# Linear stability of self-similar flow. 8. Imploding cylindrical and spherical shocks in the C-C-W approximation. Memorandum report

## Abstract

Analytical and computational techniques are developed to investigate the stability of converging shock waves in cylindrical and spherical geometry. The linearized Chester-Chisnell-Whitham (C-C-W) equations describing the evolution of an arbitrary perturbation about an imploding shock wave in an ideal fluid are solved exactly in the strong-shock limit for a density profile rho(r) approx (r to the -q power). All modes are found to be relatively unstable (i.e., the ratio of perturbation amplitude to shock radius diverges as the latter goes to zero), provided that q is not too large. The nonlinear C-C-W equations are solved numerically for both moderate and strong shocks. The small-amplitude limit agrees with the analytical results, but some forms of perturbation which are stable at small amplitude become unstable in the nonlinear regime. The results are related to the problem of pellet compression in experiments on inertial confinement fusion.

- Authors:

- Publication Date:

- Research Org.:
- Naval Research Lab., Washington, DC (USA)

- OSTI Identifier:
- 6084083

- Report Number(s):
- AD-A-092588

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; SHOCK WAVES; STABILITY; COMPRESSION; HEATING; IMPLOSIONS; LASER RADIATION; SYMMETRY; ELECTROMAGNETIC RADIATION; RADIATIONS; 700208* - Fusion Power Plant Technology- Inertial Confinement Technology

### Citation Formats

```
Gardner, J H, Book, D L, and Bernstein, I B.
```*Linear stability of self-similar flow. 8. Imploding cylindrical and spherical shocks in the C-C-W approximation. Memorandum report*. United States: N. p., 1980.
Web.

```
Gardner, J H, Book, D L, & Bernstein, I B.
```*Linear stability of self-similar flow. 8. Imploding cylindrical and spherical shocks in the C-C-W approximation. Memorandum report*. United States.

```
Gardner, J H, Book, D L, and Bernstein, I B. Fri .
"Linear stability of self-similar flow. 8. Imploding cylindrical and spherical shocks in the C-C-W approximation. Memorandum report". United States.
```

```
@article{osti_6084083,
```

title = {Linear stability of self-similar flow. 8. Imploding cylindrical and spherical shocks in the C-C-W approximation. Memorandum report},

author = {Gardner, J H and Book, D L and Bernstein, I B},

abstractNote = {Analytical and computational techniques are developed to investigate the stability of converging shock waves in cylindrical and spherical geometry. The linearized Chester-Chisnell-Whitham (C-C-W) equations describing the evolution of an arbitrary perturbation about an imploding shock wave in an ideal fluid are solved exactly in the strong-shock limit for a density profile rho(r) approx (r to the -q power). All modes are found to be relatively unstable (i.e., the ratio of perturbation amplitude to shock radius diverges as the latter goes to zero), provided that q is not too large. The nonlinear C-C-W equations are solved numerically for both moderate and strong shocks. The small-amplitude limit agrees with the analytical results, but some forms of perturbation which are stable at small amplitude become unstable in the nonlinear regime. The results are related to the problem of pellet compression in experiments on inertial confinement fusion.},

doi = {},

url = {https://www.osti.gov/biblio/6084083},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1980},

month = {10}

}