Electron Thermal Transport Research Articles

Internal tests and improvements of the Krook model for nonlocal electron energy transport in laser produced plasmas

Electron thermal transport in a laser produced plasma cannot be described with a local approximation in many regions of a laser produced plasma because the electron mean free path is longer than the temperature gradient scale length. Since a Krook model for the electron Vlasov equation is analytically solvable in the nonlocal limit, one can find simple expressions for the electron thermal flux in the nonlocal limit, and these can be economically incorporated into fluid simulations. The Krook model provides reasonable descriptions of both preheat and flux limitation. We have analyzed the Krook model in a series of publications. Here we streamline the presentation of the model, show qualitatively just what the model predicts in certain situations, give internal tests to check the validity of the model, and provide more accurate analytic approximations to the integral formulas which the model gives rise to.

Electron cyclotron emission diagnostic for ITER

Electron temperature measurements and electron thermal transport inferences will be critical to the nonactive and deuterium phases of ITER operation and will take on added importance during the alpha heating phase. The diagnostic must meet stringent criteria on spatial coverage and spatial resolution during full field operation. During the early phases of operation, it must operate equally well at half field. The key to the diagnostic is the front end design. It consists of a quasioptical antenna and a pair of calibration sources. The radial resolution of the diagnostic is less than 0.06 m. The spatial coverage extends at least from the core to the separatrix with first harmonic O-mode being used for the core and second harmonic X-mode being used for the pedestal. The instrumentation used for the core measurement at full field can be used for detection at half field by changing the detected polarization. Intermediate fields are accessible. The electron cyclotron emission systems require in situ calibration, which is provided by a novel hot calibration source. The critical component for the hot calibration source, the emissive surface, has been successfully tested. A prototype hot calibration source has been designed, making use of extensive thermal and mechanical modeling.

Modelling of the JET current ramp-up experiments and projection to ITER

The current ramp-up phase of ITER demonstration discharges, performed at JET, is analysed and the capability of the empirical L-mode Bohm–gyroBohm and Coppi–Tang transport models as well as the theory-based GLF23 model to predict the temperature evolution in these discharges is examined. The analysed database includes ohmic (OH) plasmas with various current ramp rates and plasma densities and the L-mode plasmas with the ion cyclotron radio frequency (ICRF) and neutral beam injection (NBI) heating performed at various ICRF resonance positions and NBI heating powers. The emphasis of this analysis is a data consistency test, which is particularly important here because some parameters, useful for the transport model validation, are not measured in OH and ICRF heated plasmas (e.g. ion temperature, effective charge). The sensitivity of the predictive accuracy of the transport models to the unmeasured data is estimated. It is found that the Bohm–gyroBohm model satisfactorily predicts the temperature evolution in discharges with central heating (the rms deviation between the simulated and measured temperature is within 15%), but underestimates the thermal electron transport in the OH and off-axis ICRF heated discharges. The Coppi–Tang model strongly underestimates the thermal transport in all discharges considered. A re-normalization of these empirical models for improving their predictive capability is proposed. The GLF23 model, strongly dependent on the ion temperature gradient and tested only for NBI heated discharges with measured ion temperatures, predicts accurately the temperature in the low power NBI heated discharge (rms < 10%) while the discrepancy with the data increases at high power. Based on the analysis of the JET discharges, the modelling of the current ramp-up phase for the H-mode ITER scenario is performed with particular emphasis on the sensitivity of the sawtooth-free duration of this phase to transport model.

Development of drift-resistive-inertial ballooning transport model for tokamak edge plasmas

A new model is developed for transport driven by drift-resistive-inertial ballooning modes (DRIBMs) in axisymmetric tokamak plasmas. The model is derived using two-fluid reduced Braginskii equations in a generalized ŝ−α geometry. The unified theory includes diamagnetic effects, parallel electron and ion dynamics, electron inertia, magnetic perturbations, transverse particle diffusion, gyroviscous stress terms, electron and ion equilibrium temperature gradients, and temperature perturbations. A mixing length approximation is used to compute electron and ion thermal transport as well as particle fluxes from eigenvalues and eigenvectors of the linearized equations. The prediction for the saturation level is obtained by balancing the DRIBM growth rate against the nonlinear E×B convection. The parametric dependence of DRIBMs is investigated in systematic scans over density gradient, electron and ion temperature gradients, magnetic-q, collision frequency, magnetic shear, and Larmor radius. The DRIBM threshold is determined as a function of the collision frequency and the density and temperature gradients. The transition from DRIBM to the toroidal ion temperature gradient (ITG) mode is observed for small density gradients. For steep density gradients, the effect of ITG on DRIBM is found to be stabilizing. The transport seen in the DRIBM is of a scale that is consistent with the observed experimental anomalous transport, suggesting that the DRIBM mode could be the principle agent responsible for edge transport in Ohmic and L-mode discharges.

Anomalous electron transport due to multiple high frequency beam ion driven Alfvén eigenmodes

We report on the simulations of recently observed correlations of the core electron transport with the sub-thermal ion cyclotron frequency instabilities in low aspect ratio plasmas of the National Spherical Torus Experiment. In order to model the electron transport the guiding centre code ORBIT is employed. A spectrum of test functions of multiple core localized global shear Alfvén eigenmode (GAE) instabilities based on a previously developed theory and experimental observations is used to examine the electron transport properties. The simulations exhibit thermal electron transport induced by electron drift orbit stochasticity in the presence of multiple core localized GAE.

Electron thermal transport within magnetic islands in the reversed-field pinch

Tearing mode induced magnetic islands have a significant impact on the thermal characteristics of magnetically confined plasmas such as those in the reversed-field pinch (RFP). New Thomson scattering diagnostic capability on the Madison Symmetric Torus (MST) RFP has enabled measurement of the thermal transport characteristics of islands. Electron temperature (Te) profiles can now be acquired at 25 kHz, sufficient to measure the effect of an island on the profile as the island rotates by the measurement point. In standard MST plasmas with a spectrum of unstable tearing modes, remnant islands are present in the core between sawtoothlike reconnection events. Associated with these island remnants is flattening of the Te profile inside the island separatricies. This flattening is characteristic of rapid parallel heat conduction along helical magnetic field lines. In striking contrast, a temperature gradient within an m=1, n=5 island is observed in these same plasmas just after a sawtooth event when the m=1, n=5 mode may briefly come into resonance near the magnetic axis. This suggests local heating and relatively good confinement within the island. Local power balance calculations suggest reduced thermal transport within this island relative to the confinement properties of standard MST discharges between reconnection events. The magnetic field and island structure is modeled with three-dimensional nonlinear resistive magnetohydrodynamic simulations (DEBS code) with Lundquist numbers matching those in MST during standard discharges. During improved confinement plasmas with reduced tearing mode activity, temperature fluctuations correlated with magnetic signals are small with characteristic fluctuation amplitudes of order T̃e/Te∼2%.

Collective scattering system for transport study on NSTX

The problem of degraded energy confinement due to excessive transport across the magnetic field remains one of the critical issues for magnetically confined plasma. Radial transport of ion energy is relatively well understood, but that of the electrons has remained as anomalous, greatly exceeding the neoclassical prediction. It has been suggested that the anomalous electron thermal transport is explained by an electron gyro-scale turbulence driven by the electron temperature gradient (ETG) instability. A 280-GHz collective Thomson scattering system has been employed to address the electron gyro-scale fluctuations in National Spherical Torus Experiment (NSTX) plasmas. The spatial resolution of the targeting wavenumber is greatly affected by the configuration of the magnetic field since the radial fluctuation is perpendicular to the local magnetic field line. The effect of the toroidal field curvature and magnetic shear on the spatial resolution of the scattering system is investigated numerically. An absolute power calibration was performed to determine the power response of the heterodyne detection system. These spatial resolution studies and absolute power calibration were applied to estimate the normalized density fluctuations from the measured scattering signals in NSTX plasmas.

Simultaneous measurement of core electron temperature and density fluctuations during electron cyclotron heating on DIII-D

New measurements show that long-wavelength (kθρs&amp;lt;0.5) electron temperature fluctuations can play an important role in determining electron thermal transport in low-confinement mode (L-mode) tokamak plasmas. In neutral beam-heated L-mode tokamak plasmas, electron thermal transport and the amplitude of long-wavelength electron temperature fluctuations both increase in cases where local electron cyclotron heating (ECH) is used to modify the plasma profiles. In contrast, the amplitude of simultaneously measured long-wavelength density fluctuations does not significantly increase. Linear stability analysis indicates that the ratio of the trapped electron mode (TEM) to ion temperature gradient (ITG) mode growth rates increases in the cases with ECH. The increased importance of the TEM drive relative to the ITG mode drive in the cases with ECH may be associated with the increases in electron thermal transport and electron temperature fluctuations.

Electron gyroscale fluctuation measurements in National Spherical Torus Experiment H-mode plasmas

A collective scattering system has measured electron gyroscale fluctuations in National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] H-mode plasmas to investigate electron temperature gradient (ETG) turbulence. Observations and results pertaining to fluctuation measurements in ETG-stable regimes, the toroidal field scaling of fluctuation amplitudes, the relation between fluctuation amplitudes and transport quantities, and fluctuation magnitudes and k-spectra are presented. Collectively, the measurements provide insight and guidance for understanding ETG turbulence and anomalous electron thermal transport.

The characteristics of the internal transport barrier under reactor relevant conditions in JT-60U weak shear plasmas

The characteristics of the internal transport barrier (ITB) have been investigated under reactor relevant conditions with edge fuelling and electron heating in JT-60U weak shear plasmas. In order to investigate the effects of edge fuelling and electron heating separately, two independent classes of experiments were performed, i.e. one with edge fuelling and ion dominant heating and the other with central beam fuelling and additional electron heating. High confinement was sustained at high density with edge fuelling by shallow pellet injection or supersonic molecular beam injection. The ion temperature (Ti) in the central region inside the ITB decreased due to cold pulse propagation even with edge fuelling. By optimizing the injection frequency and the penetration depth, the decreased central Ti recovered and a good ITB was sustained with enhanced pedestal pressure. The Ti-ITB also degraded significantly with electron cyclotron heating (ECH), when the stiffness feature was strong in the electron temperature (Te) profile. The ion thermal diffusivity in the ITB region increased with the electron thermal diffusivity, indicating the existence of a clear relation between ion and electron thermal transport. On the other hand, the Ti-ITB remained unchanged or even grew, when the stiffness feature was weak in the Te profile. The density fluctuation level at the ITB seemed unchanged during ECH; however, the correlation length became longer in the Ti-ITB degradation case and shorter in the Ti-ITB unchanging case.

Studies of turbulence and transport in Alcator C-Mod ohmic plasmas with phase contrast imaging and comparisons with gyrokinetic simulations

Recent advances in gyrokinetic simulation have allowed for quantitative predictions of core turbulence and associated transport. However, numerical codes must be tested against experimental results in both turbulence and transport. In this paper, we present recent results from ohmic plasmas in the Alcator C-Mod tokamak using phase contrast imaging (PCI) diagnostic, which is capable of measuring density fluctuations with wave numbers up to 55 cm−1. The experiments were carried out over the range of densities covering the ‘neo-Alcator’ (linear confinement time scaling with density, electron transport dominates) to the ‘saturated ohmic’ regime. We have also simulated these plasmas with the gyrokinetic code GYRO and compared numerical predictions with experimentally measured turbulence through a synthetic PCI diagnostic method. The key role played by the ion temperature gradient (ITG) turbulence has been verified, including measurements of turbulent wave propagation in the ion diamagnetic direction. It is found that the intensity of density fluctuations increases with density, in agreement between simulation and experiments. The absolute fluctuation intensity agrees with the simulation within experimental error (±60%). In the saturated ohmic regime, the simulated ion and electron thermal diffusivities also agree with experiments after varying the ion temperature gradient within experimental uncertainty. However, in the linear ohmic regime, GYRO does not agree well with experiments, showing significantly larger ion thermal transport and smaller electron thermal transport. Our study shows that although the short wavelength turbulence in the electron temperature gradient (ETG) range is unstable in the linear ohmic regime, the nonlinear simulation with kθρs up to 4 does not raise the electron thermal diffusivity to the experimental level, where kθ is the poloidal wavenumber and ρs is the ion-sound Larmor radius. At the present time, it is not known whether even shorter wavelength turbulence would account for the measured electron transport.

Simulation of electron thermal transport in H-mode discharges

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phys. Plasmas 4, 2482 (1997)] is below threshold. In simulations of DIII-D discharges, the observed shape of the H-mode edge pedestal is produced when transport associated with the TEM component of the GLF23 model is suppressed and transport given by the paleoclassical model is included. In a study involving 15 DIII-D H-mode discharges, it is found that with a particular combination of electron thermal transport models, the average rms deviation of the predicted electron temperature profile from the experimental profile is reduced to 9% and the offset to −4%.

A collective scattering system for measuring electron gyroscale fluctuations on the National Spherical Torus Experiment

A collective scattering system has been installed on the National Spherical Torus Experiment (NSTX) to measure electron gyroscale fluctuations in NSTX plasmas. The system measures fluctuations with k( perpendicular)rho(e) less, similar0.6 and k( perpendicular) less, similar20 cm(-1). Up to five distinct wavenumbers are measured simultaneously, and the large toroidal curvature of NSTX plasmas provides enhanced spatial localization. Steerable optics can position the scattering volume throughout the plasma from the magnetic axis to the outboard edge. Initial measurements indicate rich turbulent dynamics on the electron gyroscale. The system will be a valuable tool for investigating the connection between electron temperature gradient turbulence and electron thermal transport in NSTX plasmas.

Effect of Quasihelical Symmetry on Trapped-Electron Mode Transport in the HSX Stellarator

This Letter presents theory-based predictions of anomalous electron thermal transport in the Helically Symmetric eXperiment stellarator, using an axisymmetric trapped-electron mode drift wave model. The model relies on modifications to a tokamak geometry that approximate the quasihelical symmetry in the Helically Symmetric eXperiment (particle trapping and local curvature) and is supported by linear 3D gyrokinetic calculations. Transport simulations predict temperature profiles that agree with experimental profiles outside a normalized minor radius of rho>0.3 and energy confinement times that agree within 10% of measurements. The simulations can reproduce the large measured electron temperatures inside rho<0.3 if an approximation for turbulent transport suppression due to shear in the radial electric field is included.

Electron thermal transport analysis in Tokamak à Configuration Variable

A Tokamak à Configuration Variable (TCV) [G. Tonetti, A. Heym, F. Hofmann et al., in Proceedings of the 16th Symposium on Fusion Technology, London, U.K., edited by R. Hemsworth (North-Holland, Amsterdam, 1991), p. 587] plasma with high power density (up to 8MW∕m3) core deposited electron cyclotron resonance heating at significant plasma densities (⩽7×1019m−3) is analyzed for the electron thermal transport. The discharge distinguishes itself as it has four distinct high confinement mode (H-mode) phases. An Ohmic H-mode with type III edge localized modes (ELMs), which turns into a type I ELMy H-mode when the ECRH is switched on. The ELMs then vanish, which gives rise to a quasistationary ELM-free H-mode. This ELM-free phase can be divided into two, one without magnetohydrodynamics (MHD) and one with. The MHD mode in the latter case causes the confinement to drop by ∼15%. For all four phases both large-scale trapped electron (TEM) and ion temperature gradient (ITG) modes and small-scale electron temperature gradient (ETG) modes are analyzed. The analytical TEM formulas have difficulty in explaining both the magnitude and the radial profile of the electron thermal flux. Collisionality governs the drive of the TEM, which for the discharge in question implies it can be driven by either the temperature or density gradient. The TEM response function is derived and it is shown to be relatively small and to have sharp resonances in its energy dependence. The ETG turbulence, predicted by the Institute for Fusion Studies electron gyrofluid code, is on the other hand driven solely by the electron temperature gradient. Both trapped and passing electrons add to the ETG instability and turbulent thermal flux. For easy comparison of the results of the above approaches and also with the Weiland model, a dimensionless error measure, the so-called average relative variance is introduced. According to this method the ETG model explains 70% of the variation in the electron heat diffusivity whereas the predictive capabilities of the TEM-ITG models are poor. These results for TCV support the conclusion that the ETG model is able to explain a wide range of anomalous electron transport data, in addition to existing evidence from ASDEX [F. Ryter, F. Leuterer, G. Pereverzev, H.-U. Fahrbach, J. Stober, W. Suttrop, and the ASDEX Upgrade Team, Phys. Rev. Lett. 86, 2325 (2001)], Tore Supra [G. T. Hoang, W. Horton, C. Bourdelle, B. Hu, X. Garbet, and M. Ottaviani, Phys. Plasmas 10, 405 (2003)] and the Frascati Tokamak Upgrade [A. Jacchia, F. D. Luca, S. Cirant, C. Sozzi, G. Bracco, A. Brushi, P. Buratti, S. Podda, and O. Tudisco, Nucl. Fusion 42, 1116 (2002)].

Systematic study of Rayleigh–Taylor growth in directly driven plastic targets in a laser-intensity range from ∼2×1014to∼1.5×1015W∕cm2

Direct-drive, Rayleigh–Taylor (RT) growth experiments were performed using planar plastic targets on the OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] at laser intensities between ∼2×1014 and ∼1.5×1015W∕cm2. The primary purpose of the experiments was to test fundamental physics in hydrocodes at the range of drive intensities relevant to ignition designs. The target acceleration was measured with a streak camera using side-on, x-ray radiography, while RT growth was measured with a framing camera using face-on radiography. In a laser-intensity range from 2to5×1014W∕cm2, the measured RT growth agrees well with two-dimensional simulations, based on a local model of thermal-electron transport. The RT growth at drive intensities above ∼1.0×1015W∕cm2 was strongly stabilized compared to the local model predictions. The experiments demonstrate that standard simulations, based on a local model of electron thermal transport, break down at peak intensities of ignition designs, although they work well at lower intensities. These results also imply that direct-drive ignition targets are significantly more stable than previously calculated using local electron-transport models at peak intensities of ignition designs. The preheating effects by nonlocal electron transport and hot electrons were identified as some of the stabilizing mechanisms.

Rayleigh-Taylor Growth Stabilization in Direct-Drive Plastic Targets at Laser Intensities of∼1×1015 W/cm2

Direct-drive, planar-target Rayleigh-Taylor growth experiments were performed for the first time to test fundamental physics in hydrocodes at peak drive intensities of ignition designs. The unstable modulation growth at a drive intensity of approximately 1 x 10(15) W/cm2 was strongly stabilized compared to the growth at an intensity of approximately 5 x 10(14) W/cm2. The experiments demonstrate that standard simulations based on a local model of electron thermal transport break down at peak intensities of ignition designs (although they work well at lower intensities). The preheating effects by nonlocal electron transport and hot electrons were identified as some of the stabilizing mechanisms.

Scale Separation between Electron and Ion Thermal Transport

Nonlinear gyrokinetic simulations of microturbulence simultaneously driven by electron temperature gradient modes, trapped electron modes, and ion temperature gradient modes are presented, covering both electron and ion spatiotemporal scales self-consistently. It is found that, for realistic ion heat (and particle) flux levels and in the presence of unstable electron temperature gradient modes, there tends to be a scale separation between electron and ion thermal transport. In contrast to the latter, the former may exhibit substantial or even dominant high-wave-number contributions.

Relationship between edge localized mode severity and electron transport in the National Spherical Torus Experiment

In the National Spherical Torus Experiment [J. Menard et al., Nucl. Fusion 47, S645 (2007)], “giant” edge localized modes (ELMs) can occur resulting in a loss of plasma stored energy of up to 30%. These events are distinct from type I ELMs, whose energy loss is typically 4–10%, and they are accompanied by a cold pulse that causes a global decrease in the electron temperature profile. Estimates of the electron thermal transport during the cold pulses show a large enhancement over the underlying cross-field thermal diffusivity, χe, of up to several tens of m2∕s. Following the ELM, short-wavelength fluctuations increase in the plasma edge and core, corresponding to an increase in the electron temperature gradient from the propagating cold pulse. Fast electron temperature measurements indicate that the normalized electron temperature scale length, R∕LTe, reaches the threshold value for instability predicted by a fit to linear stability calculations. This is observed on time scales that match the growth of the high-k fluctuations in the plasma core, indicating that the enhanced χe and energy loss from the “giant” ELM appears to be related to critical gradient physics and the destabilization of electron temperature gradient modes.

Progress in direct-drive inertial confinement fusion

Significant progress in direct-drive inertial confinement fusion (ICF) research has been made since the completion of the 60-beam, 30-kJUV OMEGA Laser System [Boehly, Opt. Commun. 133, 495 (1997)] in 1995. A theory of ignition requirements, applicable to any ICF concept, has been developed. Detailed understanding of laser-plasma coupling, electron thermal transport, and hot-electron preheating has lead to the measurement of neutron-averaged areal densities of ∼200mg∕cm2 in cryogenic target implosions. These correspond to an estimated peak fuel density in excess of 100g∕cm3 and are in good agreement with hydrodynamic simulations. The implosions were performed using an 18-kJ drive pulse designed to put the converging fuel on an adiabat of two. The polar-drive concept will allow direct-drive-ignition research on the National Ignition Facility while it is configured for indirect drive. Advanced ICF ignition concepts—fast ignition [Tabak et al., Phys. Plasmas 1, 1626 (1994)] and shock ignition [Betti et al., Phys. Rev. Lett. 98, 155001 (2007)]—have the potential to significantly reduce ignition driver energies and/or provide higher target gain.