Renormalized non-modal theory of the kinetic drift instability of plasma shear flows

Abstract

The linear and renormalized nonlinear kinetic theory of drift instability of plasma shear flow across the magnetic field, which has the Kelvin's method of shearing modes or so-called non-modal approach as its foundation, is developed. The developed theory proves that the time-dependent effect of the finite ion Larmor radius is the key effect, which is responsible for the suppression of drift turbulence in an inhomogeneous electric field. This effect leads to the non-modal decrease of the frequency and growth rate of the unstable drift perturbations with time. We find that turbulent scattering of the ion gyrophase is the dominant effect, which determines extremely rapid suppression of drift turbulence in shear flow.

Ion-temperature-gradient sensitivity of the hydrodynamic instability caused by shear in the magnetic-field-aligned plasma flow

“…Similar to the case of perpendicular-velocity shear, 24,25 perturbations in the case of parallel-velocity shear experience continuously increasing mode distortion that accumulates with time, causing the otherwise time-independent frequency and wavenumber of the perturbations to exhibit a nonmodal time-dependence in the perpendicular component of the wavenumber. This shearinduced time dependence of the perpendicular wavenumber results in finite-time validity for the time-independent local dispersion equation.…”

“…Beyond the time interval associated with modal-approach validity, the evolving electrostatic potential becomes principally different from the modal one and is determined by the integral equation. 24,25 To estimate the time-dependent effect of the shearing the perturbations by the parallel shear flow, a Fourier transformation of Eq. (4) is performed over the guiding center coordinates, assuming the smallness of the wavelength and of the ion Larmor radius, noted above…”

Anomalous convective transport of the tokamak edge plasma, caused by the inhomogeneous ion cyclotron parametric turbulence

“…This distortion grows with time and forms a time-dependent nonmodal processes, the linear and the renormalized nonlinear stages of which was investigated in Refs. [8][9][10] . It was found [8][9][10] , that this nonmodal process is at the foundation of the experimentally observed effect of the suppression of the drift-type instabilities by the poloidal sheared flow, which have the growth rates less than the poloidal flow velocity shearing rate V ′ 0 .…”

“…[8][9][10] . It was found [8][9][10] , that this nonmodal process is at the foundation of the experimentally observed effect of the suppression of the drift-type instabilities by the poloidal sheared flow, which have the growth rates less than the poloidal flow velocity shearing rate V ′ 0 . Equations ( 70) -( 74) display also principally different effect of the compressed convective flow along Xi .…”

“…Because of the presence of these flows with spatially inhomogeneous flow velocities, which make a dominant contribution to the evolution of inhomogeneous plasma to the equilibrium state, the conventional theory of the stability of the steady plasma cannot be applied to this problem. In this paper, the problem of the origin of the inhomogeneous convective flows and of their temporal evolution is analysed employing the nonmodal approach, which was developed in our theory of the temporal evolution and suppression of the instabilities of a plasma sheared flow across the magnetic fiels 8,9 . This approach employs the solution of the initial value problem instead of the application of the spectral transform in time variable, which is generally employed for the uniform plasmas with steady uniform flows.…”