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Title: Non-modal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field

Abstract

The temporal evolution of the kinetic ion temperature gradient driven instability and of the related anomalous transport of the ion thermal energy of plasma shear flow across the magnetic field is investigated analytically. This instability develops in a steady plasma due to the inverse ion Landau damping and has the growth rate of the order of the frequency when the ion temperature is equal to or above the electron temperature. The investigation is performed employing the non-modal methodology of the shearing modes which are the waves that have a static spatial structure in the frame of the background flow. The solution of the governing linear integral equation for the perturbed potential displays that the instability experiences the non-modal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the non-modal structure with vanishing frequency and growth rate with time. The obtained solution of the nonlinear integral equation, which accounts for the random scattering of the angle of the ion gyro-motion due to the interaction of ions with ensemble of shearing waves, reveals similar but accelerated process of the transformations of the perturbations into the zero frequency structures. Itmore » was obtained that in the shear flow the anomalous ion thermal conductivity decays with time. It is a strictly non-modal effect, which originates from the temporal evolution of the shearing modes turbulence.« less

Authors:
; ;  [1]
  1. Pusan National University, Busan 609–735 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22598975
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DISTURBANCES; ELECTRON TEMPERATURE; ELECTRONS; INSTABILITY; INTEGRAL EQUATIONS; INTEGRALS; ION TEMPERATURE; IONS; LANDAU DAMPING; MAGNETIC FIELDS; NONLINEAR PROBLEMS; PERTURBATION THEORY; PLASMA; RANDOMNESS; SCATTERING; SHEAR; TEMPERATURE GRADIENTS; THERMAL CONDUCTIVITY; TRANSPORT THEORY; TURBULENCE

Citation Formats

Mikhailenko, V. V., E-mail: vladimir@pusan.ac.kr, Mikhailenko, V. S., and Lee, Hae June, E-mail: haejune@pusan.ac.kr. Non-modal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field. United States: N. p., 2016. Web. doi:10.1063/1.4953567.
Mikhailenko, V. V., E-mail: vladimir@pusan.ac.kr, Mikhailenko, V. S., & Lee, Hae June, E-mail: haejune@pusan.ac.kr. Non-modal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field. United States. doi:10.1063/1.4953567.
Mikhailenko, V. V., E-mail: vladimir@pusan.ac.kr, Mikhailenko, V. S., and Lee, Hae June, E-mail: haejune@pusan.ac.kr. 2016. "Non-modal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field". United States. doi:10.1063/1.4953567.
@article{osti_22598975,
title = {Non-modal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field},
author = {Mikhailenko, V. V., E-mail: vladimir@pusan.ac.kr and Mikhailenko, V. S. and Lee, Hae June, E-mail: haejune@pusan.ac.kr},
abstractNote = {The temporal evolution of the kinetic ion temperature gradient driven instability and of the related anomalous transport of the ion thermal energy of plasma shear flow across the magnetic field is investigated analytically. This instability develops in a steady plasma due to the inverse ion Landau damping and has the growth rate of the order of the frequency when the ion temperature is equal to or above the electron temperature. The investigation is performed employing the non-modal methodology of the shearing modes which are the waves that have a static spatial structure in the frame of the background flow. The solution of the governing linear integral equation for the perturbed potential displays that the instability experiences the non-modal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the non-modal structure with vanishing frequency and growth rate with time. The obtained solution of the nonlinear integral equation, which accounts for the random scattering of the angle of the ion gyro-motion due to the interaction of ions with ensemble of shearing waves, reveals similar but accelerated process of the transformations of the perturbations into the zero frequency structures. It was obtained that in the shear flow the anomalous ion thermal conductivity decays with time. It is a strictly non-modal effect, which originates from the temporal evolution of the shearing modes turbulence.},
doi = {10.1063/1.4953567},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = 2016,
month = 6
}
  • 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 the 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 dominantmore » effect which determines the extremely rapid suppression of drift turbulence in shear flow.« less
  • No abstract prepared.
  • The developed kinetic theory for the stability of a magnetic-field-aligned (parallel) shear flow with inhomogeneous ion temperature [Mikhailenko et al., Phys. Plasmas 21, 072117 (2014)] predicted that a kinetic instability arises from the coupled reinforcing action of the flow velocity shear and ion temperature gradient in the cases where comparable ion and electron temperatures exist. In the present paper, the nonlinear theory was developed for the instability caused by the combined effects of ion-temperature-gradient and shear-flow (ITG–SF). The level of the electrostatic turbulence is determined for the saturation state of the instability on the basis of the nonlinear dispersion equation,more » which accounts for a nonlinear scattering of ions by the developed turbulence in a sheared flow. The renormalized quasilinear equation for the ion distribution function, which accounts for the turbulent scattering of ions by ITG–SF driven turbulence, was derived and employed for the estimation of the turbulent ion viscosity, the anomalous ion thermal conductivity, and anomalous ion heating rate at the saturation state of the instability.« less
  • The cross-magnetic-field (i.e., perpendicular) profile of ion temperature and the perpendicular profile of the magnetic-field-aligned (parallel) plasma flow are sometimes inhomogeneous for space and laboratory plasma. Instability caused either by a gradient in the ion-temperature profile or by shear in the parallel flow has been discussed extensively in the literature. In this paper, (1) hydrodynamic plasma stability is investigated, (2) real and imaginary frequency are quantified over a range of the shear parameter, the normalized wavenumber, and the ratio of density-gradient and ion-temperature-gradient scale lengths, and (3) the role of inverse Landau damping is illustrated for the case of combinedmore » ion-temperature gradient and parallel-flow shear. We find that increasing the ion-temperature gradient reduces the instability threshold for the hydrodynamic parallel-flow shear instability, also known as the parallel Kelvin-Helmholtz instability or the D'Angelo instability. We also find that a kinetic instability arises from the coupled, reinforcing action of both free-energy sources. For the case of comparable electron and ion temperature, we illustrate analytically the transition of the D'Angelo instability to the kinetic instability as (a) the shear parameter, (b) the normalized wavenumber, and (c) the ratio of density-gradient and ion-temperature-gradient scale lengths are varied and we attribute the changes in stability to changes in the amount of inverse ion Landau damping. We show that near a normalized wavenumber k{sub ⊥}ρ{sub i} of order unity (i) the real and imaginary values of frequency become comparable and (ii) the imaginary frequency, i.e., the growth rate, peaks.« less
  • It is found that the zero-order current associated with electron shear flow produces a drift wave in magnetized plasmas, which can become unstable under certain conditions. This wave will be particularly important in low density and low temperature plasmas of heavy ions. As an example, numerical estimates are presented for a barium plasma with parameters compatible with experiments.