Resistive Drift Wave Research Articles

Resistive Drift Waves in a Toroidal Heliac

A 4-field model describing collisional drift waves in arbitrary 3-dimensional plasma geometry is derived. Linear growth rates for the perturbed plasma density, electrostatic potential, parallel ion velocity and electron temperature are obtained by solving the 4-field model as an initial-value problem. The local attributes of the confining magnetic field are retained exactly. Numerical solution for toroidal heliac H1-NF is presented. It is shown that the collisional drift wave can be driven unstable and that the spatial structure of the mode is strongly ballooning in character.

Resistive coupling in drift wave turbulence

The Hasegawa - Wakatani (HW) model equations for resistive drift waves are investigated numerically and analytically. Two fundamentally different assumptions about the parallel electron dynamics have been investigated previously, and these are compared analytically and numerically. Analytically, it is found that the large-scale behaviour is different in the two cases. Numerically, it is found that the resulting quasi-two-dimensional turbulence is very sensitive to the assumption made, indicating that three-dimensional simulations are necessary for realistic simulation of the physical processes modelled by the HW system. In addition, a new numerical scheme for the time integration has enabled long-time simulations in the adiabatic regime showing that the total energy and the total generalized enstrophy do not vanish in this limit.

Lyapunov exponents and particle dispersion in drift wave turbulence

The Hasegawa-Wakatani model equations for resistive drift waves are solved numerically for a range of values of the coupling due to the parallel electron motion. The largest Lyapunov exponent, λ1, is calculated to quantify the unpredictability of the turbulent flow and compared to other characteristic inverse time scales of the turbulence such as the linear growth rate and Lagrangian inverse time scales obtained by tracking virtual fluid particles. The results show a correlation between λ1 and the relative dispersion exponent, λp, as well as to the inverse Lagrangian integral time scale τi−1. A decomposition of the flow into two distinct regions with different relative dispersion is recognized as the Weiss decomposition [J. Weiss, Physica D 48, 273 (1991)]. The regions in the turbulent flow which contribute to λ1 are found not to coincide with the regions which contribute most to the relative dispersion of particles.

Analysis of chaos in plasma turbulence

A two-dimensional slab model for resistive drift waves in plasmas consisting of two coupled nonlinear partial differential equations for the density perturbation n and the electrostatic potential perturbation φ is investigated. The drift waves are linearly unstable, and a quasi-stationary turbulent state is reached in a finite time, independent of the initial conditions. Different regimes of the turbulent state can be obtained by varying the coupling parameter \U0001d49e, related to the parallel electron dynamics. The turbulence is described by using particle tracking and tools from chaos analysis. The largest Lyapunov exponent λ1 is calculated for different values of \U0001d49e to quantify the chaoticity and compared with Lagrangian inverse time scales obtained by tracking virtual fluid particles.

Drift Wave Instability and Anomalous Particle Transport in Collisional Plasmas with High-Z Dust Impurities

The resistive drift wave instability is examined in the presence of static charged dust grains. It is found that drift waves can become unstable on account of free energy stored in the equilibrium dust and ion density gradients in collisional dusty plasmas. Nonthermal resistive drift waves can cause anomalous particle transport.

Resistive drift wave and interchange turbulence in a cylindrical plasma with magnetic and velocity shear

By solving numerically the two-field nonlinear model equations for the potential and density fluctuations in the presence of a density gradient, magnetic curvature with shear, and poloidal velocity shear, turbulent spectra and diffusion rates are studied. When the adiabatic parameter (Ωe/νe)(ρs2/R2)/(κρs) is small, a trend of a dual cascade, normal cascade of the density fluctuations, and an inverse cascade of the potential fluctuations, is seen in the wave number spectra, producing a large particle flux proportional to νe1/3. Here R is the major radius, ρs is the ion Larmor radius at the electron temperature, Ωe is the electron cyclotron frequency, νe is the electron ion collision frequency, and κ is an inverse scale length of the background density gradient. Parallel wave numbers are represented by 1/R. For large (Ωe/νe)(ρs2/R2)/(κρs), the electrons become adiabatic, with a significantly reduced particle flux proportional to νe. In the presence of an externally imposed radial electric field with a negative (positive) polarity, Er<0 (Er≳0), the poloidal velocity shear in the E×B drift motion suppresses (enhances) the fluctuation level in the growth phase; however, these effects practically disappear in the saturated state. The radial electric field produced by the inverse cascade due to the convective nonlinearity is also studied; however, its effect on the particle transport is mild.

A Transport Study for Resistive Interchange Mode Turbulence Based on a Renormalized Theory

A new formulation of renormalized theory for fluid-type turbulence to obtain wavenumber spectrum and turbulent diffusivity is presented. An application to the resistive interchange mode turbulence is discussed. The turbulent diffusivity using the reduced MHD equations agrees with evaluations based on the mixing length argument or the scale invariance except a coefficient of about four. An extended model based on finite Larmor radius magnetohydrodynamics (FLR-MHD) including coupling between the resistive drift wave and the resistive interchange mode is analyzed by the renormalized theory. The diffusivity depends on the phase difference and the relative magnitude between the density fluctuation and the potential fluctuation, and role of density gradient becomes more significant than the reduced MHD result. However, the wavenumber spectrum does not change much by the extended model.

Study of resistive drift and resistive interchange modes in a cylindrical plasma with magnetic shear

The resistive drift mode and resistive interchange mode in the presence of magnetic curvature and shear are studied theoretically as well as computationally, based on the electrostatic model equations of isothermal electrons and two-dimensional cold ions in a cylindrical geometry. There are two branches of unstable modes: one has characteristics similar to the resistive drift wave instability with a real frequency ωr of the order of a diamagnetic frequency ω*, and the other is a curvature driven mode (the resistive interchange instability) with ‖ωr‖=‖ωi‖ localized in the neighborhood of the resonant surface. The growth rates of both of these instabilities are proportional to ν1/2ei in the small νei limit, where νei is the electron–ion collision frequency. The resistive interchange instability is dominant even when the curvature drift frequency is a fraction of ω*. Nonlinear evolution of these instabilities with multihelicity modes based on the model equations demonstrates a global spectrum condensation at the m=0 mode, where m denotes the poloidal mode number. The saturated state generates a region of zonal flows in the azimuthal direction. Since particle transport across the constant φ surface vanishes, the zonal flow is expected to improve global confinement.

Scattering of ion-cyclotron alfvén waves by drift waves in a collisional plasma

The temporal modulation of ion-cyclotron Alfvén waves by extremely low-frequency resistive drift waves is considered. It is argued that in a collisional plasma the contribution of the Joule heating nonlinearity would far exceed that of the usual ponderomotive force. An expression for the growth rate of the thermal modulational instability is presented. The relevance of our study to the lower part of the ionosphere is pointed out.

Transport Driven by G Modes and Resistive Drift Waves Based on Scale Invariance

Scale transformation introduced by Connor and Taylor is applied to the model equations for the resistive interchange mode (g mode) and the resistive drift wave in a high shear helical system. The electron pressure gradient term in Ohm's law is essential in deriving the present results. Scaling of collisionless transport along stochastic fields due to the g modes coincides with the result based on the mixing length theory. When the resistive drift waves are dominant, the predicted transport is k 2 / s 2 times the pseudo-classical transport, where k is the characteristic length of density gradient and s is the shear parameter. The transport coefficient which results from the g mode and/or the resistive drift wave turbulence increases towards the edge. The density fluctuation for the resistive drift wave turbulence scales as ( T e / n ) 1/2 k which also increases toward the edge in most toroidal plasmas.

A collisional drift wave description of plasma edge turbulence

Model mode-coupling equations for the resistive drift wave instability are numerically solved for realistic parameters found in tokamak edge plasmas. The Bohm diffusion is found to result if the parallel wavenumber is chosen to maximize the growth rate for a given value of the perpendicular wavenumber. The saturated turbulence energy has a broad frequency spectrum with a large fluctuation level proportional to κ̄ (=ρs/Ln, the normalized inverse scale length of the density gradient) and a wavenumber spectrum of the two-dimensional Kolmogorov–Kraichnan type, ∼k−3.

Identification of Resistive Drift Waves in the Spherator, and their Stabilization by Shear

The observation of resistive drift waves in plasmas produced in the sheared magnetic field of the spherator is reported. The plasmas were produced by electron cyclotron heating, at a density of 1010−1011/cm3 and electron temperatures ≤1 eV. An investigation of oscillation amplitude demonstrates the existence of a stable regime (relative amplitude ≤0.5%) in toroidal fields near the condition of maximum shear (poloidal field and toroidal field approximately equal). For the purpose of further identification of the modes, experiments were carried out in a marginally unstable regime, resulting in nonturbulent single modes. An approximate theory of nonlocal normal modes using an average radial width is derived, and is confirmed by comparison in a special case with a more accurate calculation taking into account the radial dependence. This theory predicts the expected wave parameters for the most unstable modes. The wave parameters of the single modes are measured for the case of argon, and are found to be in excellent agreement with the frequencies and wavelengths predicted for the most unstable modes. Finally, the theory predicts that plasmas of low electron temperature, low ion mass, sharp density gradient, and high density should be the most unstable to resistive drift waves. A series of experiments in which these parameters were varied agrees with these predictions.

Velocity Shear and Low-Frequency Plasma Instabilities

The effects of transverse velocity shear on the low-frequency stability of a plasma are examined theoretically for a low-β resistive plasma in a uniform magnetic field. Cylindrical geometry is used and the velocity shear is introduced by a nonuniform E × B rotation. Both numerical and analytic methods are used. The principal analytic result is a dispersion relation for instabilities caused by a thin velocity shear layer. This dispersion relation describes the Q machine edge oscillation, which is identified either as a Kelvin-Helmholtz instability or as a velocity-shear analog of the resistive drift wave, depending on the parallel wavelength. The numerical results show that properties of instabilities observed in several experiments agree reasonably well with theory. The effect of velocity shear on the drift instability is to make it into either a local or nonlocal type of normal mode.

Effect of Shear on Resistive Drift Waves in the Spherator

Observations of marginally unstable resistive drift waves in a hydrogen plasma immersed in the sheared magnetic field of the Princeton spherator are reported. A theoretical treatment based on the nonlocal normal mode is proposed, which predicts the wave parameters of the most unstable mode, and provides a new stability criterion. The experimental wave parameters and observed stabilization of the resistive drift waves are found to agree well with the predicted values.

Direct Measurement of Drift Wave Growth Rates

Resistive drift waves in a Q machine can be switched on and off by applying a potential to the aperture limiter. The exponential growth of the waves can be directly observed. The measured growth rates are slower than are predicted by the usual theories of collisional drift waves.

Instabilities and Anomalous Diffusion in the Reflex Discharge

The instabilities of a cold-cathode reflex discharge are studied and their relationship to the observed increase in radial transport above a critical magnetic field is discussed. High-frequency beam-plasma instabilities occurring in bursts, owing to a relaxation phenomenon, and low-frequency resistive drift waves are both found, with the latter appearing to have an important role in transport.