribution due to sawtooth instabilities using fast ion deuterium-α spectroscopy in the mega amp spherical tokamak

A comparison between fast ion measurements and sawtooth models in the Mega Amp Spherical Tokamak (MAST) is extended to include fast ion deuterium-alpha (FIDA) data. It is concluded that FIDA data cannot be used to distinguish between three alternative models used in the plasma transport/fast particle code TRANSP/NUBEAM to simulate fast ion redistribution during sawteeth. For FIDA lines-of-sight that probe the sawtoothing region, at each sawtooth crash there is an overall drop in the emission of up to 60%. Data from passive FIDA lines-of-sight (i.e. with emission resulting from neutralisation by thermal neutrals in the plasma periphery rather than beam neutrals) show a sudden increase in the emission following sawtooth crashes. The subsequent decay in the emission in these passive channels indicates that redistributed passing fast ions are rapidly lost from the edge region, probably as a result of charge-exchange reactions with edge neutrals.

Investigation of fast particle redistribution induced by sawtooth instability in NSTX-U

The effects of sawtooth on fast ion transport have been studied in reproducible, 2 s long sawtoothing L-mode discharges during the 2016 experimental campaign on National Spherical Torus Experiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015). Analysis of the discharges demonstrated that standard sawtooth models (full/partial reconnection models) in the TRANSP code were not capable to fully reproduce the fast ion redistribution induced by sawtooth crashes. Some global parameters such as neutron rate can be recovered while detailed features, e.g. distribution functions, estimated using the models were different from the experimental observation. The standard sawtooth models in TRANSP do not take into account the different effect of sawtooth crashes depending on fast ion energy and orbit type and that may cause the disagreement between experiments and simulations. In this work, the newly developed kick model has been applied to replace the standard sawtooth models for the fast ion transport. TRANSP simulation results using the kick model, taking into account the characteristics of fast ion such as energy and pitch angle, can reproduce experimental neutron rates within 10% difference. The qualitative comparison of the measurements and synthetic diagnostics of fast ion D-alpha (FIDA) and solid state neutral particle analyser (SSNPA) using the TRANSP simulation results with kick model shows good agreements.

ASDEX Upgrade flight simulator development

Fenix, the ASDEX Upgrade (AUG) flight simulator under development, is based on the Plasma Control System Simulation Platform (PCSSP) developed for ITER, the ASTRA transport code and the SPIDER equilibrium code. Fenix will give a session leader the possibility to check whether the discharge will meet experimental goals prior to execution. It is also designed to facilitate the development of control system features and the validation of physical models. It reads the AUG discharge program and checks if all the parameters and reference waveforms are reasonable during the discharge simulation.ASTRA serves as a plant model (physical model of AUG tokamak) which outputs idealised diagnostic signals (temperature, density, etc.). ASTRA calculates these data from the particle and energy transport in the plasma core, plasma edge, Scrape of Layer (SOL) and divertor. It also includes particle balance, L-H transition and sawtooth models, and it is equipped with the 2D equilibrium reconstruction code SPIDER.The second component of Fenix is a model of the Discharge Control System (DCS) and AUG actuators. The DCS model processes diagnostic signals from ASTRA, computes commands for actuators and sends them back to ASTRA closing the feedback loop. Controllers for coil currents to control plasma current, position and shape are implemented in the model as well as gas puff valves (divertor and midplane) and the pellet injector to control electron density. The DCS model also simulates external heating actuators such as NBI, ECRH and ICRH.Fenix has methods for reading configuration files and archiving. This article presents modelling of the ASTRA and DCS components, and the first results from the simulations of the flattop phase.

Effect of sawtooth crashes on fast ion distribution in NSTX-U

During the 2016 experimental campaign of NSTX-U (Menard et al 2012 Nucl. Fusion 52 083015), long L-mode and reproducible sawtoothing plasmas have been achieved that were previously not accessible before the upgrade. This provides a good opportunity to study the effect of sawtooth crashes on fast ion confinement and redistribution in spherical tokamaks. The solid-state neutral particle analyzer (SSNPA) and fast ion D-alpha (FIDA) diagnostics on NSTX-U each have a tangentially-viewing instrument and a radially- or vertically-viewing instrument, which are mainly sensitive to passing and trapped fast ions, respectively. It has been observed on both diagnostics that passing particles are strongly expelled from the plasma core to the edge during sawtooth crashes, while trapped fast ions are weakly affected. The tangentially-viewing SSNPA observes large signal spikes at the sawtooth crashes because fast ions move to the edge and charge exchange with edge neutrals. The radially-viewing SSNPA data suggest that there is a small drop of trapped particles in the core. The tangentially-viewing FIDA (t-FIDA) system observes a depletion as large as 25% in the region inside the inversion radius, while an increase at the outer region. There is almost no change in the signals of the vertically-viewing FIDA system. The neutron emission can drop as much as 15% at the sawtooth crashes, accompanied by an increase of edge light. Simulations with the Kadomstev and Porcelli sawtooth models have been performed and compared with the measurements. The full reconnection Kadomtsev model overestimates the neutron rate drop at each sawtooth crash. When tuning the sawtooth input parameters, the partial reconnection Porcelli sawtooth model can qualitatively reproduce the neutron rate drop and t-FIDA signal drop in the core, but it fails to predict the t-FIDA signal increase at the edge.

Study of the effect of sawteeth on fast ions and neutron emission in MAST using a neutron camera

The effect of the sawtooth instability on the confinement of fast ions on MAST, and the impact it has on the neutron emission, has been studied in detail using the TRANSP/NUBEAM codes coupled to a full orbit following code. The sawtooth models in TRANSP/NUBEAM indicate that, on MAST, passing and trapped fast ions are redistributed in approximately equal number and on a level that is consistent with the observations. It has not been possible to discriminate between the different sawtooth models since their predictions are all compatible with the neutron camera observations. Full orbit calculations of the fast ion motion have been used to estimate the characteristic time scales and energy thresholds that according to theoretical predictions govern the fast ions redistribution: no energy threshold for the redistribution for either passing and trapped fast ions was found. The characteristic times have, however, frequencies that are comparable with the frequencies of a m = 1, n = 1 perturbation and its harmonics with toroidal mode numbers , suggesting that on spherical tokamaks, in addition to the classical sawtooth-induced transport mechanisms of fast ions by attachment to the evolving perturbation and the associated E × B drift, a resonance mechanism between the m = 1 perturbation and the fast ions orbits might be at play.

Food price seasonality in Africa: Measurement and extent

Everyone knows about seasonality. But what exactly do we know? This study systematically measures seasonal price gaps at 193 markets for 13 food commodities in seven African countries. It shows that the commonly used dummy variable or moving average deviation methods to estimate the seasonal gap can yield substantial upward bias. This can be partially circumvented using trigonometric and sawtooth models, which are more parsimonious. Among staple crops, seasonality is highest for maize (33 percent on average) and lowest for rice (16½ percent). This is two and a half to three times larger than in the international reference markets. Seasonality varies substantially across market places but maize is the only crop in which there are important systematic country effects. Malawi, where maize is the main staple, emerges as exhibiting the most acute seasonal differences. Reaching the Sustainable Development Goal of Zero Hunger requires renewed policy attention to seasonality in food prices and consumption.

Collective Thomson scattering measurements of fast-ion transport due to sawtooth crashes in ASDEX Upgrade

Sawtooth instabilities can modify heating and current-drive profiles and potentially increase fast-ion losses. Understanding how sawteeth redistribute fast ions as a function of sawtooth parameters and of fast-ion energy and pitch is hence a subject of particular interest for future fusion devices. Here we present the first collective Thomson scattering (CTS) measurements of sawtooth-induced redistribution of fast ions at ASDEX Upgrade. These also represent the first localized fast-ion measurements on the high-field side of this device. The results indicate fast-ion losses in the phase-space measurement volume of about 50% across sawtooth crashes, in good agreement with values predicted with the Kadomtsev sawtooth model implemented in TRANSP and with the sawtooth model in the EBdyna_go code. In contrast to the case of sawteeth, we observe no fast-ion redistribution in the presence of fishbone modes. We highlight how CTS measurements can discriminate between different sawtooth models, in particular when aided by multi-diagnostic velocity-space tomography, and briefly discuss our results in light of existing measurements from other fast-ion diagnostics.

Modelling of the Faba bean (Vicia faba L.) Sprouting Reaction to Temperature in Farm Condition

The main goal of this study is to developa Faba bean plant sprouting model that includes a cardinal temperature determination and a required biologic day for Faba bean sprouting ( or to determine the Faba bean sprouting reaction to temperature). For this purpose, in a farm test, 4 cultivars of Faba bean plants (Barekat, Saraziri, Eraghi and Gavi) were cultivated on 11 sowing dates (one in each month ) and the required days to their sprouting were recorded. Beta, curve, quadratic and Sawtooth models were used to describe relationship between the sprouting rate and the temperature . To select the best model, it has been used an average root mean square deviation (RMSD), an R square (R2), simple linear regression coefficients (a and b) and a correlation coefficient (r). The results showed that the Faba bean sprouting reaction to temperature was better described by a Piecewise function. The estimation of the cardinal temperature by a Piecewise function indicated that the base temperature varies from 0.98C to 1.61C, and the optimum temperature varies from 24.99C to 28.8C for the different cultivars of Faba bean plants, but the ceiling temperature for all the cultivars was estimated at 35 degree centigrade. Also, the required biologic day estimation for sprouting as determined by the Piecewise model showed a significant difference between the cultivars, as the Gavi cultivars (which are smaller) germinated after 6.65 days (maximum rate is 0.09). For the other cultivars, the required biologic day fell between 8.60 and 9.31 days. The obtained data can be used to predict Faba bean sprouting in different temperature conditions.

On the Convergence of Planar Curves Under Smoothing

Curve smoothing has two important applications in computer vision and image processing: 1) the curvature scale-space (CSS) technique for shape analysis, and 2) the Gaussian filter for noise suppression. In this paper, we study how planar curves converge as they are smoothed with increasing scales. First, two types of convergence behavior are clarified. The coined term shrinkage refers to the reduction of arc-length of a smoothed planar curve, which describes the convergence of the curve latitudinally; and another coined term collapse refers to the movement of each point to its limiting position, which describes the convergence of the curve longitudinally. A systematic study on the shrinkage and collapse of three categories of curve models is then presented. The corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to. The sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the Gaussian filter. Our investigation on the closed curves shows that each curve collapses to a point at its center of mass. However, different curves may yield different limiting shapes at the infinity scale. Finally, based upon the derived results the performance of the CSS technique in corner detection and shape representation is analyzed, and a fast implementation method of the Gaussian filter for noise suppression is proposed.

Seismic Determination of Saturation in Fractured Reservoirs

Summary Detecting the saturation of a fractured reservoir using shear waves is possible when the fractures have a geometry that induces a component of movement perpendicular to the fractures. When such geometry is present, vertically traveling shear waves can be used to examine the saturation of the fractured reservoir. Tilted, corrugated, and saw-tooth fracture models are potential examples.

Seasonal variation in radiocesium levels of largemouth bass (Micropterus salmoides): Implications for humans and sensitive wildlife species

AbstractTo examine seasonal variation in levels of radiocesium (137Cs) within largemouth bass (Micropterus salmoides; N = 589), fish were collected monthly over a one‐year period from an abandoned reactor cooling reservoir. Month of collection, sex, age, and body mass (log transformed) were all significant factors influencing 137Cs concentrations. Levels of 137Cs reached a peak in late winter/early spring (February/March), and minimum values occurred in the fall (October). An asymmetric sawtooth model with a four‐month period of increase and an eight‐month period of decrease fit the data for monthly 137Cs values significantly better than symmetric sinusoidal and sawtooth models. The mean concentration of 137Cs for bass collected during all months was 7.09 Bq/g wet mass. All individuals examined, regardless of month, sex, age, or body mass, had 137Cs levels (2.95–12.60 Bq/g) that were much higher than the maximum level (0.60 Bq/g wet mass) generally considered safe for human consumption. Radiocesium is relatively long‐lived within this reservoir and will continue to remain an important issue in risk assessments for both humans and wildlife species.

Fast particle experiments in JT-60U

Results of fast particle experiments in JT-60U are presented. The fast particles were created with ICRF heating and negative ion based neutral beam injection (N-NBI) heating. With both heating systems Alfvén eigenmodes (AEs) were excited. The AEs that were excited with ICRF during sawtooth stabilization experiments are used to extract information about the magnetic safety profile in the plasma centre. These measurements are compared with motional Stark effect measurements and with sawtooth models. The first results on the radial mode structure of TAEs as measured with an X mode reflectometer system are also given. When the N-NBI beam was injected into a sawtoothing plasma, a significant increase in sawtooth period was observed. A survey is given of the bursting, chirping and stationary frequency modes that have been found in the Alfvén range of frequencies when N-NBI was injected. Most, but not all, of these modes scale with the Alfvén velocity. One group of modes that starts in the continuum and chirps up to the toroidicity induced Alfvén eigenmode (TAE) gap in typically 200 ms can be identified as resonant TAEs, whereas another group of modes appears as short bursts (up to 20 ms) in the Alfvén continuum.

Chaotic intermittency-sawtooth map model of aggregate self-similar traffic streams

A new model, combining intermittency and sawtooth chaotic maps, is presented for aggregate packet traffic streams. The intermittency map models the ON-OFF activity of the aggregate process, and the sawtooth map models the batch size when active. Results show that the model accurately reflects the impact of long range dependent traffic behaviour on queueing performance, while reducing the computational burden for simulation.

On the quantum cat and sawtooth maps—Return to generic behaviour

The quantization of the continuous cat maps on the torus has led to rather pathological quantum objects [1]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this note we introduce the quantum sawtooth models, since this is the natural family to which the cap maps belong. Thus, a simple propagator depending on a parameter is constructed which for integer values of the parameter becomes pathological quantum cat maps, while away from integer values we find a return to the generic behaviour of non-integrable quantum systems.

Poloidal field measurements during sawteeth and disruptions on MTX

A fifteen chord far infrared polarimeter has been used to measure internal poloidal field profiles in the Microwave Tokamak Experiment (MTX) during sawteeth, disruptions and electron cyclotron heating (ECH). A brief overview is presented of the instrument and the techniques used to analyse the profile data, followed by experimental results. Polarimeter current density (J) measurements are shown to be in good agreement with the expected resistivity profile based on Te measurements. Measurements of safety factor (q) profiles during sawtoothing ohmic discharges are presented and are compared with various sawtooth models. It is found that q0 approximately 0.7-0.85 during sawteeth and q0>1 without sawteeth. The change in q0 during the sawtooth ramp is small, at delta q0 approximately 0.01. Finally, data are presented for ohmic discharges with higher core impurity radiation levels. The large radiated power produces hollow Te and J profiles, and often leads to a disruption. This type of disruption has been stabilized on MTX by peaking the J profile through ECH in the core

Numerical constraints on rates of metamorphism, fluid production, and fluid flux during regional metamorphism

One-dimensional numerical models of regional metamorphism were constructed in order to constrain rates of metamorphism, rates of fluid production, and fluid flux as a function of time and position in thickened continental crust. Four end-member numerical experiments result from combinations of sawtooth (single thrust) versus homogeneous crustal thickening geometries and continuous versus discontinuous metamorphic reactions that release up to 5 wt% volatiles from the lower half of the thickened crust. Metamorphic reactions consume substantial amounts of heat and retard the thermal evolution of thickened continental crust by several million years. Peak rates of metamorphism, defined as the rate of advance of the 400 °C isotherm, range from 1.4 to 5.7 mm yr -1 in the saw-tooth models and from 0.5 to 0.6 mm yr -1 in the homogeneous models. Maximum rates of fluid production range from 90 mg (fluid) m -3 yr -1 in the sawtooth, discontinuous-reaction model to 6 mg (fluid) m -3 yr -1 in the homogeneous, continuous-reaction model. Fluid production in the sawtooth models produce a maximum fluid flux of ∼0.2 kg (fluid) m -2 yr -1 out of the 40-km-thick lower plate. The maximum fluid flux in the homogeneous models are lower, -2 yr -1 . Fluid fluxes resulting from all models require significant focusing into channels, spaced greater than 10 km apart, in order to perturb the overlying thermal structure of the continental crust. In these numerical experiments, most fluid flow infiltrates overlying rocks at temperatures substantially below peak metamorphic temperatures, suggesting that strongly focused or multi-pass fluid-circulation systems may be required to explain reported high fluid/rock ratios.

X-ray absorption near-edge structure of adsorbate-induced reconstruction: (2x1)O on Cu(110)

Abstract We present O K-edge near-edge absorption spectra for (2 sx 1)O on Cu(110) and accompanying multiple-scattering calculations for models with an unreconstructed substrate and with missing-row and saw-tooth adsorbate-induced reconstructions. The calculated NEXAFS has been analysed to assess the importance of multiple scattering as a function of the azimuthal angle of the electric field vector, and to identify the dominant structure-sensitive multiple-scattering paths. We find strong support for an oxygen-induced reconstruction of the Cu(110) substrate, though an unequivocal resolution between the missing-row and saw-tooth models must await further measurements.

X-ray absorption near-edge structure of adsorbate-induced reconstruction: (2 × 1)O on Cu(110)

We present O K-edge near-edge absorption spectra for (2 sx 1)O on Cu(110) and accompanying multiple-scattering calculations for models with an unreconstructed substrate and with missing-row and saw-tooth adsorbate-induced reconstructions. The calculated NEXAFS has been analysed to assess the importance of multiple scattering as a function of the azimuthal angle of the electric field vector, and to identify the dominant structure-sensitive multiple-scattering paths. We find strong support for an oxygen-induced reconstruction of the Cu(110) substrate, though an unequivocal resolution between the missing-row and saw-tooth models must await further measurements.

A study of sawtooth phenomena in TEXT: Comparison between theory and experiment

Through a detailed analysis of soft-X-ray emissions from TEXT, comparisons were made between the observed phenomena and the often accepted theoretical model according to which a growing m = 1 mode is responsible for the sawtooth collapse. The sawtooth period was measured over a broad range of plasma conditions and compared with previously published theoretical and empirical scalings. The observed sawtooth period scaling was not found to depend strongly on the inversion radius, in contrast with previously published scalings. The time evolution of the often observed sinusoidal oscillations superimposed on sawteeth was analysed and compared with that predicted by Kadomtsev type reconnection sawtooth models. The sawtooth collapse is often in phase with the fall of the superimposed odd-m oscillation (assumed m = 1), but other cases show that the sawtooth collapse is independent of the phase of the m = 1 oscillations. Sawteeth in TEXT occur without clear m = 1 activity, and m = 1 oscillations occur before the crash, throughout the sawtooth period and after the crash, with the relative phase being independent of the collapse.