THE ARBITRARY EXPANSION OF A FREELY STREAMING PLASMA BUBBLE INTO EITHER VACUUM MAGNETIC FIELD OR AN IONIZED ATMOSPHERE: SMOOTH FLOWS AND THE FORMULATION OF THE GENERAL STABILITY PROBLEM. Chap. 5 of THEORETICAL STUDY OF HYDROMAGNETIC STABILITY AND TURBULENCE. INVESTIGATIONS AND DETAILED RESULTS. Annual Report, Period: January 1-December 31, 1961
The general formulation of the free expansion of a perfectly conducting fluid either into an ideal hydromagnetic fluid or into a vacuum magnetic field is presented. The kinematics and dynamics of the snowplow model for an arbitrary interface between the freely expanding matter and the external medium are presented. The problem of the stability of the snowplow model against small perturbations is then foimulated. The theory is preserted in terms of the Lagrangian displacement of an element of surface from its unperturbed location. Linear equations of motion for the surface mass density and displacement vector are found. For the spherical case of an unperturbed spherical motion against a constant pressure the linear equations are reduced by the introduction of vector spherical harmonics. The stability of the motion against small perturbations when the ambient mediiim is an ideal hydromagnetic fluid is then formulated in terms of the Lagrangian displacement of an element of fluid from its unperturbed motion. The coefficients in this equation involve the perturbed shock conditions by integrals along unperturbed trajectories of the element of fluid. This formulation for the natural extension of the method is employed for analyzing the stubility of magnetohydrostatic equilibria when there is no shock or mass velocity in the unperturbed state. Lastly, these equations are examined wIth the limiting situation of a spherical motion into a medium containing no magnetic field and characterized by constant pressure and density. The next case investigated is one wherein the ambient medium is assumed to be a vacuum magnetic field. The associated potential problem in an infinite domain exterior to a topological sphere is transformed by inversion into an equivalent problem in the interior or topological sphere. The axisymmetric case is treated in the same fashion by a magnetic stream function which has a simpler boundary condition. The snowplow equations governing the interface between the freely expanding plasma and the vacuum magnetic field are given in Eulerian form for the axisymmetric case. One can then introduce convenient dimensionless variables such that for the expansion into a constant magnetic field it is necessary to solve the problem only once; all other solutions can then be obtained by scaling. (auth)
- Research Organization:
- Radio Corp. of America. Missile and Surface Radar Div., Moorestown, N.J.
- NSA Number:
- NSA-16-022715
- OSTI ID:
- 4825635
- Report Number(s):
- AFSWC-TDR-62-12(Vol.II)(Chap.5
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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