# Stability criteria for current-driven drift wave eigenmodes

## Abstract

Eigenmodes of current-driven collisionless electrostatic drift waves in a sheared magnetic field are re-examined in the light of the recent discovery that their non-current-driven counterparts are stable. Conditions for instability are determined from numerical finite difference and variational solutions of the slab model differential equation. It is found that three stringent conditions are required for instability: (1) very weak shear, (2) low ion temperature, and (3) very large parallel drift velocity. For L/sub n//L/sub s/=0.02 and T/sub i//T/sub e/=0, the instability threshold is u/sub d//c/sub s/=0.85, where L/sub n/ and L/sub s/ are the density and shear scale lengths, respectively, u/sub d/ is the drift velocity, and c/sub s/ is the sound speed. For larger shear and finite ion temperature the critical drift velocity is even larger. It is concluded that drift wave fluctuations in tokamaks cannot be described in terms of these eigenmodes.

- Authors:

- Publication Date:

- Research Org.:
- Fusion Research Center, The University of Texas at Austin, Austin, Texas 78712

- OSTI Identifier:
- 6503739

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Fluids; (United States)

- Additional Journal Information:
- Journal Volume: 22:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PLASMA WAVES; DRIFT INSTABILITY; BOUNDARY CONDITIONS; COLLISIONLESS PLASMA; DIFFERENTIAL EQUATIONS; EIGENFREQUENCY; FINITE DIFFERENCE METHOD; MAGNETIC FIELDS; SHEAR; TOKAMAK DEVICES; VARIATIONAL METHODS; WKB APPROXIMATION; CLOSED PLASMA DEVICES; EQUATIONS; INSTABILITY; ITERATIVE METHODS; NUMERICAL SOLUTION; PLASMA; PLASMA INSTABILITY; PLASMA MICROINSTABILITIES; THERMONUCLEAR DEVICES; 700108* - Fusion Energy- Plasma Research- Wave Phenomena; 700107 - Fusion Energy- Plasma Research- Instabilities

### Citation Formats

```
Ross, D W, and Mahajan, S M.
```*Stability criteria for current-driven drift wave eigenmodes*. United States: N. p., 1979.
Web. doi:10.1063/1.862580.

```
Ross, D W, & Mahajan, S M.
```*Stability criteria for current-driven drift wave eigenmodes*. United States. https://doi.org/10.1063/1.862580

```
Ross, D W, and Mahajan, S M. Thu .
"Stability criteria for current-driven drift wave eigenmodes". United States. https://doi.org/10.1063/1.862580.
```

```
@article{osti_6503739,
```

title = {Stability criteria for current-driven drift wave eigenmodes},

author = {Ross, D W and Mahajan, S M},

abstractNote = {Eigenmodes of current-driven collisionless electrostatic drift waves in a sheared magnetic field are re-examined in the light of the recent discovery that their non-current-driven counterparts are stable. Conditions for instability are determined from numerical finite difference and variational solutions of the slab model differential equation. It is found that three stringent conditions are required for instability: (1) very weak shear, (2) low ion temperature, and (3) very large parallel drift velocity. For L/sub n//L/sub s/=0.02 and T/sub i//T/sub e/=0, the instability threshold is u/sub d//c/sub s/=0.85, where L/sub n/ and L/sub s/ are the density and shear scale lengths, respectively, u/sub d/ is the drift velocity, and c/sub s/ is the sound speed. For larger shear and finite ion temperature the critical drift velocity is even larger. It is concluded that drift wave fluctuations in tokamaks cannot be described in terms of these eigenmodes.},

doi = {10.1063/1.862580},

url = {https://www.osti.gov/biblio/6503739},
journal = {Phys. Fluids; (United States)},

number = ,

volume = 22:2,

place = {United States},

year = {1979},

month = {2}

}