Resistive Drift Wave 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.

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.

Mitigation of resistive drift wave and ion temperature gradient instabilities by velocity shear

The effects of velocity shear on the resistive drift wave instability in the non-adiabatic limit and the toroidal ion temperature gradient instability are investigated for a plasma of inhomogeneous density/ion temperature, respectively. For the resistive drift wave, we find that the instability growth rate decreases monotonically with increasing magnitude of shear, but we find that complete stabilization is impossible. For the ion temperature gradient instability, we find that the standard WKB approximation is insufficient to describe the full behavior of the instability, and that an analysis of the localized eigenmode problem reveals two separate unstable solutions, which the WKB approximation does not predict. The impact of flow shear on these two new unstable solutions is discussed. In both resistive drift wave and ion temperature gradient instabilities, the sheared flow causes a shifting, tilting, and sharpening of the electrostatic potential eddies.

Nonlinear simulation of resistive drift waves in cylindrical magnetized plasmas in the presence of symmetry breaking particle source

Nonlinear fluid simulation of drift wave turbulence in the presence of symmetry breaking particle source is performed for the cylindrical magnetized plasmas. It is demonstrated that the symmetry breaking of the system directly affects the selection rule of structure formations, the streamers disappear, and the zonal flows are enhanced in the case with the symmetry breaking. The symmetry breaking is introduced in the flux-driven simulation by inducing the particle source whose amplitude depends on the azimuthal angle. The symmetry breaking mode is driven stationarily, and the nonlinear process of the drift waves is significantly modified. By scanning the amplitude of the symmetry breaking source, the structure formation processes are systematically investigated. In addition, the nonlinear forces of the turbulence show the relaxation of the density gradient and the drive of the perpendicular/parallel flows in a two-dimensional manner.

Wave Number Dependence on Ion Mass Number of Resistive Drift Wave Instabilities

Wave Number Dependence on Ion Mass Number of Resistive Drift Wave Instabilities

Numerical turbulence simulations of intermittent fluctuations in the scrape-off layer of magnetized plasmas

Intermittent fluctuations in the boundary of magnetically confined plasmas are investigated by numerical turbulence simulations of a reduced fluid model describing the evolution of the plasma density and electric drift vorticity in the two-dimensional plane perpendicular to the magnetic field. Two different cases are considered: one describing resistive drift waves in the edge region and another including only the interchange instability due to unfavorable magnetic field curvature in the scrape-off layer. Analysis of long data time series obtained by single-point recordings is compared to predictions of a stochastic model describing the plasma fluctuations as a superposition of uncorrelated pulses. For both cases investigated, the radial particle density profile in the scrape-off layer is exponential with a radially constant scale length. The probability density function for the particle density fluctuations in the far scrape-off layer has an exponential tail. Radial motion of blob-like structures leads to large-amplitude bursts with an exponential distribution of peak amplitudes and the waiting times between them. The average burst shape is well described by a two-sided exponential function. The frequency power spectral density of the particle density is simply that of the average burst shape and is the same for all radial positions in the scrape-off layer. The fluctuation statistics obtained from the numerical simulations are in excellent agreement with recent experimental measurements on magnetically confined plasmas. The statistical framework defines a new validation metric for boundary turbulence simulations.

Influence of zonal flow and density on resistive drift wave turbulent transport

The generations of zonal flow (ZF) and density (ZD) and their feedback on the resistive drift wave turbulent transport are investigated within the modified Hasegawa-Wakatani model. With proper normalization, the system is only controlled by an effective adiabatic parameter, α, where the ZF dominates the collisional drift wave (DW) turbulence in the adiabatic limit α>1. By conducting direct numerical simulations, we found that the ZF can significantly reduce the transport by trapping the DWs in the vicinities of its extrema for α>1, whereas the ZD itself has little impact on the turbulence but can only assist ZF to further decrease the transport by flattening the local plasma density gradient.

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.

Neutral impact on anomalous edge plasma transport and its correlation with divertor plasma detachment

The impact of neutrals on anomalous edge plasma transport and zonal flow (ZF) is considered. As an example, it is assumed that edge plasma turbulence is driven by the resistive drift wave (RDW) instability. It is found that the actual effect of neutrals is not related to a suppression of the instability per se, but due to an impact on the ZF. Particularly, it is shown that, whereas the neutrals make very little impact on the linear growth rate of the RDW instability, they can largely reduce the zonal flow generation in the non-linear stage, which results in an enhancement of the overall anomalous plasma transport. Even though only RDW instability is considered, it seems that such an impact of neutrals on anomalous edge plasma transport, i.e. neutrals enhance the transport via the reduction of ZF, has a very generic feature. It is conceivable that such neutral induced enhancement of anomalous plasma transport is observed experimentally in a detached divertor regime, which is accompanied by a strong increase of neutral density.

Different responses of the Rayleigh–Taylor type and resistive drift wave instabilities to the velocity shear

The effects of velocity shear on the unstable modes driven by the effective gravity (Rayleigh–Taylor and interchange) and resistive drift wave instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed for the localized eigenmode problems. It is shown that the effect of the velocity shear drastically depends on the type of instability. Whereas the velocity shear can significantly suppress both Rayleigh–Taylor and interchange instabilities, it has only a weak impact on the growth rate of the resistive drift wave. This is directly related to the physical nature of these instabilities. For the Rayleigh–Taylor and interchange instabilities, the shear flow tilts the eddies of the stream functions, while for the resistive drift wave instability the shear flow simply shifts the eddies in the radial direction with no tilting. However, for a large velocity shear, the eigenmode solutions for resistive drift waves cease to exist.

Influence of flow shear on localized Rayleigh–Taylor and resistive drift wave instabilities

AbstractThe impact of velocity shear on the localized solutions of Rayleigh–Taylor (RT) and resistive drift wave (DW) instabilities has been investigated. Slab geometry is used, and the plasma density gradient is assumed to have a finite spatial structure. It demonstrates that the velocity shear has quite different effects on these instabilities: while it stabilizes RT instability and causes tilting of the eddies of equipotential contour, it has a very mild impact on the resistive DW instability and simply shifts the eddies with no tilting.

Electromagnetic Viscous-Resistive-Drift-Wave Instability in Burning Plasma

Drift wave instabilities (DWI) might be take a part for anomalous transport in modern day tokamaks due to contributions of edge turbulence and zonal flows. Experimentally, it is found that micro-level turbulence (associated with two-fluid dynamics) braced with macro-level (associated with single-fluid dynamics) magnetohydrodynamics-type processes. In this paper, additional two-fluid effect viz. ion viscosity on the electromagnetic (EM) linear resistive drift wave instability is analyzed by using a two-fluid MHD model. A modify dispersion relation for EM drift modes in a nonuniform magnetized plasma is derived, taken into account equilibrium pressure gradients, effect of finite ion-sound gyro-radius associated with electron–ion decoupling and viscous effect due to ions. The dispersion relation is then analyzed both analytically as well as numerically. It is shown, how additional two-fluid effects modify the growth rate for DWI in different regimes. The standard resistive drift-Alfven mode is reproduced in the cold ion case. Moreover, it is estimated that these effects provide the possibility of novel effects on EM instabilities in a nonuniform magnetized plasma. The results should be useful in the interpretation of EM fluctuations in nonuniform magneto-plasmas in which resistivity is a key element in calculations of dissipative drift instabilities.

Two-fluid MHD regime of resistive drift-wave instability

Drift instabilities contribute to the formation of edge turbulence and zonal flows and thus the anomalous transport in tokamaks. Experiments often found micro-scale turbulence strongly coupled with large-scale magnetohydrodynamic (MHD) processes, whereas a general framework has been lacking that can cover both regimes, in particular, their coupling. In this paper, the linear resistive drift wave instability is investigated using a full 2-fluid MHD model, as well as its numerical implementation in the NIMROD code. Both analytical and numerical analyses reveal a macro-scale global drift wave eigenmode coupled with MHD dynamics and illustrate a non-monotonic dispersion relation with respect to both perpendicular and parallel wavenumbers. NIMROD results also reveal an edge-localized behavior in the radial mode structure as the azimuthal mode number increases, implying the dependence of the 2-fluid effects due to the inhomogeneous density profile. The edge-localization introduces a non-trivial dependence of the effective perpendicular wavenumber to the perpendicular mode number, which may explain the quantitative difference between the global dispersion relation and its local approximation from the conventional local theory.

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.

Intrinsic suppression of turbulence in linear plasma devices

Plasma turbulence is the dominant transport mechanism for heat and particles in magnetised plasmas in linear devices and tokamaks, so the study of turbulence is important in limiting and controlling this transport. Linear devices provide an axial magnetic field that serves to confine a plasma in cylindrical geometry as it travels along the magnetic field from the source to the strike point. Due to perpendicular transport, the plasma density and temperature have a roughly Gaussian radial profile with gradients that drive instabilities, such as resistive drift-waves and Kelvin–Helmholtz. If unstable, these instabilities cause perturbations to grow resulting in saturated turbulence, increasing the cross-field transport of heat and particles. When the plasma emerges from the source, there is a time, , that describes the lifetime of the plasma based on parallel velocity and length of the device. As the plasma moves down the device, it also moves azimuthally according to E × B and diamagnetic velocities. There is a balance point in these parallel and perpendicular times that sets the stabilisation threshold. We simulate plasmas with a variety of parallel lengths and magnetic fields to vary the parallel and perpendicular lifetimes, respectively, and find that there is a clear correlation between the saturated RMS density perturbation level and the balance between these lifetimes. The threshold of marginal stability is seen to exist where . This is also associated with the product , where is the drift-wave linear growth rate, indicating that the instability must exist for roughly 100 times the growth time for the instability to enter the nonlinear growth phase. We explore the root of this correlation and the implications for linear device design.

Gravity Wave‐Induced Ionospheric Irregularities in the Postsunset Equatorial Valley Region

AbstractPlasma irregularities in the postsunset equatorial valley region ionosphere are investigated experimentally and through numerical simulation. Coherent radar backscatter observed at the Jicamarca Radio Observatory shows two classes of irregularities in different altitude bands—one mainly below about 125 km and the other mainly above. Irregularities in both bands are organized into wavefronts with wavelengths of a few kilometers. However, only the irregularities in the high‐altitude band exhibit consistent propagation speeds and directions. Some previous observations of irregularities in the nighttime electrojet suggest that gravity waves may sometimes influence their morphology. The possibility that the valley region irregularities are also related to gravity waves (GWs) is therefore investigated numerically. A model of a GW packet propagating through a tidal wind field is used to drive another model which predicts the resulting ionospheric electrodynamics. The combined simulation shows that GWs can induce field‐aligned currents and excite resistive drift waves which could be responsible for the valley region irregularities in the high‐altitude band. The GWs also induce irregularities in the upper E region directly through simple dynamo action which subsequently deform under the influence of shear flow. This may explain the irregularities in the low‐altitude band.

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.