Resistive Drift Wave Turbulence Research Articles

On anomalous transport of multi-species plasma associated with the resistive ballooning and resistive drift waves driven turbulence

Anomalous transport of multi-species plasma related to the resistive ballooning and resistive drift wave turbulence is considered in a “cold” ion approximation. It is found that similar to the resistive drift wave turbulence [see A. R. Knyazev and S. I. Krasheninnikov, Phys. Plasmas 31, 012502 (2024); and S. I. Krasheninnikov and R. D. Smirnov, Phys. Plasmas (to be published)] the addition of the ballooning drive does not change the main features of anomalous transport of the multi-species plasma: (i) The transport of all ion species is described as a transport of the passive scalars in the turbulent field of the electrostatic potential and electron density perturbation; (ii) the density of ion species with a larger ratio of the mass to charge has the tendency to the accumulation/depletion in the vortices of plasma flow; and (iii) the cross-field transport of all plasma species (including electrons and ions) is described by the same anomalous transport coefficient.

Hysteresis in the gyrofluid resistive drift wave turbulence to zonal flow transition

The classical drift-fluid (modified) Hasegawa–Wakatani model for quasi-three-dimensional resistive drift wave turbulence in magnetized plasmas is introduced into a gyrofluid model including consistent finite Larmor radius effects. The transition from a turbulence dominated to a strong zonal flow state through variation of the dissipative coupling strength is re-visited and characterized for warm ions. The resulting zonal flow states show a dependence on initial conditions and intermediate temporary changes of parameters, and feature characteristics of hysteresis, such as longer time scales for the decay of zonal flow states into turbulence than for the formation of flows out of turbulence. Zonal flows in warm ion plasmas are also shown to be able to spontaneously merge into flow states with smaller radial mode number and higher flow energy in simulations with long run times.

Fluid simulations of resistive drift-wave turbulence with diamagnetic flow in ZPED experiments

We derive a diamagnetic resistive fluid model (DRF) and develop an associated two-dimensional fluid simulation code (DRF-2D) to explore the dynamics of resistive drift modes within the plasmas of the Zheda Plasma Experiment Device (ZPED). The validation of the linear dispersion relation for the DRF-2D code revealed a harmonious agreement between analytical theory and linear numerical simulations. Leveraging plasma parameters obtained from the ZPED experiments, we conducted a comprehensive series of nonlinear simulations using the DRF-2D code. Our simulations successfully replicate the nonlinear trends in turbulent fluctuations and transport observed in the ZPED experiments, particularly demonstrating a remarkably accurate alignment of the turning point in the magnetic field. Notably, the DRF model sheds light on the observed frequency sign reversal from the electron diamagnetic direction to the ion diamagnetic direction in the ZPED experiments. This is demonstrated through well-matched turning points in the confining magnetic field between the nonlinear simulations and ZPED experiments. The fidelity of our model in capturing these phenomena underscores its efficacy in providing valuable insights and predictive capabilities for the intricate dynamics observed in the ZPED plasmas.

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Nearly integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence

Transitionally turbulent flows frequently exhibit spatiotemporal intermittency, reflecting a complex interplay between driving forces, dissipation, and transport present in these systems. When this intermittency manifests as observable structures and patterns in the flow, the characterization of turbulence in these systems becomes challenging due to the nontrivial correlations introduced into the statistics of the turbulence by these structures. In this work, we use tools from dynamical systems theory to study intermittency in the Dimits shift regime of the flux-balanced Hasegawa–Wakatani (BHW) equations, which models a transitional regime of resistive drift-wave turbulence relevant to magnetically confined fusion plasmas. First, we show in direct numerical simulations that turbulence in this regime is dominated by strong zonal flows and coherent drift-wave vortex structures, which maintain a strong linear character despite their large amplitude. Using the framework of generalized Liouville integrability, we develop a theory of integrable Lagrangian flows in generic fluid and plasma systems and discuss how the observed zonal flows plus drift waves in the BHW system exhibit a form of “near-integrability” originating from a fluid element relabeling symmetry. We further demonstrate that the BHW flows transition from integrability to chaos via the formation of chaotic tangles in the aperiodic Lagrangian flow, and establish a direct link between the “lobes” associated with these tangles and intermittency in the observed turbulent dissipation. This illustrates how utilizing tools from deterministic dynamical systems theory to study convective nonlinearities can explain aspects of the intermittent spatiotemporal structure exhibited by the statistics of turbulent fields.

Impact of the electron density and temperature gradient on drift-wave turbulence in the Large Plasma Device

In this paper we present an experimental study of edge turbulence in the Large Plasma Device at UCLA. We utilize a scan of discharge power and prefill pressure (neutral density) to show experimentally that turbulent density fluctuations decrease with decreasing density gradient, as predicted for resistive drift-wave turbulence (RDWT). As expected for RDWT, we observe that the cross-phase between the density and potential fluctuations is close to 0. Moreover, the addition of an electron temperature gradient leads to a reduction in the amplitude of the density fluctuations, as expected for RDWT. However, counter to theoretical expectations, we find that the potential fluctuations do not follow the same trends as the density fluctuations for changes either in density gradients or the addition of a temperature gradient. The disconnect between the density and potential fluctuations is connected to changes in the parallel flows as a result of differences in the prefill pressure, i.e. neutral density. Further analysis of the density and potential fluctuation spectra show that the electron temperature gradient reduces the low frequency fluctuations up to $10 \,{\rm kHz}$ and the introduction of a temperature gradient leads to an unexpected ${\sim }{\rm \pi}$ shift of the density–potential cross-phase at ${\sim }10\,{\rm kHz}$ , while maintaining the typical resistive drift-wave cross-phase at lower frequencies. These experiments partly confirm existing knowledge on resistive drift-wave turbulence, but also introduce new observations that indicate a need for dedicated nonlinear three-dimensional turbulence simulations that include neutrals.

Effect of neutrals on the anomalous edge plasma transport

The impact of neutrals on the anomalous edge plasma transport is examined in detail within the resistive drift wave (RDW) turbulence and zonal flow (ZF) system. It is shown that the neutral impact on the RDW turbulence itself is weak, but it can largely damp the ZF and thus lead to an enhancement of the anomalous transport. Such an impact is stronger for the system with a larger adiabatic parameter, where the ZF is more dominant in the absence of neutrals. It is shown that the enhancement of the anomalous transport is related to the detrapping of fluctuations from the vicinity of the extrema of ZF when the neutrals weaken the ZF effect.

Global-in-time existence results for the two-dimensional Hasegawa–Wakatani equations

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa–Wakatani (HW) equations were proposed in 1983. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions.

On the Radial Eigenmode Structure of Drift Wave Instability with Inhomogeneous Damping in Cylindrical Plasmas

Plasma flows can be driven by turbulent stresses from excited modes in magnetized plasmas. Our recent numerical simulation of resistive drift wave turbulence in a linear device has shown that the radial inhomogeneity of the neutral density affects azimuthal flow generation by changing the phase structure of the most unstable eigenmodes. Eigenmode analyses show that the mode structure has a complex Bessel-type function shape in the central region of the plasma, and the imaginary part arises from the radial inhomogeneity of the damping term caused by ion-neutral collisions. The amplitude of turbulent stress is proportional to the inhomogeneity under a marginally stable condition. Global structural formation is an important factor for determining the plasma turbulent state, and this result clearly shows that several kinds of radial background distributions, the plasma and neutral densities in this case, can influence the global structures.

Turbulence simulation taking account of inhomogeneity of neutral density in linear devices

It is important to consider a combination of inhomogeneities, which drive and/or damp instabilities in magnetized plasmas. The inhomogeneity of neutral particle density is taken into account for analyzing turbulent states in linear devices by combining two kinds of simulations in this research. One is a simulation for 2D profiles of neutral particles and the other is that for resistive drift wave turbulence. Radial and axial profiles of neutral particles are calculated by the Monte Carlo method with a configuration of linear device PANTA. The ratio for ionization of neutral particles depends on the electron temperature, and the higher temperature in the operation range makes the neutral density smaller near the center of the plasma. Then, the radial profile of the ion-neutral collision frequency is set by introducing these neutral density profiles into resistive drift wave turbulence simulations. Smaller ion-neutral collision frequency makes the instabilities more unstable, and its inhomogeneity enhances mean electrostatic potential formation. The eigenmode structure is changed with the inhomogeneous ion-neutral collision frequency, and convective derivative nonlinearity generates the azimuthal flow near the center of the plasma. Two roles of the neutral particles on the turbulence, the direct change in linear instabilities and formation of background flows, become clear.

Statistical analysis of Hasegawa-Wakatani turbulence

Resistive drift wave turbulence is a multipurpose paradigm that can be used to understand transport at the edge of fusion devices. The Hasegawa-Wakatani model captures the essential physics of drift turbulence while retaining the simplicity needed to gain a qualitative understanding of this process. We provide a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent events in Hasegawa-Wakatani turbulence with enforced equipartition of energy in large scale zonal flows, and small scale drift turbulence. We find that for a wide range of adiabatic index values, the stochastic component representing the small scale turbulent eddies of the flow, obtained from the autoregressive integrated moving average model, exhibits super-diffusive statistics, consistent with intermittent transport. The PDFs of large events (above one standard deviation) are well approximated by the Laplace distribution, while small events often exhibit a Gaussian character. Furthermore, there exists a strong influence of zonal flows, for example, via shearing and then viscous dissipation maintaining a sub-diffusive character of the fluxes.

Almost-periodic solutions to an initial boundary value problem for model equations of resistive drift wave turbulence

In this paper we are concerned with the drift wave turbulence in a strong magnetic field. The existence and the uniqueness of a strong Stepanovalmost- periodic solution to the initial boundary value problems are established both for the model equations of the resistive drift wave turbulence and for the three-dimensional Hasegawa–Wakatani equations when the initial data are Stepanov-almost-periodic in the magnetic field direction.

On the almost-periodic solution of Hasegawa–Wakatani equations

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa–Wakatani equations were proposed in 1983. In this paper, we consider the zero-resistivity limit for the Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov-almost-periodic in the axial direction. We prove two results: one is the existence and uniqueness of a strong global in time Stepanov-almost-periodic solution to the initial boundary value problem for the Hasegawa–Mima-like equation; another is the convergence of the solution of the Hasegawa–Wakatani equations to that of the Hasegawa–Mima-like equation established at the first stage as the resistivity tends to zero. In order to obtain a priori estimates of the Stepanov-almost-periodic solutions to our problems, we have to overcome some difficulties. In the proof, we prepare some lemmas for the Stepanov-almost-periodic functions and then obtain a priori estimates.

Nonlinear competition of turbulent structures and improved confinement in magnetized cylindrical plasmas

Nonlinear competition of turbulent structures and their roles in transport are investigated by using three-dimensional simulation code of resistive drift wave turbulence in magnetized cylindrical plasmas. Selective formation of zonal flows and streamers has been obtained by controlling the strength of damping of the zonal flow. In addition, there is an energy path from the drift waves to a flute type structure, which is linearly stable, and it becomes effective just below the stability boundary of the zonal flow. The flute structure directly induces transport effectively, and affects the drift waves and the zonal flow. A large amplitude zonal flow is formed selectively even with existence of the flute structure. The property of the particle confinement is investigated by changing the particle source intensity, which controls the strength of driving of the drift waves. The characteristic of the particle confinement changes according to turbulent states, and an improved confinement regime is obtained in the zonal flow dominant state. Study on cylindrical plasmas reveals the fundamental mechanism of improved confinement in the magnetized plasma with influence of turbulent structural formation.

Electromagnetic effects on plasma blob-filament transport

Both microscopic and macroscopic impacts of the electromagnetic effects on blob dynamics are considered. Linear stability analysis and nonlinear BOUT++ simulations demonstrate that electromagnetic effects in high temperature or high beta plasmas suppress the resistive drift wave turbulence in the blob when resistivity drops below a certain value. In the course of blob’s motion in the SOL its temperature is reduced, which leads to enhancement of resistive effects, so the blob can switch from electromagnetic to electrostatic regime, where resistive drift wave turbulence become important. It is found that inhomogeneity of magnetic curvature or plasma pressure along the filament length leads to bending of the high-beta blob filaments. This is caused by the increase of the propagation time of plasma current (Alfvén time) in higher-density plasma. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfvén time.

Impact of resonant magnetic perturbations on zonal modes, drift-wave turbulence and the L–H transition threshold

We study the effects of resonant magnetic perturbations (RMPs) on turbulence, flows and confinement in the framework of resistive drift-wave turbulence. This work was motivated, in parts, by experiments reported at the IAEA 2010 conference (Xu et al 2011 Nucl. Fusion 51 062030) which showed a decrease of long-range correlations during the application of RMPs. We derive and apply a zero-dimensional predator–prey model coupling the drift-wave–zonal-mode system (Leconte and Diamond 2012 Phys. Plasmas 19 055903) to the evolution of mean quantities. This model has both density-gradient drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. This model allows a description of the full L–H transition evolution with RMPs, including the mean sheared flow evolution. The key results are the following: (i) the L–I and I–H power thresholds both increase with RMP amplitude , the relative increase of the L–I threshold scales as , where ν* is edge collisionality and ρs is the sound gyroradius. (ii) RMPs are predicted to decrease the hysteresis between the forward and back-transition. (iii) Taking into account the mean density evolution, the density profile—sustained by the particle source—has an increased turbulent diffusion compared with the reference case without RMPs which provides one possible explanation for the density pump-out effect.

Statistical Analyses of Turbulent Particle and Momentum Fluxes in a Cylindrical Magnetized Plasma

A nonlinear simulation of resistive drift wave turbulence in a cylindrical plasma is carried out. Long time evolution of turbulence with formation of a zonal flow is obtained for more than 1000 times of the typical drift wave period, which is sufficient for statistical analyses. Dynamical particle and momentum balance for the formation of the mean reveals that the radial turbulent fluxes are dominant contributors for the evolution of fluctuations. The particle flux is found to precede the momentum flux for 0.4 times of the typical drift wave period with large temporal variance. The analyses of the time series data of 3-D fields give the understanding of the dynamical structural formation mechanism. c

Impact of resonant magnetic perturbations on nonlinearly driven modes in drift-wave turbulence

In this work, we study the effects of resonant magnetic perturbations (RMPs) on turbulence, flows, and confinement in the framework of resistive drift wave turbulence. We extend the Hasegawa-Wakatani model to include RMP fields. The effect of the RMPs is to induce a linear coupling between the zonal electric field and the zonal density gradient, which drives the system to a state of electron radial force balance for large δBrB0. Both the vorticity flux (Reynolds stress) and particle flux are modulated. We derive an extended predator prey model which couples zonal potential and density dynamics to the evolution of turbulence intensity. This model has both turbulence drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. We find states that are similar to the ZF-dominated state of the standard predator-prey model, but for which the power threshold is now a function of the RMP strength. For small RMP amplitude, the energy of zonal flows decreases and the turbulence energy increases with δBrB0, corresponding to a damping of zonal flows.

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.

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.