Nonmodal 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 nonmodal 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 nonmodal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the nonmodal 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 gyromotion 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 »
 Authors:
 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., Email: vladimir@pusan.ac.kr, Mikhailenko, V. S., and Lee, Hae June, Email: haejune@pusan.ac.kr. Nonmodal 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., Email: vladimir@pusan.ac.kr, Mikhailenko, V. S., & Lee, Hae June, Email: haejune@pusan.ac.kr. Nonmodal 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., Email: vladimir@pusan.ac.kr, Mikhailenko, V. S., and Lee, Hae June, Email: haejune@pusan.ac.kr. 2016.
"Nonmodal 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 = {Nonmodal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field},
author = {Mikhailenko, V. V., Email: vladimir@pusan.ac.kr and Mikhailenko, V. S. and Lee, Hae June, Email: 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 nonmodal 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 nonmodal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the nonmodal 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 gyromotion 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 nonmodal 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 socalled nonmodal approach as its foundation, is developed. The developed theory proves that the timedependent 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 nonmodal 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 »

Renormalized theory of ion temperature gradient instability of the magneticfieldaligned plasma shear flow with hot ions
The developed kinetic theory for the stability of a magneticfieldaligned (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 iontemperaturegradient and shearflow (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 » 
Iontemperaturegradient sensitivity of the hydrodynamic instability caused by shear in the magneticfieldaligned plasma flow
The crossmagneticfield (i.e., perpendicular) profile of ion temperature and the perpendicular profile of the magneticfieldaligned (parallel) plasma flow are sometimes inhomogeneous for space and laboratory plasma. Instability caused either by a gradient in the iontemperature 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 densitygradient and iontemperaturegradient scale lengths, and (3) the role of inverse Landau damping is illustrated for the case of combinedmore » 
Electron shearflowdriven instability in magnetized plasmas with magnetic field gradient
It is found that the zeroorder 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.