Temperature Gradient Scale Length Research Articles

Nonlocal suppression of Biermann battery magnetic-field generation for arbitrary atomic numbers and magnetization

The Biermann battery term of magnetohydrodynamics (MHD) generates a magnetic field where electron density gradients and electron temperature gradients are perpendicular to one another. Kinetic simulations and experiments have shown that the rate of magnetic-field generation is lower than Biermann when the electron mean free path becomes comparable to or greater than the temperature gradient scale length, known as the nonlocal regime. We investigate the nonlocal suppression of the Biermann term using simplified Fokker–Planck simulations covering a wide range of parameters. We provide the first fit for nonlocal Biermann suppression that has physically accurate behavior for small and large values of a suitable nonlocality parameter, valid for an arbitrary atomic number, and that includes the effect of magnetization on nonlocality. The fit is intended to provide an approximate method to account for reduced magnetic-field generation in MHD codes and theory.

The role of ETG modes in JET–ILW pedestals with varying levels of power and fuelling

We present the results of GENE gyrokinetic calculations based on a series of JET–ITER-like-wall (ILW) type I ELMy H-mode discharges operating with similar experimental inputs but at different levels of power and gas fuelling. We show that turbulence due to electron-temperature-gradient (ETGs) modes produces a significant amount of heat flux in four JET–ILW discharges, and, when combined with neoclassical simulations, is able to reproduce the experimental heat flux for the two low gas pulses. The simulations plausibly reproduce the high-gas heat fluxes as well, although power balance analysis is complicated by short ELM cycles. By independently varying the normalised temperature gradients and normalised density gradients around their experimental values, we demonstrate that it is the ratio of these two quantities that determines the location of the peak in the ETG growth rate and heat flux spectra. The heat flux increases rapidly as η e increases above the experimental point, suggesting that ETGs limit the temperature gradient in these pulses. When quantities are normalised using the minor radius, only increases in produce appreciable increases in the ETG growth rates, as well as the largest increases in turbulent heat flux which follow scalings similar to that of critical balance theory. However, when the heat flux is normalised to the electron gyro-Bohm heat flux using the temperature gradient scale length , it follows a linear trend in correspondence with previous work by different authors.

Reduced models for ETG transport in the tokamak pedestal

This paper reports on the development of reduced models for electron temperature gradient (ETG) driven transport in the pedestal. Model development is enabled by a set of 61 nonlinear gyrokinetic simulations with input parameters taken from pedestals in a broad range of experimental scenarios. The simulation data have been consolidated in a new database for gyrokinetic simulation data, the multiscale gyrokinetic database (MGKDB), facilitating the analysis. The modeling approach may be considered a generalization of the standard quasilinear mixing length procedure. The parameter η, the ratio of the density to temperature gradient scale length, emerges as the key parameter for formulating an effective saturation rule. With a single order-unity fitting coefficient, the model achieves an error of 15%. A similar model for ETG particle flux is also described. We also present simple algebraic expressions for the transport informed by an algorithm for symbolic regression.

Explaining the lack of power degradation of energy confinement in wide pedestal quiescent H-modes via transport modeling

Wide pedestal quiescent H (WPQH)-mode is an attractive scenario for future burning plasmas as they operate without ELMs. WPQH is characterized by formation of a wider and higher pedestal (than quiescent H-mode), and broadband fluctuations in the pedestal. Unlike conventional H-modes, where the energy confinement time reduces with increasing heating power, the WPQH plasmas reported in this paper do not show power degradation of the energy confinement. As the injected neutral beam power was increased, reduced core (ρ ⩽ 0.45) transport calculated by transp, as well as increased core temperatures, pressure gradient and diamagnetic E × B shear rate were observed. The reduction in the heat transport and rapid decrease in the ion temperature gradient scale length suggest the formation of an ion internal transport barrier (ITB) that was accompanied by increased stored energy in the core. Quasilinear turbulent transport modeling using the trapped gyro Landau fluid (tglf) code was used to predict the ITB and its turbulence stability properties. By using profiles and equilibria produced by matching the transp transport fluxes with the tglf transport model within the tgyro transport solver, the energy confinement time captures the experimentally observed insensitivity to the increased P NBI. Linear stability analysis reveals that drift-wave instabilities in the core are stabilized by E × B shear, T i/T e ratio and Shafranov shift; the latter was found to have the strongest effect on the turbulence suppression at the highest heating level.

Fast modulating electron cyclotron emission (FMECE) diagnostic for tokamaks.

Utilizing variable-frequency channels, e.g., yttrium iron garnet (YIG) bandpass filters, in the intermediate frequency (IF) section of an electron cyclotron emission (ECE) radiometer facilitates flexibility in the volume viewed by the ECE channels as well as high resolution electron temperature and temperature fluctuation measurements in tokamaks. Fast modulating electron cyclotron emission (FMECE), a stand-alone IF section with eight channels, is a novel application of YIG filters for real-time electron temperature gradient and gradient scale length measurements. Key to FMECE is a simultaneous input/output data acquisition unit, as well as a modified type of YIG filters, which is capable of fast switching of their center (set) frequencies with a frequency slew rate of 600 µs/GHz. A new FMECE has been implemented and tested on the DIII-D tokamak, demonstrating its capability in real-time gradient measurements. The data presented here shows that FMECE can identify flattening in the electron temperature profile; the latter can be used as a sensor for real time monitoring and control of plasma instabilities. Implementation and application are planned for the EAST tokamak.

Temperature distributions and gradients in laser-heated plasmas relevant to magnetized liner inertial fusion.

We present two-dimensional temperature measurements of magnetized and unmagnetized plasma experiments performed at Z relevant to the preheat stage in magnetized liner inertial fusion. The deuterium gas fill was doped with a trace amount of argon for spectroscopy purposes, and time-integrated spatially resolved spectra and narrow-band images were collected in both experiments. The spectrum and image data were included in two separate multiobjective analysis methods to extract the electron temperature spatial distribution T_{e}(r,z). The results indicate that the magnetic field increases T_{e}, the axial extent of the laser heating, and the magnitude of the radial temperature gradients. Comparisons with simulations reveal that the simulations overpredict the extent of the laser heating and underpredict the temperature. Temperature gradient scale lengths extracted from the measurements also permit an assessment of the importance of nonlocal heat transport.

Propagation of input parameter uncertainties in transport models

The many sources of uncertainty in validation studies of plasma turbulence in magnetically confined fusion devices are well-known. In this paper, we investigate how to efficiently transform uncertainties in experimentally derived transport model inputs into model prediction uncertainties, using the quasilinear trapped-gyro-Landau-fluid (TGLF) turbulent transport model [Staebler et al., Phys. Plasmas 14, 055909 (2007)]. We use the rapidly converging and computationally inexpensive non-intrusive probabilistic collocation method (PCM) to propagate input parameter uncertainty probability distribution functions (PDFs) through TGLF, yielding PDFs of predicted transport fluxes. We observe in many cases that the flux PDFs exhibit significant non-normal features such as strong skewness, even when the input distributions were normal. To illustrate the utility of the PCM approach, we apply this methodology to transport predictions for a DIII-D ITER baseline plasma [Grierson et al., Phys. Plasmas 25, 022509 (2018)] in which the mix of neutral beam injection (NBI) and electron cyclotron heating (ECH) was varied. The model predictions show clear changes in the parametric dependencies and sensitivities of the turbulence between the two heating mixes. Specifically, when only NBI heating was used, the transport fluxes responded significantly only to the ion temperature gradient scale length. However, when both NBI and ECH were applied, the electron transport channels demonstrate a strong sensitivity to the electron temperature and density gradients not observed in the NBI-only case. Additional context for the PCM approach is provided by comparing its predictions with those obtained via a local flux-matching approach. A new set of validation metrics based on the Wasserstein distance is proposed for PDF-based comparisons.

Upgrade of the ECE diagnostic on EAST.

The electron cyclotron emission (ECE) diagnostic on the experimental advanced superconducting tokamak (EAST) was upgraded recently to provide electron temperature profile measurement with wider radial coverage and better precision. The lower limit of the ECE detection frequency band was extended from 104 GHz to 97 GHz by adding a new 8-channel heterodyne radiometer, which ensures capability for the measurement of the second harmonic ECE with toroidal magnetic field down to 1.75 T. Also, the existing 32-channel heterodyne radiometer has been upgraded, with the frequency interval for the lower frequency range up to 120 GHz reduced from 2 GHz to 1 GHz by introducing eight channels in the intermediate frequency part. In addition, a plan is presented to incorporate tunable yttrium iron garnet filters into the existing heterodyne radiometer to obtain detailed measurements of the electron temperature gradient scale length as well as finer spatial pinpointing of magnetohydrodynamic modes. Examples from DIII-D are provided where similar ECE diagnostic allowed precise measurement of the center and width of neoclassical tearing modes.

Electron critical gradient scale length measurements of ICRF heated L-mode plasmas at Alcator C-Mod tokamak

A profile for the critical gradient scale length (Lc) has been measured in L-mode discharges at the Alcator C-Mod tokamak, where electrons were heated by an ion cyclotron range of frequency through minority heating with the intention of simultaneously varying the heat flux and changing the local gradient. The electron temperature gradient scale length (LTe−1 = |∇Te|/Te) profile was measured via the BT-jog technique [Houshmandyar et al., Rev. Sci. Instrum. 87, 11E101 (2016)] and it was compared with electron heat flux from power balance (TRANSP) analysis. The Te profiles were found to be very stiff and already above the critical values, however, the stiffness was found to be reduced near the q = 3/2 surface. The measured Lc profile is in agreement with electron temperature gradient (ETG) models which predict the dependence of Lc−1 on local Zeff, Te/Ti, and the ratio of the magnetic shear to the safety factor. The results from linear Gene gyrokinetic simulations suggest ETG to be the dominant mode of turbulence in the electron scale (k⊥ρs > 1), and ion temperature gradient/trapped electron mode modes in the ion scale (k⊥ρs < 1). The measured Lc profile is in agreement with the profile of ETG critical gradients deduced from Gene simulations.

Properties of ion temperature gradient and trapped electron modes in tokamak plasmas with inverted density profiles

We perform a numerical study of linear stability of the ion temperature gradient (ITG) mode and the trapped electron mode (TEM) in tokamak plasmas with inverted density profiles. A local gyrokinetic integral equation is applied for this study. From comprehensive parametric scans, we obtain stability diagrams for ITG modes and TEMs in terms of density and temperature gradient scale lengths. The results show that, for the inverted density profile, there exists a normalized threshold temperature gradient above which the ITG mode and the TEM are either separately or simultaneously unstable. The instability threshold of the TEM for the inverted density profile is substantially different from that for normal and flat density profiles. In addition, deviations are found on the ITG threshold from an early analytic theory in sheared slab geometry with the adiabatic electron response [T. S. Hahm and W. M. Tang, Phys. Fluids B 1, 1185 (1989)]. A possible implication of this work on particle transport in pellet fueled tokamak plasmas is discussed.

Temperature gradient scale length measurement: A high accuracy application of electron cyclotron emission without calibration.

Calibration is a crucial procedure in electron temperature (Te) inference from a typical electron cyclotron emission (ECE) diagnostic on tokamaks. Although the calibration provides an important multiplying factor for an individual ECE channel, the parameter ΔTe/Te is independent of any calibration. Since an ECE channel measures the cyclotron emission for a particular flux surface, a non-perturbing change in toroidal magnetic field changes the view of that channel. Hence the calibration-free parameter is a measure of Te gradient. BT-jog technique is presented here which employs the parameter and the raw ECE signals for direct measurement of electron temperature gradient scale length.

Electron temperature critical gradient and transport stiffness in DIII-D

In a continuing effort to validate turbulent transport models, the electron energy flux has been probed as a function of electron temperature gradient on the DIII-D tokamak. In the scan of gradient, a critical electron temperature gradient has been found in the electron heat fluxes and stiffness at various radii in L-mode plasmas. The TGLF reduced turbulent transport model (Staebler et al 2007 Phys. Plasmas 14 055909) and full gyrokinetic GYRO model (Candy and Waltz 2003 J. Comput. Phys. 186 545) recover the general trend of increasing electron energy flux with increasing electron temperature gradient scale length, but they do not predict the absolute level of transport at all radii and gradients. Comparing the experimental observations of incremental (heat pulse) diffusivity and stiffness to the models’ reveals that TGLF reproduces the trends in increasing diffusivity and stiffness with increasing electron temperature gradient scale length with a critical gradient behavior. The critical gradient of TGLF is found to have a dependence on q95, contrary to the independence of the experimental critical gradient from q95.

How to apply a turbulent transport model based on a gyrokinetic simulation for the ion temperature gradient mode in helical plasmas

How to apply a reduced model for the turbulent ion heat diffusivity [Nunami M et al. 2013 Phys. Plasmas, 20 092307] derived from a gyrokinetic code to a transport simulation is proposed. The reduced model is given by the function of the linear growth rate of the ion temperature gradient (ITG) mode and the decay time of zonal flows. The ion temperature gradient scale length is chosen for the additional modeling to include the linear growth rate of the ITG mode from a gyrokinetic code. The formula for the zonal flow decay time is derived at the given magnetic field configuration. The calculation of an extremely low computational cost in this article reproduces the results of the reduced model for the turbulent ion heat diffusivity within allowable errors.

Effects of non-local electron transport in one-dimensional and two-dimensional simulations of shock-ignited inertial confinement fusion targets

In some regions of a laser driven inertial fusion target, the electron mean-free path can become comparable to or even longer than the electron temperature gradient scale-length. This can be particularly important in shock-ignited (SI) targets, where the laser-spike heated corona reaches temperatures of several keV. In this case, thermal conduction cannot be described by a simple local conductivity model and a Fick's law. Fluid codes usually employ flux-limited conduction models, which preserve causality, but lose important features of the thermal flow. A more accurate thermal flow modeling requires convolution-like non-local operators. In order to improve the simulation of SI targets, the non-local electron transport operator proposed by Schurtz-Nicolaï-Busquet [G. P. Schurtz et al., Phys. Plasmas 7, 4238 (2000)] has been implemented in the DUED fluid code. Both one-dimensional (1D) and two-dimensional (2D) simulations of SI targets have been performed. 1D simulations of the ablation phase highlight that while the shock profile and timing might be mocked up with a flux-limiter; the electron temperature profiles exhibit a relatively different behavior with no major effects on the final gain. The spike, instead, can only roughly be reproduced with a fixed flux-limiter value. 1D target gain is however unaffected, provided some minor tuning of laser pulses. 2D simulations show that the use of a non-local thermal conduction model does not affect the robustness to mispositioning of targets driven by quasi-uniform laser irradiation. 2D simulations performed with only two final polar intense spikes yield encouraging results and support further studies.

Transition between Saturation Regimes of Gyrokinetic Turbulence

A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.

Hydrogen isotope effects on ITG scale length, pedestal and confinement in JT-60 H-mode plasmas

The dependence of heat transport, edge pedestal and confinement on isotopic composition was investigated in conventional H-mode plasmas. Identical profiles for the electron density, electron temperature and ion temperature were obtained for hydrogen and deuterium plasmas, whereas the required power clearly increased for hydrogen, which resulted in a reduction in heat diffusivity for deuterium. The determination of identical temperature profiles, despite the different heating power, suggested that the characteristics of heat conduction essentially differ for hydrogen and deuterium, even at the same scale length of temperature gradient. The self-regulating physics mechanism determining the overall H-mode confinement was also addressed. The inverse of the ion temperature gradient (ITG) scale length, or ∇Ti/Ti, which is required for a given ion heat diffusivity, increased by a factor of approximately 1.2 for deuterium compared with that for hydrogen. The relationship between edge pedestal pressure and global βp holds true consistently regardless of the difference in the isotopic composition. A higher value of βp 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 in the slowing down time with an increase in isotopic mass.

Gyrokinetic Theory of Turbulent Acceleration of Parallel Rotation in Tokamak Plasmas

A mechanism for turbulent acceleration of parallel rotation is discovered using gyrokinetic theory. This new turbulent acceleration term cannot be written as a divergence of parallel Reynolds stress. Therefore, turbulent acceleration acts as a local source or sink of parallel rotation. The physics of turbulent acceleration is intrinsically different from the Reynolds stress. For symmetry breaking by positive intensity gradient, a positive turbulent acceleration, i.e., cocurrent rotation, is predicted. The turbulent acceleration is independent of mean rotation and mean rotation gradient, and so constitutes a new candidate for the origin of spontaneous rotation. A quasilinear estimate for ion temperature gradient turbulence shows that the turbulent acceleration of parallel rotation is explicitly linked to the ion temperature gradient scale length and temperature ratio Ti0/Te0. Methods for testing the effects of turbulent parallel acceleration by gyrokinetic simulation and experiment are proposed.

Resonant magnetic perturbation effects on pedestal structure and ELMs

The plasma transport processes by which externally applied resonant magnetic field perturbations (RMPs) mitigate or suppress edge-localized modes (ELMs) in low-collisionality tokamak H-mode plasmas are explored. Experimental data from DIII-D indicates the dominant RMP-induced transport occurs at the pedestal top where electron temperature gradient scale lengths increase up to 3 times more than density gradient scale lengths. The increases scale approximately with the square of the strength of the RMPs. Since flow screening is predicted to inhibit magnetic island formation and magnetic stochasticity, a plasma transport model that does not depend on stochasticity is apparently needed. Thus, a basic magnetic-flutter-based cylindrical screw-pinch model theory of plasma transport is developed. A key attribute of this new model is that while RMP-induced radial magnetic perturbations can be significantly reduced on rational surfaces by flow screening, they induce spatial magnetic flutter away from them and thereby can cause substantial radial plasma transport. The plasma transport predictions of this spatial flutter model are compared with the DIII-D transport data.

Electron profile stiffness and critical gradient studies

Electron profile stiffness was studied in DIII-D L-mode discharges by systematically varying the heat flux in a narrow region with electron cyclotron heating and measuring the local change produced in ∇Te. Electron stiffness was found to slowly increase with toroidal rotation velocity. A critical inverse temperature gradient scale length 1/LC ∼ 3 m−1 was identified at ρ=0.6 and found to be independent of rotation. Both the heat pulse diffusivity and the power balance diffusivity, the latter determined by integrating the measured dependence of the heat pulse diffusivity on –∇Te, were fit reasonably well by a model containing a critical inverse temperature gradient scale length and varying linearly with 1/LT above the threshold.

Physics of intrinsic rotation in flux-driven ITG turbulence

Global, heat flux-driven ITG gyrokinetic simulations which manifest the formation of macroscopic, mean toroidal flow profiles with peak thermal Mach number 0.05, are reported. Both a particle-in-cell (XGC1p) and a semi-Lagrangian (GYSELA) approach are utilized without a priori assumptions of scale separation between turbulence and mean fields. Flux-driven ITG simulations with different edge flow boundary conditions show in both approaches the development of net unidirectional intrinsic rotation in the co-current direction. Intrinsic torque is shown to scale approximately linearly with the inverse scale length of the ion temperature gradient. External momentum input is shown to effectively cancel the intrinsic rotation profile, thus confirming the existence of a local residual stress and intrinsic torque. Fluctuation intensity, intrinsic torque and mean flow are demonstrated to develop inwards from the boundary. The measured correlations between residual stress and two fluctuation spectrum symmetry breakers, namely E × B shear and intensity gradient, are similar. Avalanches of (positive) heat flux, which propagate either outwards or inwards, are correlated with avalanches of (negative) parallel momentum flux, so that outward transport of heat and inward transport of parallel momentum are correlated and mediated by avalanches. The probability distribution functions of the outward heat flux and the inward momentum flux show strong structural similarity.