Finite Amplitude Drift Waves Research Articles

On fast radial propagation of parametrically excited geodesic acoustic mode

The spatial and temporal evolution of parametrically excited geodesic acoustic mode (GAM) initial pulse is investigated both analytically and numerically. Our results show that the nonlinearly excited GAM propagates at a group velocity which is, typically, much larger than that due to finite ion Larmor radius as predicted by the linear theory. The nonlinear dispersion relation of GAM driven by a finite amplitude drift wave pump is also derived, showing a nonlinear frequency increment of GAM. Further implications of these findings for interpreting experimental observations are also discussed.

Evolution of nonlinearly coupled drift wave-zonal flow system in a nonuniform magnetoplasma

AbstractThe amplitude modulation of a finite amplitude drift wave by zonal flows in a non-uniform magnetoplasma is considered. The evolution of a nonlinearly coupled drift wave-zonal flow (DW-ZF) system is governed by a nonlinear equation for the slowly varying envelope of the drift waves, which drives (via the Reynolds stress of the drift wave envelope) the second equation for zonal flows. The nonlinear dispersion relation for the modulational instability of a drift wave pump is derived and analyzed. In a special case, the DW-ZF system of equations reduces to the cubic nonlinear Schrödinger equation, which admits localized solutions in the form of DW envelope solitons, accompanied by a shock-like ZF structure. Numerical solutions of the nonlinearly coupled DW-ZF systems reveal that an arbitrary spatial distribution of the DW rapidly decays into an array of localized drift wave structures, propagating with different speeds, that are robust and, in many respect, behave as solitons. The corresponding ZF evolves into the sequence of shocks that produces a strong shearing, i.e. multiple plasma flows in alternating directions.

Generation of zonal flows by electrostatic drift waves in electron-positron-ion plasmas

Generation of large-scale zonal flows by comparatively small-scale electrostatic drift waves in electron-positron-ion plasmas is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves having arbitrary wavelengths (as compared with the ion Larmor radius of plasma ions at the plasma electron temperature). Temperature inhomogeneity of electrons and positrons is taken into account assuming ions to be cold. To describe the generation of zonal flow generalized Hasegawa–Mima equation containing both vector and two scalar (of different nature) nonlinearities is used. A set of coupled equations describing the nonlinear interaction of drift waves and zonal flows is deduced. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. Enriched possibilities of zonal flow generation with different growth rates are revealed. The present theory can be used for interpretations of drift wave observations in laboratory and astrophysical plasmas.

Drift wave driven zonal flows in electron–positron–ion plasmas

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron–positron–ion (EPI) plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process, the Hasegawa–Mima equation generalized for the case of EPI plasma is used. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. Dependence of the growth rate on the spectrum purity of the wave packet is also investigated. The relevant instability conditions are determined.

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.

Drift wave driven zonal flows in plasmas

The generation of large-scale zonal flows by small-scale electrostatic drift waves in a plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process a generalized Hasegawa–Mima equation containing both vector and scalar nonlinearities is used. The drift waves are supposed to have arbitrary wavelengths (as compared with the ion Larmor radius). A set of coupled equations describing the nonlinear interaction of drift waves and zonal flows is deduced. The generation of zonal flows turns out to be due to Reynolds stresses produced by finite amplitude drift waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the drift pump wave. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with previous results is carried out. The present theory can be used for interpretations of drift wave observations in laboratory plasmas.

Vortices in an anisotropic plasma

Localized electrostatic nonlinear drift wave structures in a plasma with hot electrons and anisotropic ions are considered. The anisotropic energy distribution leads to a new nonlinearity in the evolution equation of finite amplitude drift waves. One- and two-dimensional solutions of physical interest are presented.

Dynamics of nonlinear drift waves in an inhomogeneous magnetic field

Accounting for an inhomogeneous magnetic field and finite Larmor radius effects, a set of nonlinear mode coupling equations is derived for finite amplitude drift waves in plasmas. It is shown that the present nonlinear equations admit localized dipole vortices. Conditions for the existence of these vortices are given.

Enhanced magnetostatic modes in a nonuniform plasma

Parametric excitation of the magnetostatic mode by finite-amplitude drift waves is considered. Both decay and modulational instabilities are analyzed. Expressions for the growth rates are obtained analytically. Application of our results to electron cross-field diffusion in tokamak devices is also discussed.

Nonlinear development of drift waves

This note presents a model equation which describes nonlinear evolution of finite amplitude drift waves in a non-uniform plasma. Significant nonlinearities originate from the ion polarization drift and the electron temperature gradient. Modulational instability and possible final state of unstable drift waves are investigated.

Pseudo-classical transport I: The particle and energy flux

The transport of particles and energy that accompanies the trapping of electrons by a finite amplitude drift wave is calculated. Starting from the drift kinetic equation, it is shown that, in the limit of small collision frequency, the electron entropy source is stationary with respect to variations in the electron distribution function. This variational principal is employed, together with the full Fokker–Planck collision operators, to evaluate the electron transport coefficients and, hence, the flux of particles and energy across the magnetic field. Explicit expressions for the particle and energy flux are obtained in terms of the parameters of the plasma-wave system. These expressions should be used in place of the usual quasi-linear expressions for the particle and energy flux when the autocorrelation time of the wave spectrum is sufficient to permit the trapping of electrons by individual waves. These pseudo-classical transport rates are found to be smaller than the quasi-linear expressions that they replace.

Pseudo-classical transport II: A nonlinear theory of the ’’collisionless’’ drift instability

A self-consistent theory of the evolution of a plasma slab supporting a finite amplitude drift wave that has trapped the resonant electrons is presented. Previous work is extended to include the effect of particle trapping on the evolution of the finite amplitude wave. The connection between this theory and other works, using quasi-linear theory, on the anomalous transport associated with low frequency drift waves is considered. It is shown that, for parameters typical of tokamak plasmas, particle trapping may result in the nonlinear stabilization of the wave at amplitudes, (eΦ0/T) ≃10−2, that are of the same order as those observed in experiments. The application of this work to experiments is discussed, and it is found to be potentially useful in understanding the drift wave spectrum and transport rates observed in computer simulations, stellarators, and future tokamak experiments.

Finite amplitude drift waves in a collisional plasma

By using a reductive perturbation method, a multi-dimensional modified Korteweg-de Vries equation has been derived to describe the propagation of a finite amplitude drift wave in a collisional plasma. When the viscous damping dominates the resistive growth, this equation allows a stationary shock solution. The profile of the shock wave tends to change from an oscillatory one to a monotonic one as the angle between the direction of propagation and the magnetic field increases. On the other hand, a stationary solution does not exist if the resistive growth is dominant over the viscous damping.

Plasma convection in toroidal system under weakly supercritical conditions

The laminar convection of plasma which develops through a dissipative instability of localized drift waves is investigated. A non-linear equation is derived which describes the localized finite amplitude drift waves. A stationary solution of this equation is found which corresponds to the case of small supercriticality. The plasma flux across the magnetic field is calculated and an expression for the laminar diffusion coefficient is found.