Ion Temperature Profiles Research Articles

Validation of quasi-linear turbulent transport models against plasmas with dominant electron heating for the prediction of ITER PFPO-1 plasmas

Kinetic profile predictions of ITER PFPO-1 plasmas require high accuracy in the central electron temperatures to be applied to the calculation of third harmonic electron cyclotron absorption. Correctly predicting the transition from L-mode to H-mode further requires precise estimates of the ion heat flux in the periphery of the plasma. Recent versions of the quasi-linear transport models TGLF and QuaLiKiz were tested against an extensive set of experimental results from ASDEX Upgrade (AUG) and JET-ILW, where the focus was put on AUG plasmas heated by ECRH. Spectra obtained from TGLF are compared to a set of linear gyrokinetic simulations performed with GKW. Electron and ion temperature profiles obtained with TGLF-SAT1geo show good agreement with the experimental profiles, but there is a slight tendency to underpredict central T e and T i at high ratios T e/T i. QuaLiKiz yields reasonable results for T e and T i profiles in plasmas where the ion temperature gradient mode is dominant, but predicts a significantly too weak transport in the presence of dominant trapped electron modes in conditions of strong central electron heating.

Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport

A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρ tor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρ or = 0.4 where the fast ion population and normalized plasma pressure β = 2μ 0 nT/B 2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρ tor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.

Edge turbulent transport toward the L–H transition in ASDEX Upgrade and JET-ILW

This work combines experimental observations from the ASDEX Upgrade and the JET-ILW tokamaks and related gyrokinetic simulations on the L-mode edge turbulence with different isotopes. The evolution of the edge logarithmic gradients and the edge radial electric field with increasing input power and the correlation between the two are studied. It is found that the edge ion temperature profile plays the dominant role in the evolution of the edge radial electric field in the considered cases. More input power and ion heat flux are needed in hydrogen to obtain values of Ti and R/LTi similar to the ones observed in deuterium. As a consequence, more power is needed in hydrogen to develop values of the edge radial electric field similar to those in deuterium plasmas. These observations point to a key role of the dependence of the edge turbulence on the main ion mass in determining the different L–H power thresholds with different isotopes. This dependence is found in gyrokinetic simulations to be connected to the parallel electron dynamics, i.e., to a different kinetic response of passing electrons with different main ion mass. The gyrokinetic simulations indicate different roles of R/LTe, R/LTi, and R/Ln in driving or stabilizing the edge turbulence at different wavelengths and indicate a strong role of the external flow shear in stabilizing the edge turbulence. The simulations indicate also that instabilities at finite values of kx play an important role in edge conditions.

Correction and verification of x-ray imaging crystal spectrometer analysis on Wendelstein 7-X through x-ray ray tracing.

X-ray ray tracing is used to develop ion-temperature corrections for the analysis of the X-ray Imaging Crystal Spectrometer (XICS) used at Wendelstein 7-X (W7-X) and perform verification on the analysis methods. The XICS is a powerful diagnostic able to measure ion-temperature, electron-temperature, plasma flow, and impurity charge state densities. While these systems are relatively simple in design, accurate characterization of the instrumental response and validation of analysis techniques are difficult to perform experimentally due to the requirement of extended x-ray sources. For this reason, a ray tracing model has been developed that allows characterization of the spectrometer and verification of the analysis methods while fully considering the real geometry of the XICS system and W7-X plasma. Through the use of ray tracing, several important corrections have been found that must be accounted for in order to accurately reconstruct the ion-temperature profiles. The sources of these corrections are described along with their effect on the analyzed profiles. The implemented corrections stem from three effects: (1) effect of sub-pixel intensity distribution during de-curving and spatial binning, (2) effect of sub-pixel intensity distribution during forward model evaluation and generation of residuals, and (3) effect of defocus and spherical aberrations on the instrumental response. Possible improvements to the forward model and analysis procedures are explored, along with a discussion of trade-offs in terms of computational complexity. Finally, the accuracy of the tomographic inversion technique in stellarator geometry is investigated, providing for the first time a verification exercise for inversion accuracy in stellarator geometry and a complete XICS analysis tool-chain.

Inversion technique to obtain local ion temperature profiles for an axisymmetric plasma with toroidal and radial velocities

A matrix inversion technique is derived to calculate local ion temperature from line-integrated measurements of an extended emission source in an axisymmetric plasma which exactly corrects for both toroidal velocity and radial velocity components. Local emissivity and toroidal velocity can be directly recovered from line-integrated spectroscopic measurements, but an independent measurement of the radial velocity is necessary to complete the temperature inversion. The extension of this technique to handle the radial velocity is relevant for magnetic reconnection and merging compression devices where temperature inversion from spectroscopic measurements is desired. A simulation demonstrates the effects of radial velocity on the determination of ion temperature.

Ion temperature measurements in the tokamak scrape-off layer with high temporal resolution

We present a uniquely fast (10 μs) ion temperature measurements in the tokamak edge plasma. Our approach is based on the sweeping of a ball-pen probe, where the ion temperature is obtained by fitting the electron branch of the corresponding I–V characteristic. We have performed measurements on the COMPASS tokamak during L-mode discharge. The temperature histograms reveal a non-Gaussian shape with a high-temperature tail peaking at low values. The fitted values of fast I–V measurements can be used to reconstruct (emulate) the slow swept I–V characteristic of a retarding field analyzer. The resulting ion temperature profile is nearly flat and provides a ratio of ion to electron temperature close to 1–2 in the vicinity of the last closed flux surface during L-mode discharges, as observed on other tokamaks.

Simulations of microturbulence in magnetised plasmas using a delta-f gyrokinetic approach with an evolving background Maxwellian

The gyrokinetic delta-f particle-in-cell (PIC) approach is known to be successful for simulating turbulence in the core of magnetic fusion plasmas, where fluctuations are relatively small and therefore the unperturbed particle distribution function, usually represented by a stationary Maxwellian f 0, remains a good choice of a control variate for reducing statistical sampling noise. However, towards the plasma edge, characterized by low density and temperature and strong gradients, relative deviation amplitudes typically become large, so that the essential assumption of |δf/f 0| << 1 underlying the delta-f PIC approach will not be valid, where δf is the fluctuating part of distribution. This motivates the study of the limits of the delta-f approach in a simplified system mimicking the plasma edge. To this end, simulations are run using GK-engine, which is a delta-f PIC code that solves the nonlinear gyrokinetic equation in a sheared slab geometry, using B-spline finite elements to represent the self-consistent electrostatic field. Initial radial density and ion temperature profiles exhibiting high logarithmic gradients representing plasma edge conditions are used. In order to avoid practical problems of particles exiting the simulation domain as the ion temperature profile relaxes, all profiles are mirrored at domain-centre and periodic boundary conditions are imposed. The validity of the delta-f approach is measured by statistical noise estimates, while monitoring relative deviation levels of temperature via the kinetic energy. In particular, the effect of background profile gradients on these measures is investigated. As a first step towards reducing the amplitude of the deviation δf, an adaptive Maxwellian f 0 is implemented, whose time dependent temperature profiles are obtained by locally relaxing kinetic energy accumulating in δf into f 0.

Integrated simulation of plasma current profile in HL-2A high confinement mode(H mode)

The plasma current (&lt;i&gt;I&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;&lt;italic/&gt;), magnetic field (&lt;i&gt;B&lt;/i&gt;), and safety factor distribution (&lt;i&gt;q&lt;/i&gt; profile) of the HL-2A tokamak device are crucial to monitoring the steady-state operational scenarios (in high confinement mode, H mode). Based on real experimental data and integrated modeling simulation method (OMFIT), the plasma parameters’ profiles such as magnetic field configuration and current density profiles in H mode were reconstructed. By building up an integrated simulation platform for dynamic equilibrium configuration, and combining the rapid workflow processing method and experimental data with integrated simulation models, the ion and electron temperature, density, and current density profiles were obtained. The integration simulation platform was established to reconstruct the internal magnetic surface configuration, the plasma boundary parameter distribution, the ion/electron temperature, current density, and the &lt;i&gt;q&lt;/i&gt; profile. The Ohmic current, bootstrap current, and radio-frequency current profiles with its fractions were calculated. The width of the pedestal region was about 7.52 cm according to our simulation results. It was found that the pressure gradient changes its direction at radial coordinate &lt;i&gt;ρ&lt;/i&gt;(&lt;i&gt;r/a&lt;/i&gt;) = 0.1 and reaches its maximum value near &lt;i&gt;ρ&lt;/i&gt; = 0.7, which may be the internal transport barrier (ITB) configuration caused by negative shear. The profile reconstruction and real-time monitoring of the physical parameters are conducive to evaluating the quality of H mode discharge experiment and can assist in the steady-state operation of advanced operating modes such as HL-2M high normalized beta (&lt;i&gt;β&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;) discharge.

Первые результаты исследований ионного теплопереноса на сферическом токамаке Глобус-М2

The paper presents the first ion temperature profile measurements results in the new spherical tokamak Globus-M2, which were obtained in discharges with neutral beam injection using the Charge eXchange Recombination Spectroscopy (CXRS) and the Neutral Particle Analyzer (NPA). Ion heat transport modeling using ASTRA code was carried out based on the obtained experimental ion temperature. The results of the modelling indicate the predominantly neoclassical ion heat transport.

Estimation and Uncertainties of Profiles and Equilibria for Fusion Modeling Codes

The results of transport modeling codes, e.g., GENE for the plasma core or SOLPS-ITER for the plasma edge, depend critically on reliable profile and equilibrium estimates. The propagation of uncertainties (UP) of input quantities to the results of modeling codes, e.g., power and particle exhaust and plasma stability, is frequently neglected because of the costs of running the codes as well as because of the missing uncertainty quantification of input quantities. The situation becomes even more cumbersome if profile gradients and their uncertainties are of major concern for transport analyses. Two different techniques are presented to estimate profiles, profile gradients, their uncertainties, and candidate profiles for UP in modeling codes. Markov Chain Monte Carlo sampling of the posterior probability density of an integrated data analysis approach is applied to estimate electron density and temperature profiles. Nonstationary Gaussian process regression is applied to estimate ion temperature and angular velocity profiles. Both methods provide in a natural way profile gradients, profile logarithmic gradients, and their uncertainties. Modeling codes benefit also from reliable equilibrium reconstructions and quantification of the uncertainty of various equilibrium parameters. For the analysis of diagnostics data, the position and uncertainty of flux surfaces as well as of the magnetic axis are important. For plasma transport and stability codes, the estimation of uncertainties of current and q-profiles is presented. For plasma edge codes the position of the separatrix contour and its uncertainty at various poloidal positions is of primary interest especially if steep profile gradients are present. Examples of uncertainties and their sources in magnetic scalar quantities, profiles, and separatrix contours are shown.

Ion temperature measurements in a tokamak using active neutral particle analyzers diagnostics

Active ion temperature measurement in the core plasma of a tokamak using active neutral particle analyzers (NPA) diagnostics is considered. Two approaches for local ion temperature reconstruction are reviewed: semi-analytical and iterative. A semi-analytical approach allows the calculation of ion temperature using simple expression, while a more complex iterative approach provides more flexibility. Problems associated with active NPA measurements and their possible solutions are discussed. An example of the core ion temperature profile reconstruction in the compact spherical tokamak Globus-M2 using both approaches is shown. Problems associated with active ion temperature measurements in a compact reactor and possible solutions are considered.

Commissioning and initial operation of the W7-X neutral beam injection heating system

Abstract The first, of two planned, neutral beam injectors for the stellarator Wendelstein 7-X (W7-X) was commissioned for and participated in the experimental campaign (OP1.2b) from July to October 2018. The injector was equipped with two RF driven ion sources from which 90A of positive hydrogen ions were extracted at 55 kV. After neutralization, the two sources provided >3 MW of neutral beam heating power to the stellarator plasma. During the experimental campaign >300 shots were successfully performed for plasma heating or to allow for measurement of the ion temperature profile by charge exchange recombination spectroscopy (CXRS). The initial operation of the NBI system on W7-X was very successful, demonstrating both increased central plasma density and stored plasma energy, or allowing for the collection of the time resolved ion temperature over the bulk of the plasma. This paper presents, briefly, source conditioning and performance, focusing on some of the initial problems encountered. Described in more detail is the most significant challenge overcome during commissioning: failure to couple RF power into one of the sources.

Simulation of EAST edge plasma using SOLPS-ITER/BOUT++ coupling

The self-consistent simulation of transport and turbulence in tokamak edge plasma on the EAST tokamak is performed by coupling the fluid plasma/neutral 2D transport code SOLPS-ITER and the fluid 3D turbulence code BOUT++. The convergence of the coupling is validated. The changing rates between the two consecutive profiles of density, electron temperature and ion temperature are close to zero in the last several iteration steps, and the variations of the transport coefficients Dr, χe and χi also show the tendency to diminish as the iteration step increases, indicating that the coupling tends to be in a quasi-steady state. The edge plasma at the time t = 3400 ms in shot 36 780 with deuterium discharge on EAST is simulated by the SOLPS-ITER/BOUT++ coupling. The MHD equilibrium at the shot time with the lower single-null configuration is used for the production of the computational meshes for SOLPS-ITER and BOUT++, respectively. The computational profiles of electron density and temperature, particle and heat fluxes at the divertor targets from the SOLPS-ITER/BOUT++ coupling simulation are compared with the measured profiles, and it is found that the computational and measured profiles are similar.

Two-Gaussian Fitting Method for Charge Exchange Spectroscopy on Measurements of Ion Temperature and Toroidal Plasma Flow Velocity in the KSTAR Tokamak

Charge exchange spectroscopy has been widely used in fusion devices to measure ion temperature, and toroidal and poloidal flow velocities of plasma. For local measurement, especially in the core region of the plasma, the spectrum emitted by the charge exchange reaction between the main plasma ions or impurity ions and the intentionally injected neutral beam should be analyzed so that parameters can be accurately deduced. Since the line-integrated spectrum signal through the line of sight of the diagnostic optics usually contains an unnecessary overlapped spectrum signal, referred to as the background signal, that typically originates from the plasma boundary region, a beam modulation technique is commonly applied to separate the background signal from the measured spectrum. Recently, it has been demonstrated in the KSTAR tokamak that a two-Gaussian fitting (TGF) method can be applied to analyze the spectrum and deduce plasma ion temperature and toroidal rotation velocity profiles of reasonable accuracy without beam modulation. It has been realized that the measurement result by the TGF method can be alternatively used to investigate plasma transport dynamics when beam modulation is prohibited to avoid any possible disturbance inhibiting robust plasma control and stable operation of the neutral beam injection system.

Increased core ion temperatures in high-beta advanced scenarios in ASDEX upgrade

Non-inductive advanced tokamak scenarios are a possible way for future nuclear fusion power plants to run in non-pulsed operation. In these scenarios, the ohmic current is replaced on the one hand with a current driven by external sources such as NBI and ECRH and on the other hand with a substantial bootstrap-current. The bootstrap current is produced in the presence of pressure gradients. This means, to increase the bootstrap-current-fraction, it is advantageous to have regions where ITG turbulence is reduced. To be able to extrapolate from non-inductive scenarios done in smaller present day devices, it is important to have transport models that allow the user to reproduce these experiments and accurately capture the physics behind the reduction of turbulent transport. One commonly used model is the quasi-linear gyrofluid transport model TGLF, which is well tested in standard scenarios. However, in the past, TGLF has failed to reproduce the peaked ion temperature profiles of certain advanced scenario shots.In this article, progress in overcoming this issue of TGLF will be discussed. Results of a recent publication are reproduced in which TGLF was able to match the experimentally measured peaked ion temperature profiles. In these simulations, we find the E × B-shear to play an important role in the reduction of ITG turbulence. In contrast to that, experimentally we find the E × B-shear to have no effect on the formation of such regions of decreased turbulent transport. This finding is in line with simulations using the gyrokinetic code GENE. A new approach of modelling these advanced scenarios in TGLF is introduced, allowing us to match the peaked ion temperature profiles without depending on the E × B-shear.

A mechanism of ion temperature peaking by impurity pellet injection in a heliotron plasma

Experiments on the Large Helical Device with the injection of carbon pellets into discharges of low density have demonstrated a significant reduction of the ion heat conduction in the plasma core and an increase in the central ion temperature by a factor of up to 2. These results are interpreted in the framework of a transport model elaborated on the basis of those applied previously to explain the improvement in confinement by impurity seeding into the tokamak devices TEXTOR and JET. The calculations performed reproduce well the strong peaking of the ion temperature profile with increasing carbon density nZ and the consequent drop in the confinement as nZ exceeds a certain critical level. The importance of different elements in the model, such as braking of the main ion rotation by friction with impurity ones and the shape of the density profiles, are investigated. A qualitative assessment of the applicability under fusion reactor conditions, e.g. of much higher plasma density and heating power, is performed.

Data assimilation system based on integrated transport simulation of Large Helical Device plasma

A data assimilation technique is applied to the integrated transport simulation (TASK3D) of a plasma in Large Helical Device (LHD). We use the ensemble Kalman filter (EnKF) as a data assimilation method for the estimation of state variables composed of the electron and ion temperature, density, numerical coefficients of turbulence models, and NBI heat deposition. The time series data of experimentally measured temperature and density profiles are assimilated into TASK3D. The obtained electron and ion temperature profiles and temporal variations by the data assimilation system agree well with measured ones owing to the optimization of the employed turbulent transport model and the heat deposition. These results indicate the effectiveness and validity of the data assimilation approach for accurate prediction of the behavior of fusion plasmas and the possibility of advanced turbulence modeling.

Retarding field analyzer for the wendelstein 7-X boundary plasma

Abstract A bi-directional multi-channel retarding field analyzer (RFA) probe has been successfully developed for the first time on the Wendelstein 7-X (W7-X) stellarator boundary plasma. Modifications to the RFA prototype hardware and its upgrade for the two W7-X island divertor campaigns are presented, including the electronics. In this paper the experiences and challenges operation and customizing an RFA at W7-X are discussed, as well as the data analysis using a maximum coefficient of determination method to obtain the ion temperature based on the measured modulated ion current. Edge ion temperature profiles have been measured in the standard and high iota configurations.

Verification of an improved equation-free projective integration method for neoclassical plasma-profile evolution in tokamak geometry

A brute-force, long-time gyrokinetic simulation of plasma profile evolution in magnetic fusion devices is not desirable due to large computational resource requirements and a possible accumulation of numerical error. The equation-free projective integration method of Keverekidis et al. [Commun. Math. Sci. 1(4), 715–762 (2003)] is one of the outstanding candidates in projecting micro-scale simulations to a longer timescale. However, its application to tokamak plasma has not been fruitful due to the appearance of spurious transient oscillations in the lifting process, which are present when the kinetic simulations are initialized with a simplified model distribution function and which make the kinetic simulations to deviate from the desired paths. In this work, a kinetically informed lifting algorithm is added to the equation-free projective integration method, which is then verified in the electrostatic gyrokinetic particle-in-cell code XGCa [R. Hager and C. S. Chang, Phys. Plasmas 23, 042503 (2016)] for a neoclassical ion heat transport problem with adiabatic electrons. This new lifting operator is demonstrated to control spurious transients, enabling an over four-times reduction in the overall computing time in the time-evolution of the ion temperature profile in an axisymmetric toroidal plasma. Further reduction in the computing time is found to be limited due to the stability properties of the linear least squares projective integrator.

Charge exchange recombination spectroscopy at Wendelstein 7-X.

The Charge Exchange Recombination Spectroscopy (CXRS) diagnostic has become a routine diagnostic on almost all major high temperature fusion experimental devices. For the optimized stellarator Wendelstein 7-X (W7-X), a highly flexible and extensive CXRS diagnostic has been built to provide high-resolution local measurements of several important plasma parameters using the recently commissioned neutral beam heating. This paper outlines the design specifics of the W7-X CXRS system and gives examples of the initial results obtained, including typical ion temperature profiles for several common heating scenarios, toroidal flow and radial electric field derived from velocity measurements, beam attenuation via beam emission spectra, and normalized impurity density profiles under some typical plasma conditions.