Collisionless Trapped Electron Mode Turbulence Research Articles

Effects of alpha particles on the transport of helium ash driven by collisionless trapped electron mode turbulence

The effects of alpha (α) particles on the transport of helium ash driven by collisionless trapped electron mode (CTEM) turbulence are analytically studied using quasi-linear theory in tokamak deuterium (D) and tritium (T) plasmas. Under the parameters used in this work, the transport of helium ash is mainly determined by the diffusion due to very weak convection. It is found that the ratio between helium ash diffusivity and effective electron thermal conductivity (D He/χ eff) driven by CTEM turbulence, which is a proper normalized parameter for quantifying the efficiency of helium ash removal, is smaller than unity. This indicates the less efficient removal of helium ash through CTEM turbulence as compared with ion temperature gradient (ITG) turbulence in [Angioni et al 2009 Nucl. Fusion 49 055013]. However, the efficiency of helium ash removal is increased 55% by the presence of 3% α particles with their density gradient being equivalent to that of electrons, and this enhancement can be further strengthened by steeper profile of α particles. This is mainly because the enhancement of helium ash diffusivity by α particles is stronger than that of the effective electron thermal conductivity. Moreover, the higher fraction of T ions, higher temperature ratio between electrons and thermal ions as well as flatter electron density profile, the stronger enhancement of D He/χ eff, and α particles further strengthen the favorable effects of these parameters on the removal of helium ash.

Role of wave-particle resonance in turbulent transport in toroidal plasmas

A clear understanding of wave-particle interaction and associated transport mechanisms of different particle species in the drift wave instabilities is important for accurate modeling and predictions of plasma confinement properties in tokamaks. In particular, the roles of linear resonance and nonlinear scattering in turbulent transport need to be delineated when constructing reduced transport models. First-principle, global gyrokinetic simulations find that electron particle and heat transport decreases to a very low level, while ion heat transport level has no dramatic change when wave-particle resonance is suppressed in the collisionless trapped electron mode (CTEM) turbulence. On the other hand, ion heat transport in the self-consistent ion temperature gradient (ITG) turbulence simulation is qualitatively similar to that in the test-particle simulation using the static ITG turbulence fields. These simulation results show that electron transport is primarily driven by the wave-particle resonance in the CTEM turbulence, and the ion transport is mostly driven by the nonlinear wave-particle scattering in both the CTEM and ITG turbulence.

How Zonal Flow Affects Trapped-Electron-Driven Turbulence in Tokamak Plasmas.

The role of self-generated zonal flows in the collisionless trapped-electron-mode (CTEM) turbulence is a long-standing open issue in tokamak plasmas. Here, we show, for the first time, that the zonal flow excitation in the CTEM turbulence is formally isomorphic to that in the ion temperature gradient turbulence. Trapped electrons contribute implicitly only via linear dynamics. Theoretical analyses further suggest that, for short wavelength CTEMs, the zonal flow excitation is weak and, more importantly, not an effective saturation mechanism. Corresponding controlling parameters are also identified theoretically. These findings not only offer a plausible explanation for previous seemingly contradictory simulation results, but can also facilitate controlling the CTEM instability and transport with experimentally accessible parameters.

The role of collisionless trapped electron mode turbulence on removal of helium ash and transport of deuterium-tritium ions

Removal of helium ash and the anomalous transport of deuterium (D) and tritium (T) ions driven by collisionless trapped electron mode (CTEM) turbulence in tokamak plasmas with weak magnetic shear are studied. We derive the eigenvalue of CTEM with helium ash, and calculate the quasi-linear turbulent fluxes of helium ash, D and T ions simultaneously. Based on the analytical results, the parametric dependence of CTEM instability as well as the anomalous transport of helium ash and D-T ions is investigated, in order to explore the parameter region that is favorable for expelling more helium ash than D and T ions. It is found that helium ash with higher temperature and steeper density profile plays a role of destabilizing CTEM instability, and has higher transport level than that of T ions. We also find that increasing electron temperature and flattening electron density profile are favorable for exhausting helium ash. Isotopic effects (i.e. increasing the fraction of T ions) enhance the transport of both helium ash and D-T ions. Moreover, the trend of stronger transport level of helium ash than that of D-T ions is enhanced by raising electron temperature and flattening electron density profile as well as isotopic effects. Besides, the diffusivity is much larger than the convection. This indicates that the CTEM turbulence driven helium ash transport is favorable for removing helium ash under the parameter region used in the present paper. The possible relevance of our theoretical results to experimental observations is also discussed.

Gyrokinetic theory of turbulent acceleration and momentum conservation in tokamak plasmas

Understanding the generation of intrinsic rotation in tokamak plasmas is crucial for future fusion reactors such as ITER. We proposed a new mechanism named turbulent acceleration for the origin of the intrinsic parallel rotation based on gyrokinetic theory. The turbulent acceleration acts as a local source or sink of parallel rotation, i.e., volume force, which is different from the divergence of residual stress, i.e., surface force. However, the order of magnitude of turbulent acceleration can be comparable to that of the divergence of residual stress for electrostatic ion temperature gradient (ITG) turbulence. A possible theoretical explanation for the experimental observation of electron cyclotron heating induced decrease of co-current rotation was also proposed via comparison between the turbulent acceleration driven by ITG turbulence and that driven by collisionless trapped electron mode turbulence. We also extended this theory to electromagnetic ITG turbulence and investigated the electromagnetic effects on intrinsic parallel rotation drive. Finally, we demonstrated that the presence of turbulent acceleration does not conflict with momentum conservation.

Intrinsic rotation drive by collisionless trapped electron mode turbulence

Both the parallel residual stress and parallel turbulent acceleration driven by electrostatic collisionless trapped electron mode (CTEM) turbulence are calculated analytically using gyrokinetic theory. Quasilinear results show that the parallel residual stress contributes an outward flux of co-current rotation for normal magnetic shear and turbulence intensity profile increasing outward. This may induce intrinsic counter-current rotation or flattening of the co-current rotation profile. The parallel turbulent acceleration driven by CTEM turbulence vanishes, due to the absence of a phase shift between density fluctuation and ion pressure fluctuation. This is different from the case of ion temperature gradient turbulence, for which the turbulent acceleration can provide co-current drive for normal magnetic shear and turbulence intensity profile increasing outward. Its order of magnitude is predicted to be the same as that of the divergence of the residual stress [L. Wang and P. H. Diamond, Phys. Rev. Lett. 110, 265006 (2013)]. A possible connection of these theoretical results to experimental observations of electron cyclotron heating effects on toroidal rotation is discussed.

Turbulent transport of toroidal angular momentum in fusion plasmas

Global nonlinear gyrokinetic simulations of ion temperature gradient (ITG) and collisionless trapped electron mode (CTEM) turbulence find significant spinning up of a plasma in the directions opposite for CTEM and ITG turbulence. The outward momentum convection by the particle flux could be strong enough to overcome the inward momentum pinch and reverse the radial direction of the convective momentum flux. Momentum pinch velocity shows no explicit dependence on background temperature, while it is significantly affected by steepening the background density. Convective momentum fluxes are generally smaller in the CTEM turbulence than the ITG turbulence, while the intrinsic Prandtl number is similar or slightly larger in the CTEM turbulence.

Convective motion in collisionless trapped electron mode turbulence

Global gyrokinetic particle simulation of collisionless trapped electron mode turbulence in toroidal plasmas finds both diffusive and convective electron motion using a Lagrangian analysis. The convective motion is identified using simulation and analytic theory to arise from the conservation of the second invariant when resonant trapped electrons lose kinetic energy to the drift wave. A resonance broadening model fits well the diffusive and convective electron motion.

Characteristics of turbulence-driven plasma flow and origin of experimental empirical scalings of intrinsic rotation

Toroidal plasma flow driven by turbulent torque associated with nonlinear residual stress generation is shown to recover the observed key features of intrinsic rotation in experiments. Specifically, the turbulence-driven intrinsic rotation scales close to linearly with plasma gradients and the inverse of the plasma current, qualitatively reproducing empirical scalings obtained from a large experimental data base. The effect of magnetic shear on the symmetry breaking in the parallel wavenumber spectrum is identified. The origin of the current scaling is found to be the enhanced k∥ symmetry breaking induced by increased radial variation of the safety factor as the current decreases. The physics origin for the linear dependence of intrinsic rotation on the pressure gradient comes from the fact that both turbulence intensity and the zonal flow shear, which are two key ingredients for driving the residual stress, are increased with the strength of the turbulence drives, which are R/LTe and R/Lne for the collisionless trapped electron mode (CTEM). Highlighted results also include robust radial pinches in toroidal flow, heat and particle transport driven by CTEM turbulence, which emerge “in phase,” and are shown to play important roles in determining plasma profiles. Also discussed are the experimental tests proposed to validate findings from these gyrokinetic simulations.

Fluctuation characteristics and transport properties of collisionless trapped electron mode turbulence

The collisionless trapped electron mode turbulence is investigated by global gyrokinetic particle simulation. The zonal flow dominated by low frequency and short wavelength acts as a very important saturation mechanism. The turbulent eddies are mostly microscopic, but with a significant portion in the mesoscale. The ion heat transport is found to be diffusive and follows the local radial profile of the turbulence intensity. However, the electron heat transport demonstrates some nondiffusive features and only follows the global profile of the turbulence intensity. The nondiffusive features of the electron heat transport is further confirmed by nonlognormal statistics of the flux-surface-averaged electron heat flux. The radial and time correlation functions are calculated to obtain the radial correlation length and autocorrelation time. Characteristic time scale analysis shows that the zonal flow shearing time and eddy turnover time are very close to the effective decorrelation time, which suggests that the trapped electrons move with the fluid eddies. The fluidlike behaviors of the trapped electrons and the persistence of the mesoscale eddies contribute to the transition of the electron turbulent transport from gyro-Bohm scaling to Bohm scaling when the device size decreases.

Advanced simulation of electron heat transport in fusion plasmas

Electron transport in burning plasmas is more important since fusion products first heat electrons. First-principles simulations of electron turbulence are much more challenging due to the multi-scale dynamics of the electron turbulence, and have been made possible by close collaborations between plasma physicists and computational scientists. The GTC simulations of collisionless trapped electron mode (CTEM) turbulence show that the electron heat transport exhibits a gradual transition from Bohm to gyroBohm scaling when the device size is increased. The deviation from the gyroBohm scaling can be induced by large turbulence eddies, turbulence spreading, and non-diffusive transport processes. Analysis of radial correlation function shows that CTEM turbulence eddies are predominantly microscopic but with a significant tail in the mesoscale. A comprehensive analysis of kinetic and fluid time scales shows that zonal flow shearing is the dominant decorrelation mechanism. The mesoscale eddies result from a dynamical process of linear streamers breaking by zonal flows and merging of microscopic eddies. The radial profile of the electron heat conductivity only follows the profile of fluctuation intensity on a global scale, whereas the ion transport tracks more sensitively the local fluctuation intensity. This suggests the existence of a nondiffusive component in the electron heat flux, which arises from the ballistic radial E X B drift of trapped electrons due to a combination of the presence of mesoscale eddies and the weak de-tuning of the toroidal precessional resonance that drives the CTEM instability. On the other hand, the ion radial excursion is not affected by the mesoscale eddies due to a parallel decorrelation, which is not operational for the trapped electrons because of a bounce averaging process associated with the electron fast motion along magnetic field lines. The presence of the nondiffusive component raises question on the applicability of the usual quasilinear theory for the CTEM electron transport. This is in contrast to the good agreement between the quasilinear transport theory and simulation results of the electron heat transport in electron temperature gradient (ETG) turbulence, which is regulated by a wave-particle decorrelation. Therefore, the transport in the CTEM turbulence is a fluid-like eddy mixing process even though the linear CTEM instability is driven by a kinetic resonance. In contrast, a kinetic process dominates the transport in the ETG turbulence, which is characterized by macroscopic streamers.

Nonlinear saturation of collisionless trapped electron mode turbulence: Zonal flows and zonal density

Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturation phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.

Zonal flow generation in collisionless trapped electron mode turbulence

In the present work the generation of zonal flows in collisionless trapped electron mode (TEM) turbulence is studied analytically. A reduced model for TEM turbulence is utilized based on an advanced fluid model for reactive drift waves. An analytical expression for the zonal flow growth rate is derived and compared with the linear TEM growth, and its scaling with plasma parameters is examined for typical tokamak parameter values.

Role of stable eigenmodes in saturated local plasma turbulence

The excitation of stable eigenmodes in unstable plasma turbulence, previously documented in collisionless trapped electron mode turbulence, is shown to be a generic behavior of local (quasihomogeneous) systems. A condition is derived to indicate when such excited eigenmodes achieve a sufficient level in saturation to affect the turbulence, and produce changes in saturation levels, instability drive, and transport. The condition is shown to be consistent with the results of collisionless and dissipative trapped electron turbulence, and is further illustrated by an entirely different model describing simple ion turbulence driven by the ion temperature gradient. The condition suggests that all eigenmodes of the ion model affect saturation, but none dominates. This is consistent with the results of simulations, which show nonlinear modifications to eigenmode structure, growth rate, and transport that occur intermittently in time, despite fixed driving gradients.

Nonlinear stability and instability in collisionless trapped electron mode turbulence

A two-field model for collisionless trapped electron mode turbulence has both finite amplitude-induced stability and instability, depending on wave number. Effects usually identified with nonlinear plasma instability (self-trapping, kinetics, 3D mode structure, magnetic shear) are absent. Nonlinear stability and instability reside in E×B advection of density. It drives modes of a purely damped branch of the dispersion relation to finite amplitude and changes the rate at which free energy is released into the turbulence by shifting the density-potential cross phase. Analysis shows that modes of the purely damped branch cannot be ignored in saturation, and that the linear growth rate is a poor indicator of driving at finite amplitude, invalidating mixing length and quasilinear approximations. Using statistical closure theory, the nonlinear eigenmode and growth rate are determined from the saturation level of modes on all branches, stable and unstable, and the nonlinear cross phase that governs finite-amplitude instability.

Effects of nonlinear electron dynamics in a fluid model of collisionless trapped-electron mode turbulence

The role of the electron nonlinearity on saturation levels and particle transport in collisionless trapped electron mode turbulence is examined numerically using a two-dimensional fluid model. It is found that the removal of the electron nonlinearity results in an order of magnitude increase in fluctuation and particle transport levels. In addition, the qualitative behavior of the saturated state changes distinctly, including a decrease in RMS wave number in both cross-field directions, deviations from isotropy, changes in transport scalings, and changes in the spectral flow of energy. These results indicate that the electron nonlinearity is responsible for an efficient transfer of internal energy to small dissipation scales, thus resulting in lower fluctuation levels than predicted by ion mode coupling alone. The electron nonlinearity also decreases the phase angle between the density and potential leading to a decrease in the driving source. These results underscore the importance of the cross-correlation on saturation and demonstrate that numerical or theoretical use of ‘‘iδ’’ models to describe weakly collisional or collisionless trapped-electron mode turbulence is not appropriate.