Finite ion Larmour radius effects in the problem of zonal flow generation by kinetic drift-Alfvén turbulence

Abstract

A theory of spontaneous generation of zonal flows by kinetic drift-Alfvén turbulence in the finite-pressure plasma (β > m e /m i ) is generalized to include the ion diamagnetic effects and the finite ion Larmour radius effects. In the framework of the corresponding set of generalized two-fluid magnetohydrodynamic equations and on the assumption of a distinct time-and space-scale separation between the turbulent oscillations and the zonal flow, a set of coupled equations is derived to describe the interaction between the turbulence and the flow, consisting of the evolution equation for the spectral function of turbulence and the mean-field equations for zonal flow. The possibility of spontaneous zonal flow generation by the kinetic drift-Alfvén turbulence is investigated in details in several cases. In the case of kinetic drift-Alfvén turbulence with the space scale of the order of the ion Larmour radius or below, the instability caused by the resonant interaction of the wave packet with the slow modulations of zonal flow has been analysed, and the criterion for the onset of the zonal flow instability has been derived. In the case of short-wavelength turbulence, two regimes are considered. It is shown, that, when the frequency of short-wavelength oscillations is close to the electrondrift frequency and the zonal perturbation of plasma density can be described by the Boltzmann Law, the instability criterion is a generalization of the previously obtained result to the case of non-equal temperatures of the ions and electrons. The new regime is found, in which the zonal perturbation of plasma density is negligible. The condition for the onset of resonant instability is obtained.

Zonal flows generated by small-scale drift-Alfvén modes

“…An analysis of the role of additional physical effects can be the topic of following studies; see also Ref. 18. …”

“…14 An important contribution to the nonlinear theory of SSDA modes was the investigation of zonal flows generated by them, carried out originally by Smolyakov et al 17 and later continued by Lakhin. 18 The theory presented in Ref. 17 is particularly relevant because it develops the basic mathematical framework to describe the generation of zonal flows in two distinct approaches.…”

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

“…This is the reason that zonal flows driven by drift-type turbulence have been intensively investigated theoretically in recent years. [99][100][101][102][103][104][105][106][107][108][109][110][111][112][113] Another reason for the investigation carried out in the given paper are the results obtained by Kaladze et al 86 In that paper it was shown that in EPI plasma three different types of nonlinear solitary vortical structures on the electrostatic drift waves can appear. ͑1͒ Short-scale vortical structures of dipole type stipulated by the vector nonlinearity only.…”

Convective cell generation by kinetic Alfvén wave turbulence in the auroral ionosphere

“…[25][26][27][28] Such turbulence can also drive lower frequency modes, in particular the zero-frequency CCs. 29,30 To study the interaction between the CCs and the KAW turbulence, it is convenient to use the wave kinetic equation for the generalized KAW action and the hydrodynamic equations for the CCs since their dynamics involve quite different time and space scales. 14,31 References 29 and 30 considered the coupling of CCs with KAW turbulence for intermediate b plasmas, as in the auroral zone at geocentric distances above 5R E , 32 where R E is the Earth's radius.…”