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

Technical Report · Fri Oct 31 04:00:00 EST 1980

OSTI ID:6084083

Gardner, J H; Book, D L; Bernstein, I B

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.

• Research Organization: Naval Research Lab., Washington, DC (USA)
• OSTI ID: 6084083
• Report Number(s): AD-A-092588
• Country of Publication: United States
• Language: English

Related Subjects

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