# Stability analysis of dynamic Z pinches and theta pinches

## Abstract

The stability of diffuse, dynamic Z pinches and theta pinches is analyzed. Spectra of the growth rates of hydromagnetic instabilities of dynamic pinches are calculated. The acceleration of plasma pinches during compression and expansion strongly modifies the growth of bulk instabilities. Also, even a relatively weak axial magnetic field substantially suppresses instabilities in Z pinches, in agreement with recent experiments. The initial axial field B/sub z//sub //sub 0/ needed for a stable implosion of a pinch of initial radius R/sub 0/ and average current I-bar is B/sub z//sub //sub 0/ approx. >(10--30 kG) I-bar (MA)/R/sub 0/(cm). The approximate analytic solutions of the linearized equations are shown to agree well with the exact numerical solutions. The stability analysis demonstrated here for dynamic pinches is broadly applicable to the stability of dynamic plasmas in general.

- Authors:

- Publication Date:

- Research Org.:
- Institute for Physical Problems, ul. Kosygina, 2, Moscow 117334, USSR

- OSTI Identifier:
- 6526772

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 1:3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; INSTABILITY GROWTH RATES; HYDROMAGNETIC WAVES; PLASMA; PLASMA INSTABILITY; ACCELERATION; ANALYTICAL SOLUTION; COMPRESSION; CORRELATIONS; EXPANSION; IMPLOSIONS; LINEAR Z PINCH DEVICES; MAGNETIC FIELDS; STABILITY; THETA PINCH; INSTABILITY; LINEAR PINCH DEVICES; OPEN PLASMA DEVICES; PINCH DEVICES; PINCH EFFECT; THERMONUCLEAR DEVICES; 700107* - Fusion Energy- Plasma Research- Instabilities

### Citation Formats

```
Bud'ko, A B, Felber, F S, Kleev, A I, Liberman, M A, and Velikovich, A L.
```*Stability analysis of dynamic Z pinches and theta pinches*. United States: N. p., 1989.
Web. doi:10.1063/1.859207.

```
Bud'ko, A B, Felber, F S, Kleev, A I, Liberman, M A, & Velikovich, A L.
```*Stability analysis of dynamic Z pinches and theta pinches*. United States. doi:10.1063/1.859207.

```
Bud'ko, A B, Felber, F S, Kleev, A I, Liberman, M A, and Velikovich, A L. Wed .
"Stability analysis of dynamic Z pinches and theta pinches". United States. doi:10.1063/1.859207.
```

```
@article{osti_6526772,
```

title = {Stability analysis of dynamic Z pinches and theta pinches},

author = {Bud'ko, A B and Felber, F S and Kleev, A I and Liberman, M A and Velikovich, A L},

abstractNote = {The stability of diffuse, dynamic Z pinches and theta pinches is analyzed. Spectra of the growth rates of hydromagnetic instabilities of dynamic pinches are calculated. The acceleration of plasma pinches during compression and expansion strongly modifies the growth of bulk instabilities. Also, even a relatively weak axial magnetic field substantially suppresses instabilities in Z pinches, in agreement with recent experiments. The initial axial field B/sub z//sub //sub 0/ needed for a stable implosion of a pinch of initial radius R/sub 0/ and average current I-bar is B/sub z//sub //sub 0/ approx. >(10--30 kG) I-bar (MA)/R/sub 0/(cm). The approximate analytic solutions of the linearized equations are shown to agree well with the exact numerical solutions. The stability analysis demonstrated here for dynamic pinches is broadly applicable to the stability of dynamic plasmas in general.},

doi = {10.1063/1.859207},

journal = {Phys Fluids B; (United States)},

number = ,

volume = 1:3,

place = {United States},

year = {1989},

month = {3}

}