Numerical and analytical studies of the nonlinear sausage instability. Memorandum report

Technical Report · Sun Aug 01 04:00:00 EDT 1976

OSTI ID:7304412

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

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 solution 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 spike-and-bubble shape. Since the spindle shape is common to both limits we conclude that it probably obtains in all cases. The results are in agreement with dense plasma focus experiments.

• Research Organization: Naval Research Lab., Washington, DC (USA)
• OSTI ID: 7304412
• Report Number(s): AD-A-028716; NRL-MR-3334
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
INSTABILITY
LINEAR PINCH DEVICES
LINEAR Z PINCH DEVICES
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
OPEN PLASMA DEVICES
PINCH DEVICES
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
SAUSAGE INSTABILITY
THERMONUCLEAR DEVICES