Dissipative Trapped Electron Mode Research Articles

Gyro-kinetic simulations of trapped electron collision effects on low-frequency drift-wave instabilities in tokamak plasmas

Low-frequency drift-wave instabilities play a crucial role in the radial transport of present-day tokamaks, and trapped electron collisions can significantly influence these instabilities. In this paper, the effects of trapped electron collisions on these instabilities are investigated based on linear gyro-kinetic simulations. The basic numerical techniques including dispersion relation integral method and orthogonal basis function expansion are presented in detail with necessary benchmark work. The results demonstrate that in medium gradients, the increase of trapped electron proportions promotes the growth rate and radial heat transport largely for quasi-linear trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. Moreover, trapped electron collisions have strong stabilizing effects, especially for TEMs driven by electron temperature gradients. Two distinctive branches, namely Mode #1 and #2, are investigated in steep gradients. Both behave in a varied instability nature during different ranges of the normalized wave vector k^θ . Mode #1 mainly induces radial heat transport during k^θ<0.5 and is significantly suppressed by the collisions. Mode #2 mainly induces radial heat transport during 0.4<k^θ<0.8 , and is largely enhanced by the collisions. When the collisionality is large enough, Mode #2 has stronger transport capacity than the other. Mode #2 at the medium wave vector, known as dissipative TEM, may provide the mechanism of the edge coherent mode observed in EAST H-mode plasmas, wherein collisionality plays an important role in the mode excitation.

Research of turbulent transport due to dissipative trapped electron mode in tokamak plasmas

The purpose of this article is to study turbulent transport for laboratory plasmas in toroidal devices by gyrokinetic analyses. Linear analysis is performed to clarify the dominant mode for tokamak plasmas. The dissipative trapped electron mode (d-TEM) and the ion temperature gradient (ITG) mode are predicted using the Sugama collision model operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)]. Nonlinear gyrokinetic analysis is used to quantify turbulent transport. The nonlinear simulation results show the levels of particle and energy transport, where the d-TEM and ITG mode are unstable. The effect of zonal flows is studied by the linear and nonlinear simulation results. The results of the analysis are compared when two types of model collision operator, which are the Sugama and Lenard–Bernstein [Phys. Rev. 112, 1456 (1958)] collision model operators, are used. In this study, the simulation results using the Sugama collision operator show a stronger effect of the zonal flows on the turbulent transport than those using the Lenard–Bernstein collision operator, as predicted by the linear simulation result such as the zonal flow decay time.

Observation of pedestal quasi-coherent mode in Type-I ELMy H-mode of HL-2A tokamak

High confinement mode plasma experiments with Type-I edge localized modes (ELMs) have been carried out on HL-2A tokamak. With neutral beam injection and lower hybrid current drive heating, a quasi-coherent mode (QCM) located at pedestal region has been observed, which exists during the ELM-free stage till the first ELM burst. Analysis based on density and magnetic fluctuations has revealed that the QCM propagating radially outward is electrostatic in nature whose radial wavenumber is kr∼0.5 cm−1 as well as the poloidal wavenumber around kθ∼1.4 cm−1, rotating in electron diamagnetic drift direction. The central frequency of the mode gradually decreases from 50 to 20 kHz, which varies almost linearly with toroidal rotation. Experimental findings indicate that the QCM is excited above a critical electron density gradient in the ELM-free phase during which the latter gradually increases due to the confinement transition. The disappearance of QCM is closely associated with the onset of ELMy H-mode, suggesting that the presence of QCM could potentially delay the occurrence of ELM bursts, consequently supporting the maintenance of an ELM-free operational regime. Moreover, the pedestal region locates more radially outside where the density gradient shows a more spanned region with QCM. A quantitative comparison between experimental measurements and linear GENE gyrokinetic simulations suggests that the dissipative trapped electron mode might be the candidate interpretation of the QCM.

Quasi-coherent mode in core plasma of SUNIST spherical tokamak

A quasi-coherent (QC) mode was observed in the core region of low-density ohmic plasmas in Sino-UNIted Spherical Tokamak. In experiments on the QC mode, two sets of moveable Langmuir probes (LPs) were used to measure the local parameters including floating potential, electron temperature, electron density, and so on, as well as their profiles. To monitor the magnetohydrodynamic activities, a Mirnov probe was used to measure the poloidal magnetic fluctuation. The QC mode can be seen in the spectra of floating potential, but there is no similar peak in the spectra of magnetic fluctuation. Thus, the QC mode is probably electrostatic. By analyzing the electrostatic potential fluctuations from the LPs, the features of the QC mode including frequency, wavenumber, propagation direction, and dependence on collisionality are identified, which are consistent with the characteristics of dissipative trapped electron mode.

Trapped-electron-mode property and role for the L-H transition in L-mode edge plasmas with relatively high electron temperature and weak ion temperature gradient

When the low-confinement mode (L-mode) edge has relatively high electron temperature and weak ion temperature gradient, for example, as observed in the ECH-heated low-density plasmas, the trapped electron mode (TEM) can play an important role in the low to high confinement (L-H) transition as well as the L-mode edge transport, instead of the resistive ballooning or ion temperature gradient mode (RBM or ITG). Motivated by this, a study is first presented about, among several types of the TEM, which one is the most dominant in the above L-mode edge condition, showing that it is dominated by a mixture of the density gradient driven and dissipative TEMs. The parameter dependence of the growth rate of this dominant TEM type is then checked, showing that it has the scaling qualitatively similar to the H-mode threshold power one observed in plasmas where the TEM can be a dominant mode. Closely related to this, a discussion is also given about the L-H transition expected in plasmas where the TEM is assumed to be dominant. Unlike the typical L-H transition that is believed to occur in the RBM-dominant plasmas, it is conjectured to take place in one-step form, with no generation or negligible role of the limit-cycle-oscillation, thus requiring a larger threshold power.

Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

Confinement regimes with edge transport barriers occur through the suppression of turbulent (convective) fluxes in the particle and/or thermal channels, i.e. , and , respectively, for drift-wave turbulence. The quantity is the turbulence intensity, while and are the crossphases. For H-mode, standard decorrelation theory predicts that it is the turbulence intensity that is mainly affected via flow-induced shearing of turbulent eddies. However, for other regimes (e.g. I-mode, characterized by high energy confinement but low particle confinement), this decrease of turbulence amplitude cannot explain the decoupling of particle versus thermal flux, since a suppression of turbulence intensity would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model (Baver et al 2002 Phys. Plasmas 9 3318) for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase δk between density and potential fluctuations, including contributions from the E × B nonlinearity. By using a parametric interaction analysis including the back-reaction on the pump, we obtain a predator–prey like system of equations for the pump amplitude ϕp, the pump crossphase δp, the zonal amplitude ϕz and the triad phase-mismatch Δδ. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate—proportional to the crossphase—shows quasi-periodic relaxations where it departs from that predicted by linear theory.

Nonlinear gyrokinetic particle simulation of dissipative trapped electron mode

Electron turbulence induced by the trapped electron mode has been widely studied. The dissipative trapped electron mode (DTEM) is an important candidate for tokamak edge turbulence. Nonlinear gyrokinetic particle simulations based on edge parameters are carried out to investigate the collisional effects on the nonlinear transport of DTEM turbulence. It is found that the collisions can induce a low level radially inward electron transport for the DTEM turbulence, which is closely related to the phase difference between the radial turbulent motion and perturbed density fluctuation induced by collisional dissipation. We observe an inverse spectral cascade of the turbulence during the nonlinear DTEM saturation, which is caused by quasimode scattering induced by trapped electrons and important for determining the magnitude of turbulent transport. The nonlinear transport of DTEM is found to be inversely proportional to the collisional frequency by gyrokinetic simulation, which is consistent with the prediction of quasilinear theory.

Gyrokinetic simulation of dissipative trapped electron mode in tokamak edge

The gyrokinetic simulation using the gyrokinetic toroidal code (GTC) is carried out for the dissipative trapped electron mode (DTEM), which is an important source for the electrostatic turbulence in the pedestal of tokamak plasmas. The DTEM instability is identified for the edge plasmas, and its dependence on the wavelength and collisional frequency is obtained by both simulation and theory. It is shown for the first time that the linear gyrokinetic simulation results are fully consistent with that from the analytic theory with edge parameters. This suggests that the GTC code can simulate accurately the DTEM instability in the pedestal. It provides a useful benchmark for verifying gyrokinetic simulation of edge plasmas.

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of non-diffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations.

Distinct turbulence sources and confinement features in the spherical tokamak plasma regime

New turbulence contributions to plasma transport and confinement in the spherical tokamak (ST) regime are identified through nonlinear gyrokinetic simulations. The drift wave Kelvin–Helmholtz (KH) mode characterized by intrinsic mode asymmetry is shown to drive significant ion thermal transport in strongly rotating national spherical torus experiment (NSTX) L-modes. The long wavelength, quasi-coherent dissipative trapped electron mode (TEM) is destabilized in NSTX H-modes despite the presence of strong shear, providing a robust turbulence source dominant over collisionless TEM. Dissipative trapped electron mode (DTEM)-driven transport in the NSTX parametric regime is shown to increase with electron collision frequency, offering one possible source for the confinement scaling observed in experiments. There exists a turbulence-free regime in the collision-induced collisionless trapped electron mode to DTEM transition for ST plasmas. This predicts a natural access to a minimum transport state in the low collisionality regime that future advanced STs may cover.

Identification of new turbulence contributions to plasma transport and confinement in spherical tokamak regime

Highly distinct features of spherical tokamaks (ST), such as National Spherical Torus eXperiment (NSTX) and NSTX-U, result in a different fusion plasma regime with unique physics properties compared to conventional tokamaks. Nonlinear global gyrokinetic simulations critical for addressing turbulence and transport physics in the ST regime have led to new insights. The drift wave Kelvin-Helmholtz (KH) instability characterized by intrinsic mode asymmetry is identified in strongly rotating NSTX L-mode plasmas. While the strong E×B shear associated with the rotation leads to a reduction in KH/ion temperature gradient turbulence, the remaining fluctuations can produce a significant ion thermal transport that is comparable to the experimental level in the outer core region (with no “transport shortfall”). The other new, important turbulence source identified in NSTX is the dissipative trapped electron mode (DTEM), which is believed to play little role in conventional tokamak regime. Due to the high fraction of trapped electrons, long wavelength DTEMs peaking around kθρs∼0.1 are destabilized in NSTX collisionality regime by electron density and temperature gradients achieved there. Surprisingly, the E×B shear stabilization effect on DTEM is remarkably weak, which makes it a major turbulence source in the ST regime dominant over collisionless TEM (CTEM). The latter, on the other hand, is subject to strong collisional and E×B shear suppression in NSTX. DTEM is shown to produce significant particle, energy and toroidal momentum transport, in agreement with experimental levels in NSTX H-modes. Moreover, DTEM-driven transport in NSTX parametric regime is found to increase with electron collision frequency, providing one possible source for the scaling of confinement time observed in NSTX H-modes. Most interestingly, the existence of a turbulence-free regime in the collision-induced CTEM to DTEM transition, corresponding to a minimum plasma transport in advanced ST collisionality regime, is predicted.

New edge coherent mode providing continuous transport in long-pulse H-mode plasmas.

An electrostatic coherent mode near the electron diamagnetic frequency (20-90kHz) is observed in the steep-gradient pedestal region of long pulse H-mode plasmas in the Experimental Advanced Superconducting Tokamak, using a newly developed dual gas-puff-imaging system and diamond-coated reciprocating probes. The mode propagates in the electron diamagnetic direction in the plasma frame with poloidal wavelength of ∼8 cm. The mode drives a significant outflow of particles and heat as measured directly with the probes, thus greatly facilitating long pulse H-mode sustainment. This mode shows the nature of dissipative trapped electron mode, as evidenced by gyrokinetic turbulence simulations.

Recurrence quantification analysis of simulations of near-marginal dissipative-trapped-electron-mode turbulence

Recurrence quantification analysis (RQA) is a powerful tool to study dynamical systems and to help us understand and characterize the underlying physics when a transition occurs. The idea is based on the fact that, given sufficiently long time lapses, every dynamical system returns to states arbitrarily close to those it had in the past. This fundamental property of dynamical systems is called recurrence. In this work, we analyze, using the RQA technique, the recurrence properties of time series obtained from a series of numerical simulations of a dissipative-trapped-electron-mode (DTEM) turbulence model in near-marginal conditions where a transition in the nature of turbulent transport was observed as a subdominant diffusive channel strength is increased from zero [J. A. Mier et al., Phys. Plasmas 15, 112301 (2008)]. The results of the RQA analysis clearly show that the degree of determinism and complexity of the dynamics closely follows the degree of non-diffusiveness in the observed transport.

Numerical study of linear dissipative drift electrostatic modes in tokamaks

The linear stability of dissipative drift electrostatic modes in tokamak plasmas is studied numerically with an extended version of the gyrokinetic code Kinezero [C. Bourdelle et al., Nucl. Fusion 42, 892 (2002)] including a modified Krook collision operator to account for collisional effects on the trapped electron response. This new version of Kinezero has been successfully tested and benchmarked against the results of a more sophisticated and complete gyrokinetic solver, GS2 [M. Romanelli, C. Bourdelle, and W. Dorland, Phys. Plasmas 11, 3845 (2004)]. The critical density and temperature gradients for ion gradient driven modes (ITG) and trapped electron modes (TEM) have been computed for different values of collisionality. The threshold for TEM disappears as the collisionality increases. A detailed study of the dependence of the growth rate of the dissipative TEM on collisionality and density gradient is presented in the paper. The range of parameters where the dissipative trapped electron modes are destabilized by increasing collisionality corresponds to very steep density gradients that can hardly be achieved in today's large tokamaks.

Study of the interaction between diffusive and avalanche-like transport in near-critical dissipative-trapped-electron-mode turbulence

The change in properties of turbulent transport is explored, in the context of dissipative-trapped-electron-mode (DTEM) turbulence, as a function of the relative strength of a (subdominant) diffusive transport channel to the turbulent one. If the diffusive channel is totally absent and the system is slowly driven, transport exhibits many features characteristic of self-organized-critical (SOC) systems. This finding is consistent with those reported by several authors in other situations, such as pressure-gradient-driven or ion-temperature-gradient turbulence. But we also find that the temporal persistence and spatial self-similarity characteristic of the SOC state remain present, at a level much higher than what one would naively expect, as the strength of the diffusive channel is increased. This observation, which has been previously made for numerical sandpile models, may give a partial answer to the question of why SOC features are so frequently observed in turbulent experimental data and numerical simulations in spite of the fact that the experimental conditions appear to be quite far from those required by the strict definition of the SOC state.

Dissipative trapped-electron instability in quasihelically symmetric stellarators

The linear electrostatic dissipative trapped-electron mode is investigated in a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the addition of a mirror contribution to the magnetic spectrum. The effect of the trapped electrons is accounted for using the drift kinetic equation with an energy-dependent Krook collision operator and an effective collision frequency giving the rate of detrapping. The ballooning mode formalism and Wentzel-Kramers-Brillouin type boundary conditions are used to solve an eigenvalue problem for a drift wave equation with nearly adiabatic electrons in a fully three-dimensional magnetohydrodynamic equilibria. The trapped-electron growth rate is calulated using a perturbative approach. Multiple classes of helically localized and toroidally localized eigenfunctions in the ballooning space are calculated. The results of the QHS configuration is compared and contrasted with the results of the mirror configuration. The helically trapped modes are found to be most destabilizing. In both configurations the magnitude of the linear growth rates are comparable, crudely indicating the same level of anomalous flux as has also been observed in the edge region of experiments.

Dissipative Trapped Electron Modes in a Heliac

The objective of the present paper is to study the dissipative trapped electron modes (DTEM) in a stellarator configuration. A perturbative-iterative process is used to study the non-adiabatic response of the electrons in the dissipative regimes on the drift wave instability. A ballooning mode formalism is used to drive the drift eigenvalue equation for adiabatic electron which is solved numerically. The eigenmodes are marginally stable. The non-adiabatic response of the electrons is calculated perturbatively which is used to re-solve the eigenvalue equation. The process is iterated until electrons response converges. The effects of different parameters such as ηe, the ballooning angle θk, normalised density scale length ϵn, radial label s, and χ are studied. The mode localisation is correlated with the geometrical properties of the magnetic field. It is found that the wave functions of the most unstable modes are highly localised in a single helical ripple with the possibility of a variety of both helical and toroidal trapping. It is further fond that a perturbative calculations of the growthrate generally is not reliable and can give substantially lower or higher growthrate than the iterative method.

Non-local theory for trapped electron modes in a magnetic quadrupole

The dispersion relations for the fundamental drift dissipative trapped electron mode and its first radial harmonic are obtained from a radially nonlocal analysis. Growth and damping rates, due to electron-neutral collisions and ion viscosity, are also calculated.

Enhanced shear damping and ion transit resonance damping of electron drift waves in low collisionality tokamaks

The overlap of potentially unstable electron drift modes, driven by trapped electrons scattering, is negligible in low collisionality tokamaks. The width, and hence the ion damping of the (then) uncoupled toroidal modes exceed those obtained in cylindrical geometry, owing to the ion excursion across the flux surfaces associated with the magnetic drift. Two regimes have to be considered: ωl > ci/⟨ν⟩χR where "shear damping" is merely enhanced, and ωl < ci/⟨ν⟩χR where even larger ion transit resonance damping takes over (ωl is the mode frequency, l the torodial mode numer, ci the ion thermal velocity, ⟨ν⟩χ the safety factor and R the major radius of the device). A contrario, the broader the eigenmode, the weaker the Landau damping on passing electrons. The ratio of the sum of the revisted stabilizing rates to the trapped electron destabilizing rate depends mainly on the ratio of the characteristic length-scales across and along the field lines, not on the absolute temperatures; it turns out to be approximately constant and of order unity throughout the confinement zone, confirming the relevance of the dissipative trapped electron mode to anomalous transport, even in low colisionality tokamak plasmas. In this confinement zone, the Landau damping rate is typically smaller than the shear damping rate, suggesting an even structure of the potential eigenfunction (and an odd structure for the associated radial magnetic field).

Experimental study of a mixed slab and toroidal ion-temperature-gradient mode

The first study of the transition of the slab toward the toroidal branch of the ion-temperature-gradient (ITG) driven mode in the Columbia Linear Machine (CLM) [Plasma Phys. 24, 185 (1982)] is reported. This has been achieved by first exciting the slab ITG mode and gradually increasing the magnetic curvature by energizing a magnetic mirror coil. The magnetic curvature can then be adjusted either by moving the mirror coil axially (to change the mirror cell length) or by varying the mirror coil current (to change the mirror ratio). The effects of the modest levels of magnetic curvature are seen to be further destabilization and reduction of the real frequency of the mode. However, with a further increase in the mirror ratio, the mode amplitude decreased. A kinetic model of the mixed slab and ‘‘toroidal’’ ITG mode with trapped particles has been developed to predict the mode behavior. Computational results from this with the plasma parameters in the CLM corroborate the existence of an instability with the observed real frequency and mode amplitude, and which has the appearance of a hybrid ITG–dissipative trapped electron mode.