The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background density gradients. In this regime we report on corrections by factors of order one to the eigenvalue analysis of former OB approximated approaches as well as on spatially localised eigenfunctions, that contrast strongly with their OB approximated equivalent. Remarkably, non-modal phenomena arise for large density inhomogeneities and for all collisionalities. As a result, we find initial decay and non-modal growth of the free energy and radially localised and sheared growth patterns. The latter non-modal effect sustains even in the nonlinear regime in the form of radially localised turbulence or zonal flow amplitudes.
We investigate the low-frequency wave mode associated with heavy particles and its instability in a collisional complex plasma with drifting ions. The effect of the ion drift on the sound velocity of this mode is discussed. The general condition of the instability is derived for subthermal ion drifts, taking into account strong coupling of the particle component. As a general tendency, strong coupling effects reduce the sound velocity and facilitate the occurrence of the ion drift instability. A wide parameter range is considered from the weakly collisional to strongly collisional regimes for …
Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum and pressures in drift-fluid turbulence models and thereby obviate the customary use of artificial diffusion in turbulence simulati…
The low-frequency instability of a cylindrical poorly magnetized plasma with an inward-directed radial electric field is studied changing the gas pressure and the ion cyclotron frequency. The unstable frequency always decreases when the gas pressure is increased indicating collisional effects. At a fixed pressure, the unstable frequency increases with the magnetic field when the B-field is low and decreases at larger magnetic field strength. We find that the transition between these two regimes is obtained when the ion cyclotron frequency equals the ion-neutrals collision frequency. This is in…
The collisional drift wave instability is reexamined taking into account the ion response in the direction parallel to the magnetic field lines, which appears due to friction with electrons and which can not be omitted in view of the momentum conservation. A modified instability threshold is obtained. In plasmas with dominant electron collisions with neutrals, the instability threshold is shifted towards higher frequencies, compared to the case of dominant electron collisions with ions. The difference between the two cases vanishes when the ion sound response is negligible, i.e., when the inst…
A semiclassical 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 perturbati…
A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis, to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations…
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
We present turbulent properties of electrostatic drift waves in a nonuniform collisional plasma composed of magnetised electrons and ions in the presence of immobile dust particles. For this purpose, we derive a pair of nonlinear quasi-two-dimensional equations exhibiting the coupling between the generalized ion vorticity and density fluctuations associated with collisional drift waves. The effect of a dust density gradient on the initial drift instability and fully developed turbulence is examined numerically.
The ion drag force arising from plasma flow past an embedded spherical grain is calculated self-consistently and non-linearly using particle in cell codes, accounting for ion-neutral collisions. Using ion velocity distribution appropriate for ion drift driven by a force field gives wake potential and force greatly different from a shifted Maxwellian distribution, regardless of collisionality. The low-collisionality forces are shown to be consistent with estimates based upon cross-sections for scattering in a Yukawa (shielded) grain field, but only if non-linear shielding length is used. Finite…
The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift…
The collisional dynamics of test impurity ions in spherical tokamak plasmas with strongly-sheared radial electric fields is investigated by means of a test particle full orbit simulation code. The strength of the shear is such that the standard drift ordering can no longer be assumed and a full orbit approach is required. The effect of radial electric field shear on neoclassical particle transport is quantified for a range of test particle mass and charge numbers and electric field parameters. It is shown that the effect of a sheared electric field is to enhance the confinement of impurity spe…
A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG) instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.
Toroidal drift waves with unconventional mode structures and non-ground eigenstates, which differ from typical ballooning structure mode, are found to be important recently by large scale global gyrokinetic simulations and especially become dominant at strong gradient edge plasmas [cf., Xie and Xiao, Phys. Plasmas, 22, 090703 (2015)]. The global stability and mode structures of drift wave in this steep edge density and temperature gradients are examined by both direct numerical solutions of a model two-dimensional eigen equation and analytical theory employing WKB-ballooning approach. Theory a…
Experimental observation of drift acoustic cnoidal waves in a magnetized plasma
Institute for Plasma Research, HBNI（等离子体研究所，HBNI）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Columbia Astrophysics Laboratory, Columbia University（哥伦比亚大学天体物理实验室，哥伦比亚大学）
In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice. For sufficiently low collision frequencies (below the values that define the $1/ν$ regime), the components of the drifts tangential to the flux surface become relevan…
We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated …
In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-ExB-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly o…
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas the heavy species are modeled within a fluid description. Validity of the popular drift-diffusion approximation is verified against a "full" fluid model accounting for the ion inertia and a fully kinetic PIC/MCC code for ions as well as electrons. The fluid models require knowledge of the momentum exchange frequency and dependence of the ion mobilities on the…
Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the po…
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant NTV regimes including superbanana plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbation…
The Buneman instability occurring when an electron population is drifting with respect to the ions is analyzed in the quantum linear and nonlinear regimes. The one-dimensional low-frequency and collisional model of Shokri and Niknam [Phys. Plasmas, v. 12, p. 062110 (2005)] is revisited introducing the Bohm potential term in the momentum equation. The linear regime is investigated analytically, and quantum effects result in a reduction of the instability. The nonlinear regime is then assessed both numerically and analytically, and pure quantum density oscillations are found to appear during the…
Perpendicular electron dynamics and the associated collisions are discussed in relation to the collisional drift wave instability. In addition, the limit of small parallel wave numbers of this instability is studied and it is shown to yield a reduced wave frequency. It is also shown that in this case the growth rate in fact {\em decreases} for smaller parallel wave numbers, instead of growing proportional to $1/k_z^2$. As a result, the growth rate appears to be angle dependent and to reach a maximum for some specific direction of propagation. The explanation for this strange behavior is given.…
BOUT++ turbulence simulations are conducted to capture the underlying physics of the small ELM characteristics achieved by increasing separatrix density via controlling strike points from vertical to horizontal divertor plates for three EAST discharges. BOUT ++ linear simulations show that the most unstable modes change from high-n ideal ballooning modes to the intermediate-n peeling-ballooning modes and eventually to peeling-ballooning stable plasmas in the pedestal. Nonlinear simulations show that the fluctuation is saturated at a high level for the lowest separatrix density. The elm size de…
This study traces the emergence of sheared axial flow from collisional drift wave turbulence with broken symmetry in a linear plasma device---CSDX. As the density profile steepens, the axial Reynolds stress develops and drives a radially sheared axial flow that is parallel to the magnetic field. Results show that the non-diffusive piece of the Reynolds stress is driven by the density gradient and results from the spectral asymmetry of the turbulence and thus is dynamical in origin. Taken together, these findings constitute the first simultaneous demonstration of the causal link between the den…
Studies have shown that in sheared $\mathbf{E}\times\mathbf{B}$ flows in an inhomogeneous ionospheric plasma, the gradient drift (GDI) or the Kelvin-Helmholtz (KHI) instability may grow. This work examines the conditions that cause one of these instabilities to dominate over the other using a novel model to study localized ionospheric instabilities. The effect of collisions with neutral particles plays an important role in the instability development. It is found that the KHI is dominant in low collisionality regimes, the GDI is dominant in high collisionality regimes, and there exists an inte…
We propose a new reduced fluid model for the study of the drift wave -- zonal flow dynamics in magnetically confined plasmas. Our model can be viewed as an extension of the classic Hasegawa-Wakatani (HW) model, and is based on an improved treatment of the electron dynamics parallel to the field lines, to guarantee a balanced electron flux on the magnetic surfaces. Our flux-balanced HW (bHW) model contains the same drift-wave instability as previous HW models, but unlike these models, it converges exactly to the modified Hasegawa-Mima model in the collisionless limit. We rely on direct numerica…
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 dyn…
Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conv…
The drift wave in the presence of impurity ions was investigated numerically in reversed field pinch (RFP) plasmas, using the gyrokinetic integral eigenmode equation. It was found that in RFP plasmas with hollow density profiles, an increase in $k_θρ_s$ increases the growth rate of the ion temperature gradient (ITG). Comparing the results of regular and hollow plasma density profile shows that the ITG mode under the hollow density profile is much harder to be excited. For the impurities' effects, when the impurities' density gradient is opposite to the primary ions, namely when $L_{ez}$ is neg…
Stronger impurity density in-out poloidal asymmetries than predicted by the most comprehensive neoclassical models have been measured in several tokamaks around the world during the last decade, calling into question the reduction of turbulence by sheared radial electric fields in H-mode tokamak pedestals. However, these pioneering theories neglect the impurity diamagnetic drift, or fail to retain it self-consistently; while recent measurements indicate that it can be of the same order as the ExB drift. We have developed the first self-consistent theoretical model retaining the impurity diamag…
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 [Y. Xu {\it et al}, Nucl. Fusion \textbf{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 [M. Leconte and P.H. Diamond, Phys. Plasmas \textbf{19}, 055903] to the evolution of mean quantities. This model has both …
Two-fluid, three-dimensional, flux-driven, global, electromagnetic turbulence simulations carried out by using the GBS code are used to identify the main parameters controlling turbulent transport in the tokamak boundary and to delineate an electromagnetic phase space of edge turbulence. Four turbulent transport regimes are identified: (i) a regime of fully developed turbulence appearing at intermediate values of collisionality and $β$, with turbulence driven by resistive ballooning modes, related to the L-mode operation of tokamaks, (ii) a regime of reduced turbulent transport at low collisio…
Detailed measurements of intrinsic axial flow generation parallel to the magnetic field in the controlled shear decorrelation experiment linear plasma device with no axial momentum input are presented and compared to theory. The results show a causal link from the density gradient to drift-wave turbulence with broken spectral symmetry and development of the axial mean parallel flow. As the density gradient steepens, the axial and azimuthal Reynolds stresses increase and radially sheared azimuthal and axial mean flows develop. A turbulent axial momentum balance analysis shows that the axial Rey…
One special interest for the industrial development of Hall thruster is characterizing the anomalous cross-field electron transport observed after the channel exit. Since the ionization efficiency is more than 90%, the neutral atom density in that domain is so low that the electron collisions cannot explain the high electron flux observed experimentally. Indeed this is 100 times higher than the collisional transport. In Hall thruster geometry, as ions are not magnetized the electric and magnetic field configuration creates a huge difference in drift velocity between electrons and ions, which g…
The local intrinsic parallel current density driven by electron drift wave (DW) turbulence including electromagnetic (EM) effects is analytically studied. The scalings of the ratios of intrinsic current density driven by residual turbulent flux and by turbulent source to the bootstrap current density with electron density and temperature are predicted to be $T_e^{3/4}T_i/n_e$ and $T_eT_i/n_e$, respectively. Based on the typical parameters in DIII-D pedestal region, the local intrinsic current density driven by both the residual turbulent flux and the turbulent source is negligible. However, de…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the drift-diffusion approximation for electrons and ions coupled to Poisson equation for electric field. In addition, the electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperatu…
Simulations are performed to investigate turbulent properties of nonlinearly interacting two-dimensional (2D) magnetic electron drift vortex (MEDV) modes in a nonuniform unmagnetized plasma. The relevant nonlinear equations governing the dynamics of the MEDV modes are the wave magnetic field and electron temperature perturbations in the presence of the equilibrium density and temperature gradients. The important nonlinearities come from the advection of the electron fluid velocity perturbation and the electron temperature, as well as from the nonlinear electron Lorentz force. Computer simulati…
It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outwards. A class…
We investigate the electron-hole two-stream instability (or Coulomb drag) in intrinsic bilayer graphene in the hydrodynamic regime, accounting for the effects of temperature, initial drift velocity, magnetic field, and collisions. The threshold drift speed for the onset of instabilities is of the order of the thermal velocity of the carriers. We put in evidence an unprecedented purely electrostatic mechanism leading to current relaxation, giving rise to a well-defined dc longitudinal conductivity $\propto T^{3/2}$. Due to competition between electrostatic and collisional processes, two distinc…
