Excitation Of Zonal Flows Research Articles

Improved model of quasi-particle turbulence (with applications to Alfvén and drift wave turbulence)

We consider the classical problem of wave stability and dispersion in a turbulent plasma background. We adopt a kinetic description for the quasi-particle turbulence. We describe an improved theoretical approach, which goes beyond the geometric optics approximation and retains the recoil effects associated with the emission and absorption of low frequency waves by nearly resonant quasi-particles. We illustrate the present approach by considering two particular examples. One is the excitation of zonal flows by drift wave turbulence or driftons. The other is the coupling between ion acoustic waves and Alfvén wave turbulence, eventually leading to saturation of Alfvén wave growth. Both examples are relevant to anomalous transport in magnetic fusion devices. Connection with previous results is established. We show that these results are recovered in the geometric optics approximation.

Nonlinear excitation of zonal flows and streamers in plasmas

Nonlinear excitation of zonal flows and streamers in plasmas is considered. The emphasis is given to the nonlinear interaction of low- and high-frequency drift waves which can result in the excitation of zonal flows and streamers in a plasma of fusion devices. For this purpose, an inhomogeneous nonisothermal plasma in a strong external magnetic field whose characteristic frequencies are lower than the ion Langmuir frequency but higher than the collision frequency is studied. The excitation of a long-wavelength low-frequency drift wave during the development of the nonlinear modulational interaction of a high-frequency drift pump wave is investigated. The growth rates of the modulational instability are obtained, and the conditions for its development are determined. Self-organized structures described by solutions of evolutionary equations for the modulational interaction are associated with zonal flows and streamers. A possible relation of the modulational interaction in Earth’s ionospheric plasma to the formation of dust flows and transport of dust particles in the ionosphere is also discussed. It is shown that one of the ways of transport of dust particles in the ionosphere is vertical flows (streamers), which are generated by dust vortices as a result of development of the modulational instability.

Study of the Effect of the Helical Ripple Transport on the Confinement via Zonal Flows in Helical Plasmas

The role of the effective helical ripple in the helical plasma confinement is analyzed using the transport code via the effect of zonal flows. One-dimensional coupled transport equations are calculated in the different cases of the effective helical ripple. The reduction of the effective helical ripple ratio lowers the criterion for the excitation of zonal flows in helical plasmas. It is demonstrated that the reduction of the turbulent transport can be obtained in the case of the smaller neoclassical transport when zonal flows are excited.

Transient excitation of zonal flows by geodesic acoustic modes

Zonal flows (ZFs) are excited transiently by geodesic acoustic modes (GAMs) in toroidal plasmas. When GAMs have radially inward and outward propagating components, these components interact to excite the zero frequency modes (ZFs) transiently, in addition to exciting higher harmonics of GAM. A fluid model is used to study this transient excitation. The Reynolds stress is evaluated from the action conservation equation, and a set of equations to analyze nonlinear couplings among GAMs and ZFs is derived. GAMs are driven by the drift wave (DW) turbulence, and ZFs are transiently driven by nonlinear self-interaction of GAMs. The dependences of the peak amplitudes of ZFs on coupling coefficients are explained theoretically. A new energy path from the DW turbulence to ZFs is found under a situation in which there is only energy transfer from the DW turbulence to GAMs.

Nonlinear excitation of zonal flows by Rossby wave turbulence

We apply the wave-kinetic approach to study nonlinearly coupled Rossby wave-zonal flow fluid turbulence in a two-dimensional rotating fluid. Specifically, we consider for the first time nonlinear excitations of zonal flows by a broad spectrum of Rossby wave turbulence. Short-wavelength Rossby waves are described here as a fluid of quasi-particles, and are referred to as the ‘Rossbyons’. It is shown that Reynolds stresses of Rossbyons can generate large-scale zonal flows. The result should be useful in understanding the origin of large-scale planetary and near-Earth atmospheric circulations. It also provides an example of a turbulent wave background driving a coherent structure.

Influence of the mean flow on zonal flow generation

Excitation of zonal flow by the modulational instability in the presence of mean shear flow is considered. The presence of the mean flow without large amplitude increases the modulational instability growth rate and favors zonal flow generation, whereas sufficiently strong mean shear significantly reduces the instability growth rate.

Simulation of zonal flow excitation by drift mode turbulence: applications to tokamaks and the magnetopause

Recently, we investigated the interaction between broadband drift mode turbulence and zonal flows near the edge of a region of magnetized plasma (Trines et al 2005 Phys. Rev. Lett. 94 165002). Our simulation results showed the development of a zonal flow through the modulational instability of the drift wave distribution, as well as the existence of solitary zonal flow structures about an ion gyroradius wide, drifting towards steeper relative density gradients. Both the growth rate of the turbulence and the particle/energy transport across the plasma boundary can be stabilized by adjusting the plasma density gradient. This spontaneous formation of solitary wave structures has also been found in Cluster satellite observations (Trines et al 2007 Phys. Rev. Lett. 99 205006), confirming our earlier theoretical predictions. We will discuss the consequences of our results for our understanding of the Earth's magnetopause, as well as for the study of zonal flows in tokamaks.

Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

Progress on anomalous transport in tokamaks, drift waves and nonlinear structures

Fluid and kinetic theory of drift wave turbulence and zonal flows are compared. The result from particle in cell codes that transport is reduced and zonal flows become stronger when the parallel nonlinearity is included is interpreted in terms of removing dissipative kinetic resonances from a fluid model. Also a kinetic derivation is given of the excitation of zonal flows and recent results on momentum transport are discussed. The recent results on particle pinches in fluid and kinetic codes are also interpreted in a similar way. General aspects of different fluid closures are discussed.

Bifurcation theory of the transition to collisionless ion-temperature-gradient-driven plasma turbulence

The collisionless limit of the transition to ion-temperature-gradient-driven plasma turbulence is considered with a dynamical-systems approach. The importance of systematic analysis for understanding the differences in the bifurcations and dynamics of linearly damped and undamped systems is emphasized. A model with ten degrees of freedom is studied as a concrete example. A four-dimensional center manifold (CM) is analyzed, and fixed points of its dynamics are identified and used to predict a “Dimits shift” of the threshold for turbulence due to the excitation of zonal flows. The exact value of that shift in terms of physical parameters is established for the model; the effects of higher-order truncations on the dynamics are noted. Multiple-scale analysis of the CM equations is used to discuss possible effects of modulational instability on scenarios for the transition to turbulence in both collisional and collisionless cases.

Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach

The transition to collisionless ion-temperature-gradient-driven plasma turbulence is considered by applying dynamical systems theory to a model with 10 degrees of freedom. The study of a four-dimensional center manifold predicts a "Dimits shift" of the threshold for turbulence due to the excitation of zonal flows and establishes (for the model) the exact value of that shift.

Excitation of zonal flows by kinetic Alfvén waves

Nonlinear couplings between dispersive kinetic Alfvén waves (DKAWs) and electrostatic convective cells∕zonal flows are reexamined. A set of equations that exhibit nonlinear couplings between the scalar and parallel vector potentials of the DKAWs and the scalar potential of zonal flows that are reinforced by the Reynolds stresses of the DKAWs in a magnetized plasma is presented. The equations are then Fourier-analyzed to obtain the nonlinear dispersion relation. The latter exhibits modulational instabilities, which could be responsible for enhanced zonal flows in a uniform magnetized plasma. Zonal flows can regulate the transport of plasma particles in laboratory magnetoplasmas as well as in the Earth’s magnetosphere and in the solar corona.

Self-consistent theory of zonal flows in ion temperature gradient turbulence

A self-consistent theory of nonlinear zonal flows amidst complex background of ion temperature gradient (ITG) turbulence is presented. Starting with a reactive fluid model, a set of coupled nonlinear equations has been obtained in the form of Zakharov-like equations using the reductive perturbation method. These equations represent dynamical evolution of nonlinearly excited zonal flows and potential fluctuations of ITG turbulence. The derived equations have the potential to provide a qualitative explanation of the evolution of zonal flows and drift wave turbulence and their mutual interaction, which have been observed in recent gyrokinetic simulations [A. Dimits et al., Phys. Plasmas 7, 969 (2000)]. The nonlinear coupling coefficients are studied and show that the excitation of zonal flows is due to a resonance in the energy nonlinearity. The resonance turns out to be sensitive to fluid closure.

Generation of zonal flows by Rossby waves in the atmosphere

Abstract. A novel mechanism for the short-scale Rossby waves interacting with long-scale zonal flows in the Earth's atmosphere is studied. The model is based on the parametric excitation of convective cells by finite amplitude Rossby waves. We use a set of coupled equations describing the nonlinear interaction of Rossby waves and zonal flows which admits the excitation of zonal flows. The generation of such flows is due to the Reynolds stresses of the finite amplitude Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the pump Rossby wave. We calculate the maximum instability growth rate and deduce the optimal spatial dimensions of the zonal flows as well as their azimuthal propagation speed. A comparison with previous results is made. The present theory can be used for the interpretation of existing observations of Rossby type waves in the Earth's atmosphere.

Zonal flow excitation in plasmas by electron-temperature-gradient modes

The nonlinear coupling between short-wavelength electron-temperature-gradient (ETG) modes and zonal flows in plasmas is considered. The mode-coupling equations are derived by using a Boltzmann ion distribution and a fluid electron response described by the hydrodynamic and energy equations. A dispersion relation for the nonlinearly coupled ETG modes and the zonal flows is derived. The results show enhanced zonal flows, which can affect the electron energy transport in tokamaks and stellarators.

Dynamics of zonal flow based on resistive interchange mode turbulence

Dynamics of zonal flow excitation in tokamak plasmas is investigated based on th e re sistive interchange mode turbulence. Employing lowfreedom approach, the resist i ve interchange mode turbulencezonal flow system is solved both analytically an d numerically. Our results show that the largescale zonal flow or oscillating z o nal flow can be excited in the case of sufficiently high pressure gradient (driv ing force).

Generation of zonal flows in nonuniform rotating astrophysical fluids

The generation of large scale zonal flows by flute-like wave modes in nonuniform rotating self-gravitating fluids is considered. In the geostrophic approximation, viz. when the mode frequencies are much smaller than the Coriolis frequency, the coupled mode equations are obtained by using the continuity, momentum and Poisson equations. The equations are then Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the parametric excitation of zonal flows by the nonlinear force of the flute-like wave modes. Nonlinearly excited zonal flows undergo further cascading and constitute a new turbulent state. They also contribute to the formation of large scale structures in astrophysical fluids.

Parametric Excitation of Zonal Flows by Ion Temperature Gradient Modes

Previous theory of zonal flow generation by incoherent toroidal ion-temperature-gradient (ITG) modes is complemented by a theory for coherent ITG modes including all possible vector nonlinearities. A new dispersion relation for nonlinearly coupled ITG and zonal flows is presented.

Generation of zonal flows by Rossby waves

It is shown that large scale zonal flows in a rotating fluid can be excited due to the Reynolds stresses of short scale Rossby waves. By employing the equations for a shallow rotating fluid in the geostrophic approximation, we obtain a Charney equation for nonlinearly coupled Rossby waves and zonal flows. The equation is then decomposed into two equations; one for short scale (comparable to the Rossby radius) Rossby waves in the presence of zonal flows, and another for zonal flows which are driven by the Reynolds stresses of the Rossby waves. Our pair of equations is then Fourier transformed to obtain a nonlinear dispersion relation, which admits the excitation of zonal flows due to the Rossby pumping energy. The present investigation thus provides a nonlinear mechanism for the energy transfer from short scale Rossby waves to large scale zonal flows.

Generation of zonal flows by interchange modes in a plasma

The generation of zonal flows by flute-like interchange modes in a nonuniform magnetoplasma is considered. The guiding center particle drifts are then used to derive a system of coupled mode equations. The latter are Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the excitation of zonal flows by the ponderomotive force of the interchange modes. The growth rate of the parametrically driven zonal flows is obtained.