Nonlinear evolution of the sausage instability

Journal Article · Wed Dec 01 04:00:00 EST 1976 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.861429· OSTI ID:7325821

Book, D L; Ott, E; Lampe, M

Sausage instabilities of an incompressible, uniform, perfectly conducting Z pinch are studied in the nonlinear regime. In the long wavelength limit (analogous to the ''shallow water theory'' of hydrodynamics), a simplified set of universal fluid equations is derived, with no radial dependence, and with all parameters scaled out. Analytic and numerical solutions of these one-dimensional equations show that an initially sinusoidal perturbation grows into a ''spindle'' or cylindrical ''spike and bubble'' shape, with sharp radial maxima. In the short wavelength limit, the problem is shown to be mathematically equivalent to the planar semi-infinite Rayleigh--Taylor instability, which also grows into a spike-and-bubble shape. Since the spindle shape is common to both limits, it is concluded that it probably obtains in all cases. The results are in agreement with dense plasma focus experiments. (AIP)

• Research Organization: Naval Research Laboratory, Washington, D. C. 20375
• OSTI ID: 7325821
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 19:12; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
DISTURBANCES
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
LINEAR PINCH DEVICES
LINEAR Z PINCH DEVICES
MAGNETOHYDRODYNAMICS
MECHANICS
OPEN PLASMA DEVICES
PINCH DEVICES
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
RAYLEIGH-TAYLOR INSTABILITY
SAUSAGE INSTABILITY
THERMONUCLEAR DEVICES