Drift–Alfven turbulence of a parallel shearing flow of the finite beta plasma with warm ions

Abstract

It was predicted [Mikhailenko et al., Phys. Plasmas 23, 020701 (2016)] that two distinct drift–Alfven instabilities may be developed in the parallel shearing flow of finite beta plasmas (1≫β≫me/mi) with comparable ion and electron temperatures. The first one is the shear-flow-modified drift–Alfven instability, which develops due to the inverse electron Landau damping and exists in the shearless plasma as well. The second one is the shear-flow-driven drift–Alfven instability, which develops due to the combined effect of the velocity shear and ion Landau damping and is absent in the shearless plasma flows. In the present paper, these drift–Alfven instabilities are examined numerically and analytically by including the electromagnetic response of the ions. The levels of the drift–Alfven turbulence, resulted from the development of both instabilities, are determined from the renormalized nonlinear dispersion equation, which accounts for the nonlinear effect of ion scattering by the electromagnetic turbulence. The renormalized quasilinear equation for the ion distribution function, which accounts for the same nonlinear effect of ion scattering, is derived and employed for the analysis of the ion viscosity and ions heating resulting from the interactions of ions with drift–Alfven turbulence.

Drift-Alfven instabilities of a finite beta plasma sheared flow along a magnetic field with inhomogeneous ion temperature

“…appeared to be the same as the obtained in Ref. 9 for the electron kinetic shear flow modified DAS instability.…”

“…This estimate is the same as was obtained in Ref. 9 for the perturbed potential in the steady state of the ion kinetic shear flow driven DAS instability of a plasma with homogeneous ion temperature. Note, that the estimate (14) was obtained in Ref.…”

“…Certainly, because γ (k) ∼ ω (k) for this instability the nonlinear analysis of this instability with can't be performed on the base of the weak turbulence approach. Also, the renormalized nonlinear theory 9 , which accounts for the scattering of ions by the DAS turbulence, for which γ (k) ∼ ω (k) also 9 , may give analytically only the approximate estimate for the saturated amplitude of the electric field. The phase randomization of the waves in the wave packet with wave number spectrum width ∆k ⊥ ∼ k ⊥ and the frequency ω (k) occurs at time t ∼ γ −1 (k) when…”

“…Note, that the estimate (14) was obtained in Ref. 9 employing the renormalized nonlinear theory, which accounts for the scattering of ions by the ensemble of DAS waves with random phases. The mixing length estimate may be employed for the estimating the steady state level for the electron kinetic DAS-ITG instability.…”