# 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 »

- 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., 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. Wed .
"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 = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}