Session NI1: Electron Confinement and Zonal Flows

Experimental Studies of Zonal Flow and Field in CHS Plasma

Turbulence is a fundamental phenomenon ubiquitously observed in nature. In the fusion and plasma research, the drift-wave turbulence has been extensively studied to clarify the anomalous transport that degrades plasma confinement properties. Recently, a new paradigm for plasma turbulence has come up: the turbulence is regarded as a system of drift waves and the zonal flows. This paper provides full reports on the pioneer works in CHS, which have propelled the paradigm shift by dual heavy ion beam probes (HIBPs) and by modern data-processing techniques (wavelet, bicoherence, etc). In the experiments up to date, I) zonal flow was identified for the first time with the oscillatory branch of zonal flow, geodesic acoustic modes. II) The coupling between zonal flow and turbulence was confirmed. III) The difference in the energy partition between zonal flow and turbulence is found to be a cause of the confinement improvement for the states with and without a transport barrier. Very recently, the experiments have evolved into a new stage by exploring the potentiality of HIBP, that is, the ability to measure local magnetic field perturbation. The application resulted in discovery of zonal magnetic field and the coupling with turbulence. Similarly to the zonal flow, the zonal field is a symmetric structure around the magnetic axis with a finite radial wavelength in meso-scale. The discovery presents clear evidence that turbulence can generate the structured magnetic field, giving an insight into the field generation like geomagnetism. The works provide a modern framework for a fundamental understanding of the turbulence and its related structural formation. The observations of structured electric and magnetic fields generated by turbulence in laboratory are important for fluid mechanics and astronomy as well as the plasma physics.   

Electron Temperature Fluctuations in the Core of High-Performance DIII-D Plasmas

Electron temperature fluctuations have been measured for the first time in the core of high-performance, neutral-beam-heated DIII-D plasmas. Simultaneous local characterization of temperature and density fluctuations presents an opportunity to challenge theoretical/simulation predictions. Data from long-duration quiescent H-mode plasmas indicate that, at $r/a$=0.75, \underline {normalized} fluctuation levels are reduced by a factor of 5 below L-mode levels, with a detectability limit of $\le $0.25{\%}. In these QH-mode plasmas, the \underline {absolute} temperature fluctuation amplitude is observed to decrease by a factor of 2, correlating with increasing electron temperatures and improved electron thermal confinement. Temperature fluctuation levels and frequency spectra, $k_{\theta}\rho_{s}\le $0.5, are determined via correlation electron cyclotron emission radiometry [1]. In L-mode, temperature fluctuations (20$ [Preview Abstract]

Gyrokinetic $\delta\! f$ particle simulation of trapped electron mode driven turbulence

Turbulent transport driven by collisionless trapped electron modes (CTEM) is systematically studied using gyrokinetic delta-f particle-in-cell simulation. Scaling with local plasma parameters, including density gradient, electron temperature gradient, magnetic shear, temperature ratio and aspect ratio, is investigated. Simulation results are compared with previous simulations and theoretical predictions. Nonlinearly the transport level increases with increasing magnetic shear. We explain the nonlinear magnetic shear scaling by differences in the radial correlation lengths caused by toroidal coupling. The turbulence is more radially elongated at higher magnetic shear compared with low magnetic shear. We show that the suppression effect of zonal flow on CTEM transport depends on both the electron temperature gradient and the electron to ion temperature ratio. This helps explain the previous contradictory conclusions on the importance of zonal flows in different parameter regimes.\footnote{T. Dannert, F. Jenko, Phys. Plasmas 12, 072309 (2005); D. Ernst, et al., Phys. Plasmas 11, 2637 (2004).} Zonal flow suppression is consistent with the rate of $EXB$ shearing from the ambient turbulence as well as the radial broadening of the spectra. Strong geodesic acoustic modes (GAMs) are generated along with zonal flows and the frequency of the GAMs agrees well with kinetic theory.\footnote{T. Watari, et al., Phys. Plasmas 13, 062504 (2006).} We further explore the nonlinear saturation mechanism when the zonal flows are not important. We find that when only a single toroidal mode (and its conjugate) is kept, reasonable nonlinear saturation is obtained. Investigating a range of $n$, modes with larger mode number $n$ saturate at a higher level relative to lower $n$ modes, indicating a turbulent inverse cascade process.   

A quantitative account of electron energy transport in an NSTX plasma*

Anomalous electron transport in magnetized plasmas can be a major obstacle in the way toward practical nuclear fusion power, and it has been an outstanding problem for almost half a century. Here we report the first successful quantitative accounting of the electron thermal conductivity $\chi _{e}$ in a tokamak experiment due to imperfect magnetic surfaces$^{1}$ caused by the microtearing instabilities. The unstable spectrum is calculated with the GS2 code for a well-behaved H-mode plasma in NSTX (R/a=0.85m/0.67m) with 6 MW deuterium neutral beam heating at I$_{p}$=0.75 MA, B$_{t}$=0.5 T. The application of existing nonlinear theory$^{2}$ showed that the unstable modes can produce overlapping resistive layers and stochastic magnetic fields. The calculated $\chi _{e}$ based on the theory$^{1}$ is in good agreement with the values from transport analysis of the experimental data over the entire region (0.4 $<$ r/a $<$ 0.75), where the electron temperature gradient is strong enough to make microtearing the most unstable mode. There is no adjustable parameter in this comparison. In a discharge with reversed central magnetic shear and an L-mode edge, microtearing modes are found to be stable. The central electron temperature is 50{\%} higher (2 keV vs 1.3 keV) than in the comparison shot with the microtearing instability and the same controlled tokamak parameters like plasma current, density, magnetic field, plasma shape, position and neutral beam heating power. This is a strong indication that this instability may be the dominant mechanism responsible for the electron transport in this type of plasma. Since the microtearing mode is difficult to stabilize with velocity shear, this instability is an important limit$^{3}$ on the electron temperature in spherical tokamak configurations where the usual long wavelength instabilities are not present. \newline \newline *This work is carried out in collaboration with Drs. S. Kaye, D. R. Mikkelsen, J. Krommes, K. Hill, R. Bell, and B. LeBlanc. It is supported by USDoE contract No. DE-AC02-76CH03073. \newline \newline $^{1}$A. B. Rechester, M. N. Rosenbluth, Phys. Rev. Lett. \underline {40}, 38 (1978). \newline $^{2}$J. F. Drake et al., Phys. Rev. Lett. \underline {44}, 994 (1980). \newline $^{3}$M. Kotschenreuther, W. Dorland et al., Nucl. Fusion \underline {40}, 677 (2000).   

The Relationship between Type I ELM Severity and Perturbed Electron Transport in NSTX

NSTX provides a unique test bed for probing electron transport due both to its significant role in the steady-state power balance and features of the electron response to transient perturbations. In neutral-beam-heated plasmas in NSTX, most of the heating power is deposited on the electrons. Following large Type I ELMs in some H-mode NSTX discharges, global Te profile declines of 10-30{\%} amplitude are observed. While the soft X-ray data indicates that the ELM itself is causing only a peripheral T$_{e}$ perturbation, the inward propagation of the cold pulse initiated by the ELM is unusually fast ($\sim $ms timescale) and can extend to the core of the plasma. The perturbed electron thermal diffusivity is $\sim $300 m$^{2}$/s for r/a $>$ 0.4, and $\sim $30 m$^{2}$/s for r/a $<$ 0.4. However, in high-triangularity regimes, which exhibit smaller Type I ELM perturbations and an energy loss of a few percent, the perturbation propagation time of several ms implies a perturbed electron thermal diffusivity of 10-20 m$^{2}$/s across the plasma radius. Comparison of the ELM energy loss with the electron thermal diffusivity inferred from both ELM and pellet induced `cold pulses', shows a rough proportionality between the ELM magnitude and the perturbed electron thermal diffusivity. Furthermore, comparisons of the linear growth rates of instabilities calculated with the GS2 code show large differences between the large and small Type I ELM regimes. In particular, the ETG mode is the dominant instability following large ELMs, but absent during the small Type I ELM. Interestingly, high-k measurements during ELM events show an increase of short wavelength fluctuations in both the core and edge regions of the plasma, with the increase in amplitude most prominent at wavenumbers of 14-16 cm$^{-1}$. These results suggest that electron thermal transport plays an important role in determining the total energy loss from Type I ELMs.   

Spectral Features of the Geodesic Acoustic Mode and its Interaction with Turbulence in a Tokamak Plasma

The measurements of the geodesic acoustic mode (GAM) by a set of probe arrays with large poloidal and toroidal separations in the edge region of the HL-2A tokamak have been performed. By the two-point cross-correlation technique, the three-dimensional wavenumber and frequency spectrum for the GAM is measured for the first time. The spectrum for the GAM exhibits a anisotropic feature: the poloidal and toroidal wavenumber spectra are peaked at $k_\theta =k_\phi =0$ with a width given by the spectral variance, while the radial spectrum shows a peak in the range of $q_r \rho _i \simeq 0.05\sim 0.09$ with the FWHM of$\Delta q_r \rho _i \simeq 0.04\sim 0.07$. The spectrum also shows the GAM propagates in the radially outward direction. Using a newly developed method based on the poloidal momentum equation, the generation of the GAM by the triad interaction of turbulence via the Reynolds stress has been directly measured. The result manifests that the energy is transferred from small scale turbulence into the GAM by the gradient of the Reynolds stress and the GAM saturation amplitude is determined by balancing between the generation and damping rates of the GAM. In addition, it is found that the envelope of the radial electric field fluctuations $\tilde {E}_r $ is modulated by the GAM and the cross-phase between the envelope and GAM oscillation is about$\pi $. The numerical investigation shows that the modulation of the $\tilde {E}_r $ envelope is dominantly induced by the amplitude modulation. This fact together with the anti-phase relation between the $\tilde {E}_r $ envelope and GAM oscillation imply that the modulation of the $\tilde {E}_r $envelope is accompanied with the GAM generation in the energy-conserving triad interaction. These results suggest that the GAM is generated dominantly by the parametric instability driven by the turbulent Reynolds stress. In collaboration with T. Lan, A.D. Liu (USTC, China); L.W. Yan, W.Y. Hong, K.J. Zhao, J. Q. Dong, Q.W. Yang (SWIP, China).