Drift Wave Turbulence Research Articles

Amplification of ion acoustic wave in an inhomogeneous plasma through nonlinear wave-particle interaction with drift wave turbulence

A study on the amplification of ion acoustic wave in an inhomogeneous plasma has been made on the basis of a nonlinear wave-particle interaction process called plasma maser effect. The drift wave instability, which is a universal phenomenon of an inhomogeneous confined plasma system, is found to be strongly in phase relation with thermal particles and may transfer its wave energy nonlinearly through a modulated field to ion acoustic wave. Considering a Maxwellian distribution function model for inhomogeneous plasmas under the standard local approximation, we have estimated the growth rate for ion acoustic wave, which is obtained by using the nonlinear dispersion relation. It has been found that amplification of ion acoustic wave is possible at the expense of drift wave turbulent energy. This result may be particularly important for stability of various drift modes in magnetically confined plasma as well as for transport of momentum and energy in such inhomogeneous systems.

Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition

We assess two techniques for extracting coherent vortices out of turbulent flows: the wavelet based Coherent Vorticity Extraction (CVE) and the Proper Orthogonal Decomposition (POD). The former decomposes the flow field into an orthogonal wavelet representation and subsequent thresholding of the coefficients allows one to split the flow into organized coherent vortices with non-Gaussian statistics and an incoherent random part which is structureless. POD is based on the singular value decomposition and decomposes the flow into basis functions which are optimal with respect to the retained energy for the ensemble average. Both techniques are applied to direct numerical simulation data of two-dimensional drift-wave turbulence governed by Hasegawa-Wakatani equation, considering two limit cases: the quasi-hydrodynamic and the quasi-adiabatic regimes. The results are compared in terms of compression rate, retained energy, retained enstrophy and retained radial flux, together with the enstrophy spectrum and higher order statistics.

Experimental Observation of Zonal Flow and Its Scalings in Axisymmetric Magnetic Field

The anomalous radial transport generated by drift wave turbulence is a fundamental open physics question in magnetic confinement systems, both in modern tokamaks and current and next generation mirror machines. The role of self-generated zonal flows (ZF) in transport regulation via its shear is a potent concept and a physics issue. ZF are believed to be spontaneously excited by drift wave turbulence via Reynolds stress from small-scale fluctuations to large-scale flow.A basic physics experimental study of zonal flows associated with ITG (ion temperature gradient) drift modes has been performed in the Columbia Linear Machine (CLM). The difficult problem of detection of ZF has been solved via a novel diagnostic using the paradigm of FM (frequency modulation) in radio transmission. We find a power spectrum peak at ITG (‘carrier’) frequency of ~120 kHz and FM sidebands at frequency of ~2 kHz. We have definitively identified ZF with azimuthal and axial symmetry (kθ = 0, k// ≈ 0) and radially inhomogeneous (kr [not equal] 0) flow structures in cylindrical plasmas in uniform axisymmetric magnetic field. However, quantitatively, the stabilizing effect of ZF shear appears to be small and no significant isotopic effects are observed. The unique complementary roles of ion acoustic damping and ZF shearing in the saturation of ITG have been experimentally demonstrated using stabilizing and destabilizing feedback techniques. Theoretically ZF is supposed to be saturated via νii. As this is very small both in tokamaks and CLM, we investigate the scaling ZF with in νin which can be significant in CLM.

Initial Boundary Value Problem for Model Equations of Resistive Drift Wave Turbulence

In this paper we consider the drift wave turbulence in a strong magnetic field. Here we first establish the existence and uniqueness of a strong global solution to the initial boundary value problem for the model equations of the resistive drift wave turbulence. Second, by the standard method of passing to the limit, we establish the existence and uniqueness of a strong solution to the initial boundary value problem for three-dimensional Hasegawa–Wakatani equations.

Gyrofluid Simulation of Slab ITG Turbulence in Plasmas Including Pressure Profile Corrugation

Ion temperature gradient driven drift wave instability and turbulence are investigated based on a gyrofluid slab model in the presence of a pressure gradient corrugation (PPC). It is shown that the PPC cannot only stabilize or destabilize the ITG mode through local flattening or steepening of the radial pressure gradient, but most importantly also play a stabilizing role due to the global effect of the wave-type corrugation. The latter effect dominates in the highly corrugated cases and is identified to result from a nonlocal mode coupling in radial wave-number space, which scatters the spectra from unstable modes to high dissipation region. While the local stabilization/destabilization is stronger than the global stabilization in the cases with less corrugation, the global stabilization effect dominates the highly corrugated cases. Interestingly, it is found that the global stabilization of the PPC causes ion heat intermittency, which closely connects to the zonal flow dynamics.

Trapped gyro-Landau-fluid transport modeling of DIII-D hybrid discharges

Previous work has summarized the physics and first results of benchmarking the trapped gyro-Landau-fluid (TGLF) model for turbulent transport driven by trapped ion and electron modes, ion and electron temperature gradient (ETG) modes, and electromagnetic kinetic ballooning modes including the effects of shaped geometry. Recently, an improved collision model was implemented which provides a more accurate fit to a transport database of nonlinear collisional GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] simulations of long wavelength driftwave turbulence. The impact of the new collision model on TGLF modeling results was unknown. Using the improved TGLF model we obtain excellent agreement with the ion and electron temperature profiles from 30 DIII-D [A. Mahdavi and J. L. Luxon, Fusion Sci. Technol. 48, 2 (2005)] hybrid discharges. The transport results show that the electron energy transport tends to be dominated by short wavelength ETG modes in cases where the ion energy transport approaches neoclassical levels. The hybrid regime has significant energy confinement improvement from E×B velocity shear which is well predicted by TGLF. Weak magnetic shear and low safety factor are also shown to enhance the hybrid regime energy confinement. In high normalized β hybrids, we find that finite β effects noticably reduce the predicted electron energy transport and improve agreement with the measured electron temperature profiles.

Non-linear dynamics and plasma flows in a basic toroidal plasma experiment

Analyses of non-linear interactions in drift-wave turbulence were carried out in wavenumber space on experimental data obtained from multi-probe measurements in the toroidally confined plasma of the stellarator TJ-K. Recent results are reported. The inverse cascade of energy from small to large scales as typical for two-dimensional turbulence is verified. The transfer in k space is found to be governed by non-local processes. The same way, large-scale zonal flows (ZFs) are found to tap energy from small-scale turbulence, as consistent with the vortex-thinning mechanism. An enhancement of the correlation between ZF shear and Reynolds stress as a source of ZF energy is observed, when strong background shear flows are imposed, which comes along with increased long-range correlations.

Long-range correlations induced by the self-regulation of zonal flows and drift-wave turbulence

By means of a unique probe array, the interaction between zonal flows and broad-band drift-wave turbulence has been investigated experimentally in a magnetized toroidal plasma. Homogeneous potential fluctuations on a magnetic flux surface, previously reported as long range correlations, could be traced back to a predator-prey-like interaction between the turbulence and the zonal flow. At higher frequency the nonlocal transfer of energy to the zonal flow is dominant and the low-frequency oscillations are shown to result from the reduced turbulence activity due to this energy loss. This self-regulation process turns out to be enhanced with increased background shear flows.

Observation of Anomalous Ion Heating by Broadband Drift-Wave Turbulence

Using laser induced fluorescence and passive spectroscopy on a magnetically confined low-temperature plasma, anomalous ion heating is observed which exceeds collisional heating from the electrons by a factor of up to five. Direct wave heating due to the 2.45GHz microwave as well as stochastic heating by large-amplitude fluctuations could be ruled out as explanations. Good quantitative agreement is found when comparing the missing power in the ion species with heating power due to the dissipation of drift-wave turbulence. This turbulent energy transfer into the ion channel could have important consequences for the interpretation of transport in fusion plasmas.

Ultrafast spectroscopy diagnostic to measure localized ion temperature and toroidal velocity fluctuations

A dual-channel high-efficiency, high-throughput custom spectroscopic system has been designed and implemented at DIII-D to measure localized ion thermal fluctuations associated with drift wave turbulence. A large-area prism-coupled transmission grating and high-throughput collection optics are employed to observe C VI emission centered near λ=529 nm. The diagnostic achieves 0.25 nm resolution over a 2.0 nm spectral band via eight discrete spectral channels. A turbulence-relevant time resolution of 1 μs is achieved using cooled high-speed avalanche photodiodes and ultralow-noise preamplifiers. The system sensitivity is designed to provide measurements of normalized ion temperature fluctuations on the order of δT(i)/T(i)≤1%.

Origin of Lagrangian Intermittency in Drift-Wave Turbulence

The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This exponential distribution is shown to be a robust feature independent of the Reynolds number. For small adiabaticity, algebraic tails are observed, suggesting the strong influence of point-vortex-like dynamics on the acceleration. A causal connection is found between the shape of the probability density function and the autocorrelation of the norm of the acceleration.

Turbulent transport of fast ions in the Large Plasma Device

Strong drift wave turbulence is observed in the Large Plasma Device [H. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] on density gradients produced by a plate limiter. Energetic lithium ions orbit through the turbulent region. Scans with a collimated ion analyzer and with Langmuir probes give detailed profiles of the fast ion spatial distribution and the fluctuating fields. The fast ion transport decreases rapidly with increasing fast ion gyroradius. Unlike the diffusive transport caused by Coulomb collisions, in this case the turbulent transport is nondiffusive. Analysis and simulation suggest that such nondiffusive transport is due to the interaction of the fast ions with stationary two-dimensional electrostatic turbulence.

Applications of the wave kinetic approach: from laser wakefields to drift wave turbulence

AbstractNonlinear wave-driven processes in plasmas are normally described by either a monochromatic pump wave that couples to other monochromatic waves, or as a random phase wave coupling to other random phase waves. An alternative approach involves a random or broadband pump coupling to monochromatic and/or coherent structures in the plasma. This approach can be implemented through the wave-kinetic model. In this model, the incoming pump wave is described by either a bunch (for coherent waves) or a sea (for random phase waves) of quasi-particles. This approach has been applied to both photon acceleration in laser wakefields and drift wave turbulence in magnetized plasma edge configurations. Numerical simulations have been compared to experiments, varying from photon acceleration to drift mode-zonal flow turbulence, and good qualitative correspondences have been found in all cases.

Fluid models of impurity transport via drift wave turbulence

Turbulent transport due to drift waves is a critical issue for fusion physics across all magnetic confinement geometries. Three-component fluid equations are used to find the eigenmodes and eigenfrequencies of a nonuniform, magnetized plasma with a four dimensional fluctuation vector composed of fluctuations of the electron density, the working gas ion density, the impurity density, and the electrostatic plasma potential. This structure of the eigenmodes and eigenvectors is shown for two collisionality regimes: (i) the collisional drift waves appropriate for the scrape-off-layer and the edge plasma in limiter discharges and (ii) the trapped electron mode taken in the limit of a Terry-Horton fluid description for the core plasma. From the eigenmodes and eigenvectors the part of the density and potential fluctuations that are out-of-phase is computed. The quasilinear particle fluxes are analyzed as a function of the power spectrum of the plasma potential fluctuations and the gradient parameters characterizing the Ohmic, H, and internal transport barrier confinement modes. A reversal in a direction of impurity flux is observed by changing the sign of the impurity density gradient length. After reversal, the impurity flux is directed outward and it is a favorable for fusion plasmas.

Wave-number spectral scaling law of drift wave-zonal flow turbulence in gyrofluid simulations

Wave-number spectral characteristics of ion temperature gradient (ITG) turbulence are investigated based on three-dimensional gyrofluid simulation. The focus is on the back reaction of the self-generated zonal flows (ZFs) on the ambient turbulence through nonlinear mode coupling. Detailed spectral analyses evidently show that the radial wave-number spectra of the ITG-ZF turbulence is characterized by an exponential-law scaling, which is deformed from the usual Kolmogorov-like power law by the back reaction of the ZFs. These results are qualitatively in agreement with a theoretical prediction [Gürcan et al., Phys. Rev. Lett. 102, 255002 (2009)] and fairly match with the experimental observation of the density fluctuation spectrum [Hennequin et al., Plasma Phys. Controlled Fusion 46, B121 (2004)]. The generality of such spectral characteristics in drift wave turbulence with large-scale coherent structures is discussed.

Nonlinear subcritical magnetohydrodynamic beta limit

Published gyrokinetic simulations have had difficulty operating beyond about half the ideal magnetohydrodynamic (MHD) critical beta limit with stationary and low transport levels in some well-established reference cases. Here it is demonstrated that this limitation is unlikely due to numerical instability, but rather appears to be a nonlinear subcritical MHD beta limit [R. E. Waltz, Phys. Rev. Lett. 55, 1098 (1985)] induced by the locally enhanced pressure gradients from the diamagnetic component of the nonlinearly driven (zero frequency) zonal flows. Strong evidence that the zonal flow corrugated pressure gradient profiles can act as a MHD-like beta limit unstable secondary equilibrium is provided. It is shown that the addition of sufficient E×B shear or operation closer to drift wave instability threshold, thereby reducing the high-n drift wave turbulence nonlinear pumping of the zonal flows, can allow the normal high-n ideal MHD beta limit to be reached with low transport levels. Example gyrokinetic si...

Linear study of the nonmodal growth of drift waves in dusty plasmas

The main effect of dust on drift wave turbulence is the enhancement of the nonadiabaticity. Previous work found that nonmodal behavior is important in the nonadiabatic regime of the drift wave system. Here, the modal and nonmodal properties of the linear Hasegawa–Wakatani system of dusty plasmas are investigated. The non-normality of the linear evolution operator can lead to enhanced transient growth rates compared to the modal growth rates.

Two-dimensional bispectral analysis of drift wave turbulence in a cylindrical plasma

Bispectral analysis and multichannel measurement are becoming attractive investigation tools in plasma fluctuation studies. In the Large Mirror Device-Upgrade, the measurement of fluctuations in the ion saturation-current with a 64-channel poloidal Langmuir probe array was performed. The two-dimensional (2D) (poloidal wave number and frequency) power spectrum showed a number of pronounced peaks and broadband fluctuations in the poloidal wave number-frequency space. We applied 2D bispectral analysis, which considers both the matching conditions of poloidal wave number and frequency, to the spatiotemporal waveform, and confirmed the nonlinear couplings between coherent-coherent, coherent-broadband, and broadband-broadband fluctuation components. More than ten peaks were revealed to have as their origins only three original parent modes generated in the plasma. Comparison between the theoretical estimate and experimental observation for the bicoherence showed good agreement.

Development and Applications of Axisymmetric Magnetic Mirror Concepts

Recent results from Russia and Japan have sparked renewed interest in magnetic mirror concepts. The Russian Gas Dynamic Trap experiment achieved 60% beta in an axisymmetric magnetic mirror. The Japanese Gamma-10 experiment demonstrated the suppression of radial transport due to drift-wave turbulence. This paper describes the evolution of magnetic mirrors, identifies a number of methods to stabilize axisymmetric mirrors, and suggests areas of needed research. The simple axisymmetric configuration has applications ranging from a source for material testing with plasma and neutrons to a driver for fusion-fission hybrid to the possibility of a fusion power plant.

Experiments with liquid metal walls: Status of the lithium tokamak experiment

Abstarct Liquid metal walls have been proposed to address the first wall challenge for fusion reactors. The lithium tokamak experiment (LTX) at the Princeton Plasma Physics Laboratory (PPPL) is the first magnetic confinement device to have liquid metal plasma-facing components (PFC's) that encloses virtually the entire plasma. In the current drive experiment-upgrade (CDX-U), a predecessor to LTX at PPPL, the highest improvement in energy confinement ever observed in ohmically heated tokamak plasmas was achieved with a toroidal liquid lithium limiter. The LTX extends this liquid lithium PFC by using a conducting conformal shell that almost completely surrounds the plasma. By heating the shell, a lithium coating on the plasma-facing side can be kept liquefied. A consequence of the low-recycling conditions from liquid lithium walls is the need for efficient plasma fueling. For this purpose, a molecular cluster injector is being developed. Future plans include the installation of a neutral beam for core plasma fueling, and also ion temperature measurements using charge-exchange recombination spectroscopy (CHERS). Low edge recycling is also predicted to reduce temperature gradients that drive drift wave turbulence. Gyrokinetic simulations are in progress to calculate fluctuation levels and transport for LTX plasmas, and new fluctuation diagnostics are under development to test these predictions.