Nonlinear triad interactions and the mechanism of spreading in drift-wave turbulence

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.     

Turbulent particle transport in magnetized plasmas

Particle transport in magnetized plasmas is investigated with a fluid model of drift wave turbulence. An analytical calculation shows that magnetic field curvature and thermodiffusion drive an anomalous pinch. The curvature driven pinch velocity is consistent with the prediction of turbulence equipartition theory. The thermodiffusion flux is found to be directed inward for a small ratio of electron to ion pressure gradient, and it reverses its sign when increasing this ratio. Numerical simulations confirm that a turbulent particle pinch exists. It is mainly driven by curvature for equal ion and electron heat sources. The sign and relative weights of the curvature and thermodiffusion pinches are consistent with the analytical calculation.     

Ion-acoustic turbulence and anomalous transport

We present results for the dynamics of evolution of non-linear state plasmas in a d.c. electric field which causes ion-acoustic turbulence (IAT). We look at (1) the time variation of the drift electron velocity and of the effective collision frequency, (2) features of the redistribution and heating of resonance ions, (3) the evolution of the spectral and angular distribution of turbulent pulsations, (4) processes of heating of the bulk of the particles. The results of an analytical IAT theory are compared with computer simulations.Special attention is paid to the theory of inhomogeneous plasmas with IAT. A self-consistent theory of anomalous transport is presented. We discuss the anisotropy of anomalous transport and the influence of non-Maxwellian particle velocity distributions on the transport processes. The electromagnetic properties, self-organization and hydrodynamic instability of plasmas with IAT are discussed.     

Classical impurity ion confinement in a toroidal magnetized fusion plasma

High-resolution measurements of impurity ion dynamics provide first-time evidence of classical ion confinement in a toroidal, magnetically confined plasma. The density profile evolution of fully stripped carbon is measured in MST reversed-field pinch plasmas with reduced magnetic turbulence to assess Coulomb-collisional transport without the neoclassical enhancement from particle drift effects. The impurity density profile evolves to a hollow shape, consistent with the temperature screening mechanism of classical transport. Corroborating methane pellet injection experiments expose the sensitivity of the impurity particle confinement time to the residual magnetic fluctuation amplitude.     

Cosmic-Ray Modulation: an Ab Initio Approach

A better understanding of cosmic-ray modulation in the heliosphere can only be gained through a proper understanding of the effects of turbulence on the diffusion and drift of cosmic rays. We present an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. This model is solved for periods of minimum solar activity, utilizing boundary values chosen so that model results are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the solar ecliptic plane but also along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra. The latter spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this study. The modelled turbulence spectra are used as inputs for parallel mean free path expressions based on those derived from quasi-linear theory and perpendicular mean free paths from extended nonlinear guiding center theory. Furthermore, the effects of turbulence on cosmic-ray drifts are modelled in a self-consistent way, employing a recently developed model for drift along the wavy current sheet. The resulting diffusion coefficients and drift expressions are applied to the study of galactic cosmic-ray protons and antiprotons using a three-dimensional, steady-state cosmic-ray modulation code, and sample solutions in fair agreement with multiple spacecraft observations are presented.     

Internal transport barriers in plasmas with reversed plasma flow

Evidences of internal particle transport barriers have been observed in plasma discharges with reversed plasma flow. To investigate the influence of the radial electric field profile on these barriers, we apply a drift wave map that describe the plasma particle transport and allows the integration of particle drift in the presence of a given electrostatic turbulence spectrum. With this procedure we show that transport barriers due to the shearless flow invariant lines are created inside the plasma. Moreover, by varying the radial electric field profile, we observe the formation and destruction of internal transport barriers constituted by shearless invariant lines, as well as its effects on the transport in the map's phase space. Applicability of our results are discussed for the Texas Helimak, a toroidal plasma device in which the radial electric field can be changed by application of bias potential.     

Drift wave turbulence in a dense semi-classical magnetoplasma

A semi-classical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbations. The relevance to nanoscale turbulence in nonuniform dense magnetoplasmas is discussed.     

Linear and Nonlinear Magnetic Electron Drift Waves in a Nonuniform Strong Magnetic Field

Linear and nonlinear propagation of magnetic electron drift vortex waves in a nonuniform magnetic field is investigated by means of a generalized adiabatic law which takes into account the effect of strong fields and reduces in the appropriate limits to several well known energy conservation equations in a collisionless plasma. In the linear limit, an instability is shown to exist, whereas in the nonlinear regime, steady-state dipole vortices associated with the electron drift vortex waves may appear. The anomalous electron energy transport associated with the unstable magnetic electron drift vortex waves is investigated by means of a quasilinear theory.     

The transport of slow ions in gases: Experiment, theory, and applications

This review is concerned with the two most important transport phenomena in involving slow ions in gases, namely their drift and diffusion in an externally applied electric field. The energy range of interest extends from thermal values at low temperatures up to about 10 eV. The transport phenomena are first discussed in physical terms, and experimental techniques for measuring ionic drift velocities and diffusion coefficients are then described. Brief coverage is given to ionic transport theory up to the time of Wannier's landmark contributions in 1951–1952; later theoretical developments are treated in more detail. Special emphasis is placed on aspects of modern theory that permit the determination of interaction potentials and collision frequencies for momentum transfer from experimental transport data. The review ends with a discussion of several applications of transport data to ionospheric problems.     

Cyclokinetic models and simulations for high-frequency turbulence in fusion plasmas

Gyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlinearly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency (ion cyclotron frequency) regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1.This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22(5), 056101 (2015)] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian (or continuum) scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 (2015)]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy.By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω* values with stable ion cyclotron modes. The gyrokinetic approximation is found to break down when the density perturbation exceeds 20%, or when the ratio of nonlinear E×B frequency over ion cyclotron frequency exceeds 20%. This result indicates that the density perturbation of the Tokamak L-mode near-edge is not sufficiently large for breaking the gyro-phase averaging. For cyclokinetic simulations with sufficiently unstable ion cyclotron (IC) modes and sufficiently low Ω* ～10, the high-frequency component of the cyclokinetic transport can exceed that of the gyrokinetic transport. However, the low-frequency component of the cyclokinetic transport does not exceed that of the gyrokinetic transport. For higher and more physically relevant Ω* ?50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport remains smaller than that of the gyrokinetic transport. In conclusion, the “L-mode near-edge short-fall” phenomenon, observed in some low-frequency gyrokinetic turbulence transport simulations, does not arise owing to the nonlinear coupling of high-frequency ion cyclotron motion to low-frequency drift motion.     

Transport Equations of Plasma in a Curvilinear Magnetic Field

The problem of transport equations of a collisional plasma in a curvilinear magnetic field is studied. Two main approaches to this problem are presented: that based on using the Boltzmann kinetic equation and the drift kinetic equation approach. In the frame of the first approach a multimoment transport equation set is found which is more general than the transport equation sets of Braginskii and Grad. The tensor equations of this set are described in an arbitrary curvilinear coordinate system. This allow to use these equations in problems of a plasma confined in toroidal magnetic configurations. Simplification of the multimoment transport equation set in the case of high magnetic field is performed. In the frame of the drift kinetic equation approach, a generalization of the drift transport equations derived earlier by the authors (Zh. Eksp. Teor. Fiz. 83 (1982) 139) is given.     

Suppression of plasma turbulence during optimized shear configurations in JET

Correlation of density turbulence suppression and reduced plasma transport is observed in the internal transport barrier (ITB) region of JET tokamak discharges with optimized magnetic shear. The suppression occurs in two stages. First, low frequency turbulence and ion transport are reduced across the plasma core by a toroidal velocity shear generated by intense auxiliary heating. Then with the ITB formation, high frequency turbulence and electron transport are reduced locally within the steep pressure gradient region of the ITB.     

TOKAM-3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks

We present a new code aiming at giving a global and coherent approach for transport and turbulence issues in the edge plasma of Tokamaks. The TOKAM-3D code solves 3D fluid drift equations in full-torus geometry including both closed field lines and SOL physics. No scale separation is assumed so that interactions between large scale flows and turbulence are coherently treated. Moreover, the code can be run in transport regimes ranging from purely anomalous diffusion to fully established turbulence. Specific numerical schemes have been developed which can solve the model equations whether the presence of a limiter in the plasma is taken into account or not. Example cases giving an overview of the field of application of the code as well as verification results are also presented.     

Investigation of intense sheet electron beam transport using the macroscopic cold-fluid model and the single-particle orbit theory

The focusing and the stable transport of an intense elliptic sheet electron beam in a uniform magnetic field are investigated thoroughly by using the macroscopic cold-fluid model and the single-particle orbit theory.The results indicate that the envelopes and the tilted angles of the sheet electron beam obtained by the two theories are consistent.The single-particle orbit theory is more accurate due to its treatment of the space-charge fields in a rectangular drift tube.The macroscopic cold-fluid model describes the collective transport process in order to provide detailed information about the beam dynamics,such as beam shape,density,and velocity profile.The tilt of the elliptic sheet beam in a uniform magnetic field is carefully studied and demonstrated.The results presented in this paper provide two complete theories for systemically discussing the transport of the sheet beam and are useful for understanding and guiding the practical engineering design of electron optics systems in high power vacuum electronic devices.     

Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence

Spectroscopic techniques are increasingly used for field laser applications in industry and research. Under field conditions complex gas sensors cannot be considered as stable and therefore drift characterization is a key issue to distinguish between sample data and sensor drift. In this paper the history of von Neumann’s two-sample variance and Allan variance stability investigations in the field of frequency metrology and the relationship to wavelet analysis are reviewed. The concept has been used to characterize accuracy and precision of spectroscopic data in the time domain and practical guidelines for the interpretation of σ/τ plots are presented. Two topics relevant for spectroscopic measurements are discussed: First, the optical fringe effect, which is present in any spectrometer, limits the precision and accuracy of spectroscopic measurements by forming time dependent background structures superimposed to the signal under investigation. The two-sample variance is used to characterize optical etalons and long-term drift using σ/τ plots. Second, the short-term instrument stability characteristic in the presence of atmospheric turbulence is discussed. This is important for laser-based gas monitors measuring the turbulent transport of trace gases between the biosphere and the atmosphere using the eddy-covariance technique. It will be shown how the spectral characteristics of turbulence in the Kolmogorov inertial subrange can be identified in the time domain and how the effect of optical fringes can be separated from atmospheric signals.     

Influence of the static Dynamic Ergodic Divertor on edge turbulence properties in TEXTOR

Systematic measurements on the edge turbulence and turbulent transport have been made by Langmuir probe arrays on TEXTOR under various static Dynamic Ergodic Divertor (DED) configurations. Common features are observed. With the DED, in the ergodic zone the local turbulent flux reverses sign from radially outwards to inwards. The turbulence properties are profoundly modified by energy redistribution in frequency spectra and suppression of large scale eddies. The fluctuation poloidal phase velocity changes direction from electron to ion diamagnetic drift, consistent with the observed reversal of the Er x B flow. In the laminar region, the turbulence is found to react to an observed reduced flow shear.     

Dynamics of fully nonlinear drift wave-zonal flow turbulence system in plasmas

We present numerical simulations of fully nonlinear drift wave-zonal flow (DW-ZF) turbulence systems in a nonuniform magnetoplasma. In our model, the drift wave (DW) dynamics is pseudo-three-dimensional (pseudo-3D) and accounts for self-interactions among finite amplitude DWs and their coupling to the two-dimensional (2D) large amplitude zonal flows (ZFs). The dynamics of the 2D ZFs in the presence of the Reynolds stress of the pseudo-3D DWs is governed by the driven Euler equation. Numerical simulations of the fully nonlinear coupled DW-ZF equations reveal that short scale DW turbulence leads to nonlinear saturated dipolar vortices, whereas the ZF sets in spontaneously and is dominated by a monopolar vortex structure. The ZFs are found to suppress the cross-field turbulent particle transport. The present results provide a better model for understanding the coexistence of short and large scale coherent structures, as well as associated subdued cross-field particle transport in magnetically confined fusion plasmas.     

平行速度剪切驱动湍流引起的粒子输运

通过离子温度梯度及平行速度剪切的准线性湍流理论，得到了由杂质离子及抵频E×B湍流所驱动的径向离子流及相应的输运系数．理论分析表明，主要离子和杂质离子的径向离子流具有相反的方向，并随着平衡流速剪切以及杂质离子的密度梯度的变化而改变．增强平行速度剪切对主要离子的约束可产生有利影响 关键词：     

Fractal structures in turbulence

We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.