# Finite. beta. and nonlocal calculation of collisionless and dissipative drift instabilities

## Abstract

Collisionless and dissipative drift waves, driven by gradients in the plasma density and/or temperatures, are believed to dominate or at least influence the transport properties of a variety of plasma confinement devices. In a study begun in reference to transport in the Field Reversed Configuration (FRC), we have developed a theory of these waves in a high {beta} plasma, including the effect of perturbed flow in the direction of the plasma density. This study was a natural extension of previous calculations; the {beta} = 1 nature of the FRC makes a proper treatment of high {beta} effects vital to an understanding of that device. In the course of this study we have obtained a comprehensive dispersion relation which shows clearly how the numerical dissipative drift wave instabilities evolve in wavenumber as {beta} increases. A major finding from this is that the effect of finite {beta} begins to dominate long before {beta} {yields} 1; the expansion parameter is {beta}f(k, a{sub i}, K, {omega}, L{sub n}) where f can be substantially greater than 1, depending on the wavenumber of the wave parallel to the magnetic field (K), the wavenumber parallel to the particle drifts (k), the wave frequency ({omega}), the strength ofmore »

- Authors:

- Publication Date:

- Research Org.:
- Krall Associates, Del Mar, CA (United States)

- Sponsoring Org.:
- USDOE; USDOE, Washington, DC (United States)

- OSTI Identifier:
- 5125639

- Report Number(s):
- DOE/ER/53280-T3; KA-91-08

ON: DE92001928

- DOE Contract Number:
- FG03-88ER53280

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PLASMA WAVES; DRIFT INSTABILITY; REVERSED-FIELD MIRRORS; CHARGED-PARTICLE TRANSPORT; BOLTZMANN-VLASOV EQUATION; COLLISIONLESS PLASMA; HIGH-BETA PLASMA; PLASMA DENSITY; PRESSURE GRADIENTS; PROGRESS REPORT; DIFFERENTIAL EQUATIONS; DOCUMENT TYPES; EQUATIONS; INSTABILITY; MAGNETIC MIRRORS; OPEN PLASMA DEVICES; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA; PLASMA INSTABILITY; PLASMA MICROINSTABILITIES; RADIATION TRANSPORT; THERMONUCLEAR DEVICES; 700107* - Fusion Energy- Plasma Research- Instabilities; 700108 - Fusion Energy- Plasma Research- Wave Phenomena; 700103 - Fusion Energy- Plasma Research- Kinetics

### Citation Formats

```
Krall, N A.
```*Finite. beta. and nonlocal calculation of collisionless and dissipative drift instabilities*. United States: N. p., 1991.
Web. doi:10.2172/5125639.

```
Krall, N A.
```*Finite. beta. and nonlocal calculation of collisionless and dissipative drift instabilities*. United States. https://doi.org/10.2172/5125639

```
Krall, N A. Mon .
"Finite. beta. and nonlocal calculation of collisionless and dissipative drift instabilities". United States. https://doi.org/10.2172/5125639. https://www.osti.gov/servlets/purl/5125639.
```

```
@article{osti_5125639,
```

title = {Finite. beta. and nonlocal calculation of collisionless and dissipative drift instabilities},

author = {Krall, N A},

abstractNote = {Collisionless and dissipative drift waves, driven by gradients in the plasma density and/or temperatures, are believed to dominate or at least influence the transport properties of a variety of plasma confinement devices. In a study begun in reference to transport in the Field Reversed Configuration (FRC), we have developed a theory of these waves in a high {beta} plasma, including the effect of perturbed flow in the direction of the plasma density. This study was a natural extension of previous calculations; the {beta} = 1 nature of the FRC makes a proper treatment of high {beta} effects vital to an understanding of that device. In the course of this study we have obtained a comprehensive dispersion relation which shows clearly how the numerical dissipative drift wave instabilities evolve in wavenumber as {beta} increases. A major finding from this is that the effect of finite {beta} begins to dominate long before {beta} {yields} 1; the expansion parameter is {beta}f(k, a{sub i}, K, {omega}, L{sub n}) where f can be substantially greater than 1, depending on the wavenumber of the wave parallel to the magnetic field (K), the wavenumber parallel to the particle drifts (k), the wave frequency ({omega}), the strength of the density gradient (L{sub n}), and the ion gyroradius (a{sub i}). The fact that finite {beta} effects can onset for quite small {beta} make this study applicable to confinement schemes such as tokamak in which {beta} {approximately} 1--10% in addition to the natural application to the FRC. A second surprising fact from the study was that including finite {beta} could result in a compressional flow in the direction of the density gradient, and also a perturbed electric field in that direction, which changes the perturbed orbits.},

doi = {10.2172/5125639},

url = {https://www.osti.gov/biblio/5125639},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1991},

month = {4}

}