Electron Temperature Gradient Instability Research Articles

ETG turbulence in a tokamak pedestal

This paper explores the fundamental characteristics of electron-temperature-gradient (ETG)-driven turbulence in the tokamak pedestal. The extreme gradients in the pedestal produce linear instabilities and nonlinear turbulence that are distinct from the corresponding ETG phenomenology in the core plasma. The linear system exhibits multiple (greater than ten) unstable eigenmodes at each perpendicular wave vector, representing different toroidal and slab branches of the ETG instability. Proper orthogonal decomposition of the nonlinear fluctuations reveals no clear one-to-one correspondence between the linear and nonlinear modes for most wave vectors. Moreover, nonlinear frequencies deviate strongly from those of the linear instabilities, with spectra peaking at positive frequencies, which is opposite the sign of the ETG instability. The picture that emerges is one in which the linear properties are preserved only in a narrow range of k-space. Outside this range, nonlinear processes produce strong deviations from both the linear frequencies and eigenmode structures. This is interpreted in the context of critical balance, which enforces alignment between the parallel scales and fluctuation frequencies. We also investigate the nonlinear saturation processes. We observe a direct energy cascade from the injection scale to smaller scales in both perpendicular directions. However, in the bi-normal direction, there is also nonlocal inverse energy transfer to larger scales. Neither streamers nor zonal flows dominate the saturation.

Gyrokinetic benchmark of the electron temperature-gradient instability in the pedestal region

Transport from turbulence driven by the electron temperature-gradient (ETG) instability is likely a major source of electron heat losses through the pedestal. Due to extreme gradients and strong shaping, ETG instabilities in the pedestal are distinct from those in the core, having, for example, multiple branches (toroidal and slab) in different wavenumber ranges. Due to its importance for pedestal transport, and its rather exotic character, a rigorous multi-code benchmarking exercise is imperative. Here, we describe such an exercise, wherein we have carried out a detailed comparison of local linear pedestal ETG simulations using three gyrokinetic codes, CGYRO, GEM, and GENE and testing different geometric parameters (such as circular, Miller, and equilibrium EFIT geometry). The resulting linear frequencies, growth rates, and eigenfunctions show very good agreement between the codes in the three types of employed geometries. A nonlinear benchmark between CGYRO and GENE is also described, exhibiting good agreement (a maximum of 20% difference in the heat fluxes computed) at two locations in the pedestal. This lays the foundation for confidently modeling ETG turbulence in the pedestal.

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, ky is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and ρi is the ion gyroradius. At , the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, , where Kx is the effective radial wavenumber. Here, ρe is the electron gyroradius, R0 is the major radius of the last closed flux surface, and 1/LTe is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by shear. ETG modes are very resilient to shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.

Linear and nonlinear fluctuations of electron‐temperature‐gradient driven mode and electron acoustic mode in a two‐electron temperature nonthermal magnetized plasma

AbstractNonlinear vortical structures and soliton formation are investigated for electron temperature gradient instability in a two‐electron temperature non‐Maxwellian magnetoplasma. The inhomogeneity in magnetic field is also considered. A new set of nonlinear equations, using transport equations of Braginskii”s model, are formulated to study the nonlinear structures. A modified linear dispersion relation of coupled electron temperature gradient (ETG) mode and electron acoustic wave is derived. The ETG instability is found to increase with increase in ηec value that increases with sharp density gradients. The results are applied to auroral region of earth's magnetosphere and the calculated values of the nonlinear electric field of fast solitary waves are found to be in agreement with the Viking satellite observations.

First implementation of gyrokinetic exact linearized Landau collision operator and comparison with models

Gyrokinetic simulations are fundamental to understanding and predicting turbulent transport in magnetically confined fusion plasmas. Previous simulations have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. We have implemented the linearized Fokker–Planck collision operator with exact field-particle terms and full FLR effects in a gyrokinetic code (GENE). The new operator, referred to as “exact” in this paper, allows the accuracy of model collision operators to be assessed. The conservative Landau form is implemented because its symmetry underlies the conservation laws and the H-theorem, and enables numerical methods to preserve this conservation, independent of resolution. The implementation utilizes the finite-volume method recently employed to discretize the Sugama collision model in GENE, allowing direct comparison between the two operators. Results show that the Sugama model appears accurate for the growth rates of trapped electron modes (TEMs) driven only by density gradients, but appreciably underestimates the growth rates as the collisionality and electron temperature gradient increase. The TEM turbulent fluxes near the nonlinear threshold using the exact operator are similar to the Sugama model for the ηe=d ln Te/d ln ne=0 case, but substantially larger than the Sugama model for the ηe=1 case. The FLR effects reduce the growth rates increasingly with wavenumber, deepening a “valley” at the intermediate binormal wavenumber as the unstable mode extends from the TEM regime to the electron temperature gradient instability regime. Application to the Hinton–Rosenbluth problem shows that zonal flows decay faster as the radial wavenumber increases and the exact operator yields weaker decay rates.

Heat transport driven by the ion temperature gradient and electron temperature gradient instabilities in ASDEX Upgrade H-modes

A study of the properties of the turbulence-driven ion and electron heat fluxes, is presented. Dedicated H-mode experiments taking advantage of the on-axis and off-axis possibilities of both neutral beam injection and electron cyclotron resonance heating available on the ASDEX Upgrade tokamak were carried out. The experimental results are interpreted by comparisons with gyrokinetic calculations. Ion heat transport is, as expected, driven by the ion temperature gradient (ITG) instability with the features predicted by theory: increase of the driven heat flux above a threshold in normalised gradient. In addition the main effects known to impact on the stability of the turbulence, temperature ratio and fast ions population, are exhibited by the experimental results and agree with the gyrokinetic calculations. It is known that the ITG also contributes to the electron heat flux, but that an electron instability can be required in addition when the ITG contribution does not drive the whole imposed electron heating. This situation, investigated by adding electron cyclotron heating, indicates that in the experiments presented here the electron temperature gradient instability develops.

Solitary waves with electron temperature inhomogeniety and shear flow in an electron ion magnetoplasma

Electron temperature gradient (ETG) driven solitons are investigated having gradients in equilibrium electron temperature and equilibrium number density and with electron shear flow. In a linear regime, using model equations, a linear dispersion relation has been analysed analytically as well as numerically. ηe and electron to ion temperature ratio effects, real frequency, and growth rate of ETG instability are determined. In the nonlinear regime, the Korteweg--de Vries equation for the ETG mode has been derived and analysed numerically which shows that it admits solitary wave solutions. It can also be noted that soliton amplitude is sensitive to ηe, the magnetic field, and the temperature ratio. This work may be helpful for low frequency electrostatic modes in nonuniform electron-ion plasma having gradients in density and electron temperature and also in tokamak plasma.

Electromagnetic electron temperature gradient driven instability in toroidal plasmas

The fluid theory of a new type of electron temperature gradient instability is proposed. This mode is closely related to the short wavelength Alfvén mode in the regime k⊥2ρi2>1. Contrary to standard electron temperature gradient modes, which are mostly electrostatic, the considered mode is fundamentally electromagnetic and does not exist in the electrostatic limit. The mechanism of instability relies on gradients in both the electron temperature and magnetic field. It is suggested that this instability may be a destabilizing mechanism for collisionless microtearing modes, which are observed in a number of gyrokinetic simulations.

Electron temperature gradient excited vortices in plasmas with impurities

Vortices formed from electron temperature gradient instabilities in impurity-containing plasmas have been investigated. It is shown that the impurities in the plasma can have a significant effect on the characteristics of the vortex, in particular its amplitude and thus its effectiveness in particle and energy transport across the confining magnetic field.

Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence

Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving new infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium “translated” pressure gradient, stable equilibria can either be energy stable, i.e., possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes. The ETG instability is then shown to arise through a Kreĭn-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, which unambiguously defines mode signature. In particular, the fast mode turns out to always be a positive energy mode, whereas the energy of the slow mode can have either positive or negative sign. A reduced model with stable equilibria shear flow that possess a continuous spectrum is also analyzed and brought to normal form by a special integral transform. In this way it is seen how continuous spectra can have signature as well.

Parallel magnetic field perturbations in gyrokinetic simulations

At low β it is common to neglect parallel magnetic field perturbations on the basis that they are of order β2. This is only true if effects of order β are canceled by a term in the ∇B drift also of order β [H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 (1977)]. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2 [Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)] to investigate whether the compressional magnetic field perturbation B∥ is required for accurate gyrokinetic simulations at low β for microinstabilities commonly found in tokamaks. The kinetic ballooning mode (KBM) demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient (ETG) driven modes do not typically exhibit this behavior; the effects of B∥ are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with ηe. The effect of B∥ on the ETG instability is shown to depend on the normalized pressure gradient β′ at constant β.

Role of secondary long wavelength structures in the saturation of electron temperature gradient driven turbulence

The dynamics of secondary long wavelength structures (LWSs) in electron temperature gradient (ETG) driven turbulence are investigated by performing gyrofluid simulations and modeling analyses in a slab geometry with an emphasis of the underlying nonlinear interaction processes. It is shown that the back-reaction of the secondary LWS on the ambient fluctuations essentially contributes to saturating ETG instability and limiting the electron transport. The LWS is nonlinearly generated mainly through the beating of the most unstable ETG modes, even a weak modulation instability. The back-reaction is identified as the enhanced stabilization of the ETG modes due to the streamer-type feature of the LWS, which dominantly produces a local poloidal mode coupling among unstable and highly damped spectral components to form a global mode, besides the suppression effect of the LWS due to the radial shearing decorrelation and/or the radial mode coupling. Finally, the correspondence between the LWS in the slab model and the quasimode observed in toroidal ETG simulation [Z. Lin et al., Phys. Plasmas 12, 056125 (2005)] and the importance of the nonlinear mode coupling in the multiscale turbulence interaction are discussed.

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)].

Large-scale structures and turbulence saturation in gyrofluid ETG simulations

The dynamics of secondary fluctuations with poloidal long wavelength and low frequency in electron-temperature-gradient (ETG) turbulence saturation is considered in sheared slab geometry. A simplified modeling analysis shows that this kind of large-scale structure including streamers may saturate primary ETG instability through poloidal mode coupling. Spectral analyses in three-dimensional ETG simulations clearly exhibit the secondary excitation and the probable relevancy to KTG saturation. The result may implicate a lower fluctuation level in ETG turbulence.

Study of electron temperature gradient instability in toroidal plasmas with negative magnetic shear

Electron temperature gradient driven instability in toroidal plasmas with negative magnetic shear is studied. Full electron kinetics is considered and the behaviours of the modes and corresponding turbulent transport in the parameter regimes close to the instability threshold are emphasized. Growing and damped modes are both investigated. The singular points of the integrand are disposed of and the fitting formulae for the critical gradient are given. The theoretical results are shown to be close to the experimental observations.

Turbulence behaviour during electron heated reversed shear discharges in JET

Low-frequency/long-wavelength density turbulence is found to be reduced withinthe volume enclosed by an electron thermal internal transport barrier generated with lower hybrid microwave heating in the JET tokamak. Theturbulence reduction coincides with a region (typically r/a<0.4) ofnegative, or reversed magnetic shear s and reduced electron thermal diffusionχe. In the tokamak edge region (r/a>0.8), the turbulenceamplitude is also reduced coinciding with large positive magnetic shears>1. Estimates of the core turbulence wavelengths (λ⊥>0.1 m) are not in agreement with expectations from electron temperaturegradient instabilities.

Gyrokinetic study of the electron temperature gradient instability in plasmas with slightly hollow density profiles

The electron temperature gradient driven instabilities in plasmas with slightly hollow density profiles are studied. The gyrokinetic integral eigenvalue equation valid for a sheared slab configuration is employed. The Debye shielding effect on the modes is investigated. The effects of a sheared E×B flow on the modes are considered. Six modes with even or odd parities are found to be simultaneously unstable. The mixing length estimate for the transport is calculated. The flow shear suppression on the modes, as well as on the transport, is demonstrated. The correlations of the results with helical system Heliotron/Torsotron and tokamak experiments are discussed.

Nonlocal theory and turbulence of the sheath-driven electron temperature gradient instability

A nonlocal linear theory of the sheath-driven ∇Te mode for a uniformly increasing temperature profile that properly includes effects of a varying Larmor radius has been developed. This theory was used to verify nonlinear fluid simulations of this mode in a two-dimensional slab. The nonlinear evolution of the mode was found to depend not only upon the growth rate, but also upon the variation of the E×B drift over the extent of the radial eigenmode. When the difference in the E×B drift frequency exceeded the growth rate, the linear mode structure was distorted at early times leading to a mixing of the vortices, which allowed a rapid nonlinear growth of the longer wavelengths. When the mode grew faster than any tilting of the vortices, the fluctuations remained coherent and localized for many growth times. Not until the fluctuations grew to very large amplitude (∼50%) did the longer wavelength modes grow and contribute to the turbulence. By comparing the analytical growth rate and the variation of the equilibrium drift frequency, a condition that predicts which state the mode will evolve to was derived in terms of physical parameters of the system.

Velocity shear effects in the problem of the electron temperature gradient instability induced by conducting end-walls

The effects of shear in the E × B rotation velocity are studied in connection with the recently discovered electron temperature gradient driven instability induced by conducting end plates. The transition between the temperature gradient driven mode and the Helmholtz-Kelvin instability is studied.

The Electron Temperature Gradient Instability in Presence of a Limiter with Tilted Plates

AbstractThe analysis of the electron temperature gradient instability in the scrape‐off layer is generalized to the case of non‐orthogonal intersections of the magnetic field with the wall surface, a situation which is most typical for a tokamak with a limiter.