Electron Temperature Gradient Modes Research Articles

Predictive modeling of NSTX discharges with the updated multi-mode anomalous transport module

The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM’s ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.

Linear stability analysis of the electrostatic drift wave in the electron thermal internal transport barrier in EAST

An alternative local electrostatic gyrokinetic eigenvalue code is developed for the ion-temperature-gradient-driven mode, the trapped-electron mode (TEM), and the electron-temperature-gradient (ETG)-driven mode. It numerically solves the linear eigenvalue problem for the electrostatic drift waves in the Fourier transformed space and benchmarks well with the HD-7 code and FULL code. The linear ETG and TEM instabilities in the electron thermal internal transport barrier (eITB) with dominant electron heating in experimental advanced superconducting tokamak are analyzed by using this code. The linear analysis results are consistent with that from the critical electron-temperature-gradient threshold analysis. Moreover, the sensitivity of ETG and TEM instabilities to parameters during the eITB formation has been investigated. For the typical eITB discharge, it is found that the instability of ETG mode is more sensitive to the stabilizing effect of the electron–ion temperature ratio (τe), while the instability of TEM is more sensitive to the destabilizing effect of ηe. In addition, mixing length estimation of the turbulent transport in the eITB is also discussed, which suggests that the TEM may be saturated by other nonlinear effects than the resonance broadening.

Multi-scale gyrokinetic simulations of JT-60U L-mode plasma: reduction of the ion scale energy loss due to the nonlinear coupling with the electron scale turbulence

We investigate the effect of the electron temperature gradient (ETG) driven turbulence on the energy transport in JT-60U L-mode plasma by means of the multi-scale gyrokinetic simulation. In the core region at r/a=0.5 , the instability in the ion scale is driven by the ion temperature gradient (ITG), meanwhile strong unstable ETG modes are found in the electron scale. The nonlinear multi-scale gyrokinetic simulation shows that ETG modes are stabilized in the nonlinear phase and the energy transport in the multi-scale simulation is similar to that obtained in the ion scale ITG simulation. In an outer region at r/a=0.6 , the ion scale instability changes to be the trapped electron mode (TEM). The multi-scale simulation shows that both the ion and the electron energy flux are reduced by ∼30% compared to those obtained in the single scale TEM simulation. Interestingly, the electron energy flux is close to the experimental value after this reduction. From the data analyses, we find that ETG turbulence damps the energy of TEM modes through the ion scale/electron scale coupling and the electron scale/electron scale coupling, and can be modeled as a turbulent diffusion of TEM modes. These results suggest that the single ion scale simulation seems to be still valid in the inner region with r/a<0.5 . However, in the outer region it is necessary to include the ETG modes in the gyrokinetic simulations to explain the energy transport in this L-mode plasma. This is the first result showing that ETG turbulence can reduce the electron energy loss via the cross-scale interaction in a real tokamak equilibrium profile.

Complex structure of turbulence across the ASDEX Upgrade pedestal

The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to the pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma $\beta$ values. The turbulent transport is found to exhibit a multi-channel, multi-scale character throughout the pedestal with the dominant contribution transitioning from ion-scale trapped electron modes/micro-tearing modes at the pedestal top to electron-scale electron temperature gradient modes in the steep gradient region. Consequently, the turbulent electron heat flux changes from ion to electron scales and the ion heat flux reduces to almost neoclassic values in the pedestal centre. $E\times B$ shear is found to strongly reduce heat flux levels in all channels (electron, ion, electrostatic, electromagnetic) and the interplay of magnetic shear and pressure gradient is found to locally stabilise ion-scale instabilities.

Nonlinear microtearing modes in MAST and their stochastic layer formation

First nonlinear gyrokinetic simulations of microtearing modes in the core of a MAST case are performed on two surfaces of the high-collisionality discharge used in Valovič et al (2011 Nucl. Fusion 51 073045) to obtain the favorable energy confinement scaling with collisionality, . On the considered surfaces microtearing modes dominate linearly at binormal length scales of the order of the ion Larmor radius. While the effect of electron collision frequency is moderate in linear simulations, a strong dependence on this parameter is found in nonlinear simulations at , where r and a are the surface and tokamak minor radius, respectively. The dynamics of magnetic islands generated by microtearing modes is analysed, showing that the radial extent of the stochastic region caused by islands overlapping plays an important role in determining the saturation level of the microtearing mode driven heat flux. Local nonlinear gyrokinetic simulations show that the microtearing mode driven heat flux, , is largely dominated by magnetic flutter and depends strongly on the magnetic shear, . Comparing two surfaces, and , reveals that is negligible at (), with the electron temperature gradient (ETG) driven heat flux, , comparable to the experimental electron heat flux, , while is significantly larger and comparable to and at (). Microtearing modes cause more experimentally significant transport in higher regions and may influence (together with ETG modes) the observed scaling of energy confinement time with collisionality (Valovič et al 2011 Nucl. Fusion 51 073045).

Linear instabilities in the hot-ion regime in a high-field spherical tokamak

The present operating high-field compact spherical tokamak ST40 is an important step toward an ST-based fusion reactor (Gryaznevich and Asunta 2017 Fusion Eng. Des. 123 177; McNamara 2023 Nucl. Fusion 63 054002). Temperature and density profiles and their uncertainties in recent hot ion ST40 plasmas with central ion temperatures exceeding 8.6 keV, have been inferred using an integrated analysis of several diagnostics including line-of-sight integration and volume average measurements, as well as limited profile information from a charge-exchange-recombination spectrometer. A linear gyrokinetic stability analysis has been carried out to identify the most unstable micro-instabilities in these hot ion plasmas. In one of these plasmas, it is found that linear growth rates of both ion- and electron-scale ( where k θ is the poloidal wavenumber and ρ s is the ion gyro-radius with sound speed) modes decrease from the edge toward the core of the plasma (i.e. from ρ = 0.8 to 0.3 where ρ is the square root of the normalized magnetic flux), while the change of linear growth rates at is non-monotonic. In particular, at ρ = 0.3 no unstable mode was found at , and about an order of magnitude reduction in the maximum linear growth rate in the ion-scale wavenumber range of is seen at ρ = 0.3 compared with the ρ = 0.8 location. It is found through parametric scans that while the ion temperature gradient (ITG) mode/trapped electron mode (TEM) and kinetic ballooning mode (KBM)/kinetic shear Alfvén (KSA) mode are more important in the plasma core, ubiquitous mode (UM) is found to be the important ion-scale instability at . At ρ = 0.8, two instabilities are found at the electron scale, with one being the typical electrostatic electron temperature gradient (ETG) mode at ρ e scale and beyond and the other being an unidentified low-real-frequency instability (at the intermediate scale between electron and ion gyroradii) which can propagate in the ion direction and is driven by ETG. The existence of UM at the ion scale and the low-real-frequency instability and ETG mode at the electron scale at ρ = 0.8 is supported by an extensive linear gyrokinetic stability analysis of another ST40 hot ion plasma in a wider parametric range, taking into account the uncertainties in the experimental profiles.

Zonal flow excitation in electron-scale tokamak turbulence

The derivation of an intermediate-scale gyrokinetic-electron theory in nonuniform tokamak plasmas (Chen et al 2021 Nucl. Fusion 61 066017) has shown that a Navier–Stokes type nonlinearity couples electron-temperature-gradient (ETG) modes and zonal flow (ZF) modes with wavelengths much shorter than the ion gyroradius but much longer than the electron gyroradius. This intermediate-scale ETG-ZF coupling is typically stronger than the Hasegawa–Mima type nonlinearity characteristic of the fluid approximation and is predicted to lead to relevant ZF generation and ETG mode regulation. Electron-scale, continuum, gyrokinetic simulation results are presented here which include both single-mode ETG and full-spectrum ETG turbulence. The ZF generation due to single ETG modes is investigated and the single-mode intermediate-scale results are found to be in agreement with theory. The full-spectrum results are then presented and explained qualitatively in terms of the single-mode results. It is found that the ETG-driven ZFs regulate intermediate-scale electron heat flux transport to levels in the predicted range.

Gyrokinetic Stability Analysis of JET Pedestal Top Plasmas with Small-ELMs

In recent years, a strong effort has been dedicated to the development of tokamak plasma regimes alternative to the standard high confinement mode (H-mode) with type-I edge localized mode (ELM), i.e. ELM-free and small-ELM regimes, given the associated hardly sustainable energy and particle fluxes on plasma facing components.In this work, we will focus on new H-mode regimes with small-ELMs, the so-called baseline small-ELMs (BSE), characterized by high thermal confinement and low core impurity accumulation, which have been recently found at JET. In order to characterize the micro-turbulence at play at the top of the pedestal, an extensive local linear gyrokinetic analysis with the GKW code has been carried out. In particular, a comparison between a reference type-I ELM (#97395) and two BSE plasmas (#96994 and #94442) has been performed.The ion-scale (0.1 ≤ k θ ρ i ≤ 2) micro-turbulence is found to have different characteristics in the two regimes. Indeed, kinetic-ballooning modes (KBM) are destabilized in the type-I ELM regime at k θ ρ i ∼ 0.1, while they are stable in BSE regimes. In addition, negative (i.e. electron-diamagnetic-direction) frequency modes, identified as electron-temperature-gradient (ETG) modes, are destabilized at k θ ρ i ∼ 1.5 in the type-I ELM regime while BSE regimes are characterized by positive (i.e. ion-diamagnetic-direction) frequency modes. Meanwhile, at electron-scale (10 ≤ k θ ρ i ≤ 700) ETG modes are the dominant micro-instabilities in both regimes. Then, since BSE regimes are characterized by a higher impurity concentration at the pedestal, particular attention has been given to the role played by them. We found that impurities represent a critical player in the linear dynamics, strongly affecting the nature of micro-instabilities at ion-scale.

The National Spherical Torus Experiment-Upgrade poloidal high-k scattering system pitch angle design modifications.

A 693GHz, eight-channel, poloidal high-k (k refers to wavenumber) collective scattering system is under development for the National Spherical Torus Experiment-Upgrade device. It will replace the previous 280GHz, five-channel, tangential scattering system to study high-k electron density fluctuations, thereby providing a measurement of the kθ-spectrum of both electron temperature gradient and ion temperature gradient modes. A tool is under development to calculate the wavenumber that exists in the presence of strong magnetic pitch angles. We use this tool to motivate a new receiver optical design for significantly improved performance, details of which are presented herein.

Electron temperature gradient driven transport model for tokamak plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β′), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

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.

Experimental Evidence of Intrinsic Current Generation by Turbulence in Stationary Tokamak Plasmas.

High-β_{θe} (a ratio of the electron thermal pressure to the poloidal magnetic pressure) steady-state long-pulse plasmas with steep central electron temperature gradient are achieved in the Experimental Advanced Superconducting Tokamak. An intrinsic current is observed to be modulated by turbulence driven by the electron temperature gradient. This turbulent current is generated in the countercurrent direction and can reach a maximum ratio of 25% of the bootstrap current.Gyrokinetic simulations and experimental observations indicate that the turbulence is the electron temperature gradient mode (ETG). The dominant mechanism for the turbulent current generation is due to the divergence of ETG-driven residual flux of current. Good agreement has been found between experiments and theory for the critical value of the electron temperature gradient triggering ETG and for the level of the turbulent current. The maximum values of turbulent current and electron temperature gradient lead to the destabilization of an m/n=1/1 kink mode, which by counteraction reduces the turbulence level (m and n are the poloidal and toroidal mode number, respectively). These observations suggest that the self-regulation system including turbulence, turbulent current, and kink mode is a contributing mechanism for sustaining the steady-state long-pulse high-β_{θe} regime.

A poloidal high-k scattering system for NSTX-U

A previous 5-channel tangential high-k scattering system is being replaced by an 8-channel, poloidal high-k scattering system on the National Spherical Torus eXperiment Upgrade (NSTX-U) device located in Princeton, NJ, USA. The 693 GHz poloidal scattering system replaces a 280 GHz tangential scattering system to study high-k electron density fluctuations on NSTX-U, thereby considerably enhancing planned turbulence physics studies by providing a measurement of the k θ -spectrum of both electron temperature gradient (ETG) and ion temperature gradient (ITG) modes. Two approaches to generating the 693 GHz probe beam are under development: an optically-pumped far-infrared (FIR) laser that generates ∼50 mW, and a compact gyrotron that can potentially generate in excess of 5 W. Large aperture optics collect radiation scattered from density fluctuations in the plasma core at 8 simultaneous scattering angles ranging from 2 to 15° corresponding to poloidal wavenumbers that extend to >40 cm−1. Steerable launch optics coupled with receiver optics mounted on a 5-axis receiver carriage allow the scattering volume to be placed radially from r/a = 0.3 out to the pedestal region (r/a ∼ 0.99) and translated horizontally as needed to satisfy wavenumber matching.

Experimental investigation and gyrokinetic simulations of multi-scale electron heat transport in JET, AUG, TCV

Tokamaks dominated by electron heating like ITER could possibly suffer from the consequences of electron temperature gradient (ETG) mode destabilisation, which could develop a turbulent electron heat flux capable of setting an upper limit to the achievable electron temperature peaking, resulting in a degradation of the fusion performance. An effort is carried out in this paper to collect and compare the results of dedicated plasma discharges performed during the last few years at three of the major European tokamaks, TCV, AUG and JET, by analysing the electron heat transport for cases presumably compatible with ETGs relevance, given the actual theoretical understanding of these instabilities. The response of the electron temperature profiles to electron heat flux changes is experimentally investigated by performing both steady state heat flux scans and perturbative analysis by radio frequency heating modulation. The experimental results are confronted with numerical simulations, ranging from simple linear gyrokinetic (GK) or quasi-linear runs, to very computationally expensive nonlinear multi-scale GK simulations, resolving ion and electron scales at the same time. The results collected so far tend to confirm the previously emerging picture, indicating that cases with a proper balance of electron and ion heating, with similar electron and ion temperatures and sufficiently large ETG, could be compatible with a non negligible impact of ETGs on the electron heat transport. The ion heating destabilises ETGs not only by increasing the ion temperature but also thanks to the stabilisation of ion-scale turbulence by a synergy of fast ions and E × B shearing, which are in some cases associated with it. The stabilising effect of plasma impurities on ETGs is still under investigation by means of multi-scale GK simulations, and also direct experimental measurements of density and temperature fluctuations at electron scales would be needed to ultimately assess the impact of ETGs.

The role of electron-scale turbulence in the JET tokamak: experiments and modelling

Dedicated electron heat transport experiments have been carried out in L- and H-mode Deuterium plasmas of the JET-ILW tokamak to identify the amount of electron heat carried by electron-scale electron temperature gradient (ETG) modes. Ion cyclotron resonance heating at different positions has been used to probe the response of the electron temperature inverse gradient length R/L Te to changes in electron heat flux q e, while different amounts of neutral beam heating allowed to scan the ratio of ion to electron temperature T e/T i, which is a key parameter for the onset of ETGs. Results indicate a steepening of the normalized q e vs R/L Te curve above R/L Te ∼ 8 for T e/T i ⩽ 1, suggestive of the ETG onset. Ion-scale gyro-kinetic (GK) simulations match the ion heat flux and the low-R/L Te part of the q e curve, but do not reproduce such steepening at high R/L Te. Multi-scale GK simulations covering both ion and electron scales and including one impurity bundling light and heavy species indicate an ETG contribution only for R/L Te values larger than the experimental ones. Sensitivity studies of such result are difficult to achieve due to limitation in numerical resources. The quasi-linear TGLF model has been used for sensitivity studies. With the same bundled impurity as the GK multi-scale, TGLF shows the q e steepening at much larger R/L Te values than in experiment, but when using the real mix of light impurities neglecting the heavy impurities, TGLF gets closer to the experimental results. Profile simulations with TGLF including both light and heavy impurities show over-prediction of T e profiles and in some cases also of density, but good T i predictions, confirming issues with the model electron stiffness for these plasmas.

Effects of ion polarization and finite-β on heat transport in slab electron-temperature-gradient driven turbulence

Effects of kinetic ions and electromagnetic fluctuations on slab electron-temperature-gradient (ETG) driven turbulence are investigated by means of gyrokinetic simulations covering scales from electron gyroradius to ion gyroradius and electron skin depth. Linear growth rates of electrostatic ETG modes are enhanced by the ion polarization at ion gyroradius scale. Nonlinear simulations show that this low-poloidal-wavenumber instability induces ion-scale eddies which cause heat transport higher than that in the adiabatic ion model. In finite-β plasma, electromagnetic fluctuations stabilize the low-wavenumber modes, and suppress the turbulent heat transport. Additionally, electromagnetic effects also weaken zonal flow generation, which slightly enhances turbulent transport than that in the electrostatic adiabatic ion model.

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

Validation of gyrokinetic simulations in NSTX and projections for high-k turbulence measurements in NSTX-U

An extensive validation effort performed for a modest-beta NSTX NBI-heated H-mode discharge predicts that electron thermal transport can be entirely explained by electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in conditions of strong and weak ETG turbulence drive. Thermal power-balance estimates computed by TRANSP as well as the shape of the high-k density fluctuation wavenumber spectrum and the fluctuation level ratio between strongly driven and weakly driven ETG-turbulence conditions can be matched by nonlinear gyrokinetic simulations and a synthetic diagnostic for high-k scattering. Linear gyrokinetic simulations suggest that the ion-scale instability in the weak ETG condition is close to the critical threshold for the kinetic ballooning mode instability, and nonlinear ion-scale gyrokinetic simulations show that turbulence might be in a state reminiscent of a Dimits' shift regime, opening speculation on the role that ion-scale turbulence might play for the weak ETG condition. A simulation that matched all experimental constraints is chosen to project high-k turbulence spectra in NSTX-U, revealing that the new high-k system [R. Barchfeld et al., Rev. Sci. Instrum. 89, 10C114 (2018)] should be sensitive to density fluctuations from radially elongated streamer structures. Two schemes are designed to characterize the radial and poloidal wavenumber dependence of the density fluctuation wavenumber power spectrum around the streamer peak, suggesting future high-k fluctuation measurements could be sensitive to an asymmetry in the kr spectrum introduced due to the presence of strong background flow shear.

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.